{"id":104104,"date":"2026-09-11T21:01:00","date_gmt":"2026-09-11T13:01:00","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/104104.html"},"modified":"2026-09-11T21:01:00","modified_gmt":"2026-09-11T13:01:00","slug":"2025%e7%a7%8b%e5%ad%a3%e6%8f%90%e9%ab%98%e7%bb%84%e6%a8%a1%e6%8b%9f%e8%b5%9b4-%e5%81%9a%e9%a2%98%e9%9a%8f%e7%ac%94-%e5%a5%97%e5%8d%b7%e9%a2%98%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/104104.html","title":{"rendered":"2025\u79cb\u5b63\u63d0\u9ad8\u7ec4\u6a21\u62df\u8d5b4 \u505a\u9898\u968f\u7b14\u2014\u2014\u5957\u5377\u9898\u89e3"},"content":{"rendered":"<h2>2025\u79cb\u5b63\u63d0\u9ad8\u7ec4\u6a21\u62df\u8d5b4\u2014\u2014\u505a\u9898\u968f\u7b14\/\u5957\u5377\u9898\u89e3<\/h2>\n<\/p>\n<h4>\u6587\u7ae0\u76ee\u5f55<\/h4>\n<ul>\n<li>2025\u79cb\u5b63\u63d0\u9ad8\u7ec4\u6a21\u62df\u8d5b4\u2014\u2014\u505a\u9898\u968f\u7b14\/\u5957\u5377\u9898\u89e3<\/li>\n<li>\n<ul>\n<li>\u505a\u9898\u611f\u53d7<\/li>\n<li>T1 \u6709\u8da3\u6811<\/li>\n<li>\n<ul>\n<li>\u9898\u610f\u7b80\u8ff0<\/li>\n<li>\u8d5b\u65f6\u60f3\u6cd5<\/li>\n<li>\u6b63\u89e3<\/li>\n<li>\u53c2\u8003\u4ee3\u7801<\/li>\n<li>\u8c03\u8bd5\u5fc3\u5f97<\/li>\n<li>\n<ul>\n<li>1. \u76f4\u5f84\u4e2d\u5fc3\u7684\u6b63\u786e\u5224\u5b9a&#xff08;\u70b9 vs \u8fb9&#xff09;<\/li>\n<li>2. \u4e24\u6b21 DFS \u6c42\u76f4\u5f84\u7684\u8fd4\u56de\u503c\u4e0e\u8def\u5f84\u6784\u9020<\/li>\n<\/ul>\n<\/li>\n<li>\u5c0f\u7ed3<\/li>\n<\/ul>\n<\/li>\n<li>T2\u70b9\u9488\u5f0f\u6253\u5370\u673a<\/li>\n<li>\n<ul>\n<li>\u9898\u610f\u7b80\u8ff0<\/li>\n<li>\u8d5b\u65f6\u60f3\u6cd5<\/li>\n<li>\u53c2\u8003\u4ee3\u7801<\/li>\n<li>\u5c0f\u7ed3<\/li>\n<\/ul>\n<\/li>\n<li>T3 \u6700\u5927\u72ec\u7acb\u96c6<\/li>\n<li>\n<ul>\n<li>\u9898\u610f\u7b80\u8ff0<\/li>\n<li>\u8d5b\u65f6\u60f3\u6cd5<\/li>\n<\/ul>\n<\/li>\n<li>\u9644\u5f55<\/li>\n<li>\n<ul>\n<li>T1\u76f8\u5173\u63a8\u8bba\u8bc1\u660e<\/li>\n<li>T3\u9898\u76ee\u76f8\u5173\u201c\u7ffb\u8bd1\u201d<\/li>\n<li>\n<ul>\n<li>\u8bf1\u5bfc\u5b50\u56fe&#xff08;Induced Subgraph&#xff09;<\/li>\n<li>\n<ul>\n<li>\u4e0e\u666e\u901a\u5b50\u56fe\u7684\u533a\u522b<\/li>\n<li>\u4e3e\u4e2a\u4f8b\u5b50<\/li>\n<\/ul>\n<\/li>\n<li>\u6700\u5927\u72ec\u7acb\u96c6&#xff08;Maximum Independent Set&#xff09;<\/li>\n<li>\n<ul>\n<li>1. \u72ec\u7acb\u96c6&#xff08;Independent Set&#xff09;<\/li>\n<li>2. \u6700\u5927\u72ec\u7acb\u96c6<\/li>\n<li>3. \u4e0e\u201c\u6781\u5927\u72ec\u7acb\u96c6\u201d\u7684\u533a\u522b<\/li>\n<li>4. \u6e29\u99a8\u63d0\u793a<\/li>\n<li>NP-hard<\/li>\n<li>\n<ul>\n<li>1. \u5148\u7406\u89e3 P \u548c NP<\/li>\n<li>2. NP-hard \u7684\u5b9a\u4e49<\/li>\n<li>3. \u6700\u5927\u72ec\u7acb\u96c6\u662f NP-hard<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr \/>\n<p>\u6ce8&#xff1a;\u6587\u7ae0\u6301\u7eed\u66f4\u65b0\u4e2d&#xff0c;\u656c\u8bf7\u671f\u5f85<\/p>\n<h3>\u505a\u9898\u611f\u53d7<\/h3>\n<p>\u4e0d\u5f97\u4e0d\u8bf4&#xff0c;\u8fd9\u786e\u5b9e\u662f\u5957\u597d\u9898\u3002\u56ca\u62ec\u4e86\u6811\u3001\u77e9\u9635\u3001\u56fe\u8bba\u3001\u54c8\u5e0c\u2026\u2026\u4f46\u6123\u662f\u6ca1\u4e00\u9053\u7ebf\u6027\u9898\u3002\u4e0d\u8fc7\u8fd9\u6837\u4e00\u6765&#xff0c;\u8865\u9898\u548c\u5199\u9898\u89e3\u5bf9\u6211\u6765\u8bf4\u5c31\u663e\u5f97\u5c24\u4e3a\u91cd\u8981~ \u56e0\u4e3a\u8fd9\u4e9b\u77e5\u8bc6\u70b9\u6211\u90fd\u4e0d\u719f<\/p>\n<p>\u8bdd\u4e0d\u591a\u8bf4&#xff0c;\u76f4\u63a5<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        s<\/p>\n<p>        t<\/p>\n<p>        a<\/p>\n<p>        r<\/p>\n<p>        t<\/p>\n<p>       start<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6151em\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/span>!<\/p>\n<hr \/>\n<h3>T1 \u6709\u8da3\u6811<\/h3>\n<h4>\u9898\u610f\u7b80\u8ff0<\/h4>\n<p>\u7ed9\u4f60\u4e00\u68f5\u5305\u542b<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        n<\/p>\n<p>        (<\/p>\n<p>        1<\/p>\n<p>        \u2264<\/p>\n<p>        n<\/p>\n<p>        \u2264<\/p>\n<p>        2<\/p>\n<p>        e<\/p>\n<p>        5<\/p>\n<p>        )<\/p>\n<p>       n (1 \\\\le n \\\\le 2e5)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7719em;vertical-align: -0.136em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord\">5<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u4e2a\u8282\u70b9\u7684\u65e0\u6839\u6811&#xff0c;\u6ca1\u6709\u8fb9\u6743\u3002\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u4e3a\u5979\u4eec\u7684\u7b80\u5355\u8def\u5f84<sup class=\"footnote-ref\">1<\/sup>\u3002<\/p>\n<p>\u7ed9\u4e88\u4f60\u4e00\u79cd\u64cd\u4f5c&#xff1a;\u5728\u4e0d\u6539\u53d8\u539f\u5148\u70b9\u4e4b\u95f4\u7684\u8fde\u8fb9\u7684\u60c5\u51b5\u4e0b&#xff0c;\u4f9d\u6b21\u6dfb\u52a0\u82e5\u5e72\u4e2a\u70b9\u8fdb\u5165\u8fd9\u68f5\u6811(\u53ef\u4ee5\u4e0d\u52a0)&#xff0c;\u4f7f\u4e4b\u6210\u4e3a\u4e00\u68f5\u65b0\u7684\u6811\u3002<\/p>\n<p>\u73b0\u5728\u95ee&#xff1a;\u81f3\u5c11\u9700\u8981\u6dfb\u52a0\u51e0\u4e2a\u70b9\u624d\u80fd\u4f7f\u5f53\u524d\u7684\u6811\u62e5\u6709\u591a\u6761\u76f4\u5f84&#xff1f;<\/p>\n<h4>\u8d5b\u65f6\u60f3\u6cd5<\/h4>\n<p>\u5b8c\u86cb&#xff0c;\u662f\u6811\u7684\u91cd\u5fc3&#xff01;\u6211\u4e0d\u4f1a\u5199&#xff01;\u4f46\u5e94\u8be5\u4e0d\u96be\u5199\u5427\u2026\u2026\u6211\u5148\u63a8\u4e00\u4e0b\u5148\u2014\u2014\u597d\u50cf\u53ef\u884c\u3002<\/p>\n<p>\u55ef&#xff0c;\u6709\u89c4\u5f8b&#xff0c;\u5bf9\u4e8e\u4e00\u822c\u6570\u636e\u7b54\u6848\u81f3\u591a\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>       1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5c0f\u4e8e\u8282\u70b9\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        4<\/p>\n<p>       4<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">4<\/span><\/span><\/span><\/span><\/span>\u7684\u7279\u5224\u4e00\u4e0b\u2026\u2026\u6b38&#xff01;\u6811\u4e0aDP&#xff1f;(\u5f53\u65f6\u73b0\u63a8\u7684\u76f4\u5f84\u627e\u6cd5\u5047\u4e86&#xff0c;\u6240\u4ee5\u4ee5\u4e3a\u53ef\u4ee5\u6811\u4e0aDP)<\/p>\n<p>\u597d&#xff0c;\u6837\u4f8b\u8fc7\u4e86&#xff1b;\u597d&#xff01;\u5927\u6837\u4f8b\u8fc7\u4e86&#xff1b;\u597d&#xff01;&#xff01;\u624b\u6413\u7279\u6b8a\u6570\u636e\u4e5f\u8fc7\u4e86&#xff01;\u8fd9\u4e0dAC\u4e0d\u793c\u8c8c\u4e86\u2026\u2026<\/p>\n<p>\u86e4\u3002\u4e0d\u51fa\u610f\u5916&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        W<\/p>\n<p>        A<\/p>\n<p>       WA<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">W<\/span><span class=\"mord mathnormal\">A<\/span><\/span><\/span><\/span><\/span> <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        80<\/p>\n<p>        p<\/p>\n<p>        t<\/p>\n<p>        s<\/p>\n<p>       80pts<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8389em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">80<\/span><span class=\"mord mathnormal\">pt<\/span><span class=\"mord mathnormal\">s<\/span><\/span><\/span><\/span><\/span>\u3002&#xff08;\u4e3b\u8981\u662f\u56e0\u4e3a\u9898\u76ee\u6ca1\u6709\u591a\u7ec4\u6d4b\u8bd5\u6570\u636e\u5bfc\u81f4\u6570\u636e\u592a\u6c34\u4e86&#xff0c;\u9762\u5411\u7b54\u6848\u7f16\u7a0b\u6709<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        60<\/p>\n<p>       60<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">60<\/span><\/span><\/span><\/span><\/span>\u5206&#xff0c;\u6572\u4e00\u4e2a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         n<\/p>\n<p>         2<\/p>\n<p>        B<\/p>\n<p>        F<\/p>\n<p>        S<\/p>\n<p>       n^2BFS<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">F<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><\/span><\/span><\/span><\/span>\u66b4\u641c\u4e5f\u6709<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        80<\/p>\n<p>       80<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">80<\/span><\/span><\/span><\/span><\/span>\u5206&#xff09;<\/p>\n<p>\u597d\u5427\u2026\u2026<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260911130059-6aa3fb8bca26a.gif\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<hr \/>\n<h4>\u6b63\u89e3<\/h4>\n<p>\u597d\u5427\u54b1\u4eec\u518d\u91cd\u6e29\u4e00\u904d\u6811\u7684\u76f4\u5f84&#xff1a;<\/p>\n<li>\u4ece\u65e0\u6839\u6811\u4efb\u4e00\u70b9\u51fa\u53d1\u8dd1\u4e00\u904dDFS\u627e\u5230\u6700\u8fdc\u7684(\u4e00\u4e2a)\u70b9<\/li>\n<li>\u4ee5\u8fd9\u4e2a\u70b9\u4e3a\u6839\u627e\u6df1\u5ea6\u6700\u6df1\u7684\u70b9\u786e\u5b9a\u76f4\u5f84<\/li>\n<p>\u8ddf\u4e0a\u54c8\u3002\u597d&#xff0c;\u73b0\u5728\u6765\u5206\u6790\u9898\u76ee&#xff1a;<\/p>\n<p>\u9996\u5148\u6709\u4ee5\u4e0b\u7279\u6b8a\u60c5\u51b5&#xff1a;<\/p>\n<ul>\n<li>\u5f53<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         n<\/p>\n<p>         &#061;<\/p>\n<p>         1<\/p>\n<p>        n&#061;1<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u65f6\u7b54\u6848\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         3<\/p>\n<p>        3<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u5f53<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         n<\/p>\n<p>         &#061;<\/p>\n<p>         2<\/p>\n<p>        n&#061;2<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span>\u65f6\u7b54\u6848\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         2<\/p>\n<p>        2<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u5f53<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         n<\/p>\n<p>         &#061;<\/p>\n<p>         3<\/p>\n<p>        n&#061;3<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span>\u662f\u7b54\u6848\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         1<\/p>\n<p>        1<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff08;\u4ece\u8fd9\u513f\u5f00\u59cb\u5176\u5b9e\u5df2\u7ecf\u53ef\u4ee5\u5f00\u59cb\u8dd1\u4e0b\u9762\u8bb2\u7684\u901a\u6cd5\u4e86&#xff09;<\/li>\n<li>\u5f53<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         n<\/p>\n<p>         &#061;<\/p>\n<p>         4<\/p>\n<p>        n&#061;4<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">4<\/span><\/span><\/span><\/span><\/span>\u65f6\u7b54\u6848\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         1<\/p>\n<p>        1<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u6216<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         0<\/p>\n<p>        0<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>&#xff08;\u6811\u7684\u7ed3\u6784\u4e0d\u552f\u4e00&#xff09;<\/li>\n<\/ul>\n<p>\u5269\u4e0b\u7684\u7b54\u6848\u5c31\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        0<\/p>\n<p>       0<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>\u6216<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>       1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u4e86<sup class=\"footnote-ref\">2<\/sup>\u3002<\/p>\n<p>\u90a3\u4e3a\u4e86\u89e3\u51b3\u95ee\u9898\u6211\u4eec\u73b0\u5728\u8981\u505a\u7684\u5c31\u662f\u2014\u2014\u770b\u662f\u5426\u80fd\u518d\u627e\u4e00\u6761\u76f4\u5f84\u3002<\/p>\n<p>\u8fd9\u91cc\u8981\u8bf4\u4e00\u6761\u5f88\u201c\u9634\u6697\u201d\u7684\u63a8\u8bba&#xff1a;\u4e00\u68f5\u6811\u4e0a\u7684\u6240\u6709\u76f4\u5f84\u5fc5\u7136\u76f8\u4ea4\u4e8e\u5979\u4eec\u7684&#034;\u4e2d\u70b9&#034;(\u4e25\u683c\u957f\u5ea6\/2&#xff0c;\u5bf9\u4e8e\u5947\u6570\/\u5076\u6570\u957f\u7684\u76f4\u5f84&#xff0c;\u4e2d\u70b9\u53ef\u4ee5\u662f\u8282\u70b9\/\u8fb9)\u3002<\/p>\n<p>\u8fd9\u4e2a\u70b9\u4e5f\u5c31\u662f\u6811\u7684\u4e2d\u5fc3\u3002\u76f8\u5173\u8bc1\u660e\u9644\u5728\u6700\u540e<\/p>\n<hr \/>\n<p>\u2014\u2014\u6b22\u8fce\u56de\u6765\u3002<\/p>\n<p>\u597d\u90a3\u4e48\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\u4e86\u6240\u6709\u76f4\u5f84\u4ea4\u4e8e\u4e2d\u70b9\u3002\u63a5\u4e0b\u6765\u518d\u627e\u4e00\u6761\u76f4\u5f84&#xff08;\u6216\u67e5\u8be2\u662f\u5426\u6709\u66f4\u591a\u76f4\u5f84&#xff09;\u5c31\u5f88\u7b80\u5355\u4e86\u3002<\/p>\n<p>\u5728\u786e\u5b9a\u7b2c\u4e00\u6761\u76f4\u5f84\u65f6\u9012\u5f52\u8fd8\u539f\u51fa\u8def\u5f84(\u53ca\u76f4\u5f84)&#xff0c;\u7136\u540e\u6298\u534a\u627e\u5230\u6811\u7684\u4e2d\u5fc3\u3002<\/p>\n<p>\u63a5\u4e0b\u6765\u518d\u8fdb\u884c\u4e00\u6b21DFS&#xff1a;\u4ece\u4e2d\u70b9\u51fa\u53d1\u641c\u7d22&#xff0c;\u5f53\u9012\u5f52\u6df1\u5ea6\u7b49\u4e8e\u76f4\u5f84\u7684\u4e00\u534a\u65f6\u8ba1\u6570\u3002\u82e5\u8ba1\u6570\u5927\u4e8e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        2<\/p>\n<p>       2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span>(\u9664\u539f\u5148\u4e24\u6761\u534a\u5f84\u5916\u53e6\u6709\u65b0\u7684\u4e00\u6761\u534a\u5f84)&#xff0c;\u5219\u8bf4\u660e\u6709\u591a\u6761\u76f4\u5f84&#xff0c;\u7b54\u6848\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        0<\/p>\n<p>       0<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u53cd\u4e4b\u4e3a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>       1<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u591a\u63d0\u4e00\u5634&#xff1a;\u82e5\u76f4\u5f84\u957f\u5ea6\u4e3a\u5076\u6570&#xff0c;\u5219\u6811\u7684\u201c\u4e2d\u70b9\u201d\u662f\u4e00\u6761\u8fb9&#xff0c;\u8fd9\u65f6\u4ece\u8fb9\u7684\u4e24\u7aef\u5206\u522b\u5411\u4e24\u4fa7\u5404DFS\u4e00\u6b21&#xff0c;\u7edf\u8ba1\u603b\u8ba1\u6570\u518d\u5224\u5b9a\u5373\u53ef\u3002<\/p>\n<h4>\u53c2\u8003\u4ee3\u7801<\/h4>\n<p><span class=\"token macro property\"><span class=\"token directive-hash\">#<\/span><span class=\"token directive keyword\">include<\/span><span class=\"token string\">&lt;bits\/stdc&#043;&#043;.h&gt;<\/span><\/span><br \/>\n<span class=\"token keyword\">using<\/span> <span class=\"token keyword\">namespace<\/span> std<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token macro property\"><span class=\"token directive-hash\">#<\/span><span class=\"token directive keyword\">define<\/span> <span class=\"token macro-name\">int<\/span> <span class=\"token expression\"><span class=\"token keyword\">long<\/span> <span class=\"token keyword\">long<\/span><\/span><\/span><br \/>\n<span class=\"token keyword\">const<\/span> <span class=\"token keyword\">int<\/span> o <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">2e5<\/span> <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">22<\/span><span class=\"token punctuation\">;<\/span>          <span class=\"token comment\">\/\/ \u6700\u5927\u8282\u70b9\u6570 &#043; \u4e00\u70b9\u4f59\u91cf<\/span><\/p>\n<p><span class=\"token keyword\">int<\/span> n<span class=\"token punctuation\">;<\/span>                            <span class=\"token comment\">\/\/ \u8282\u70b9\u6570<\/span><br \/>\nvector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> g<span class=\"token punctuation\">[<\/span>o<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span>                 <span class=\"token comment\">\/\/ \u90bb\u63a5\u8868\u5b58\u6811<\/span><\/p>\n<p><span class=\"token keyword\">int<\/span> fa<span class=\"token punctuation\">[<\/span>o<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span>                  <span class=\"token comment\">\/\/ \u7236\u8282\u70b9\u6570\u7ec4&#xff0c;\u7528\u4e8e\u8bb0\u5f55\u4ece\u8d77\u70b9s\u51fa\u53d1\u7684\u8def\u5f84<\/span><br \/>\n<span class=\"token keyword\">int<\/span> dep<span class=\"token punctuation\">[<\/span>o<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span>                 <span class=\"token comment\">\/\/ \u6df1\u5ea6\u6570\u7ec4&#xff0c;\u8bb0\u5f55\u4ece\u8d77\u70b9s\u5230\u5404\u8282\u70b9\u7684\u8ddd\u79bb<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u4ece\u8282\u70b9 u \u51fa\u53d1&#xff08;\u4e0d\u7ecf\u8fc7\u7236\u8282\u70b9 prt&#xff09;&#xff0c;\u627e\u5230\u80fd\u5230\u8fbe\u7684\u6700\u8fdc\u8282\u70b9<\/span><br \/>\n<span class=\"token comment\">\/\/ \u8fd4\u56de\u503c&#xff1a;pair&lt;\u6700\u8fdc\u8ddd\u79bb, \u6700\u8fdc\u8282\u70b9\u7f16\u53f7&gt;<\/span><br \/>\npair<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">,<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> <span class=\"token function\">dfs1<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> u<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> prt<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n    pair<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">,<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> ans <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> u<span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span>   <span class=\"token comment\">\/\/ \u521d\u59cb&#xff1a;\u8ddd\u79bb0&#xff0c;\u8282\u70b9\u81ea\u5df1<\/span><br \/>\n    <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">auto<\/span> v <span class=\"token operator\">:<\/span> g<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>v <span class=\"token operator\">&#061;&#061;<\/span> prt<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">continue<\/span><span class=\"token punctuation\">;<\/span>    <span class=\"token comment\">\/\/ \u4e0d\u8d70\u56de\u5934\u8def<\/span><br \/>\n        pair<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">,<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> k <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">dfs1<\/span><span class=\"token punctuation\">(<\/span>v<span class=\"token punctuation\">,<\/span> u<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        k<span class=\"token punctuation\">.<\/span>first<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span>                <span class=\"token comment\">\/\/ \u7ecf\u8fc7\u8fb9 u-v&#xff0c;\u8ddd\u79bb&#043;1<\/span><br \/>\n        <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>k<span class=\"token punctuation\">.<\/span>first <span class=\"token operator\">&gt;&#061;<\/span> ans<span class=\"token punctuation\">.<\/span>first<span class=\"token punctuation\">)<\/span>  <span class=\"token comment\">\/\/ \u66f4\u65b0\u66f4\u8fdc\u7684\u8282\u70b9<\/span><br \/>\n            ans <span class=\"token operator\">&#061;<\/span> k<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> ans<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u4ece\u8282\u70b9 u \u51fa\u53d1&#xff08;\u4e0d\u7ecf\u8fc7\u7236\u8282\u70b9 prt&#xff09;&#xff0c;\u8bb0\u5f55\u6bcf\u4e2a\u8282\u70b9\u7684\u7236\u8282\u70b9\u548c\u6df1\u5ea6<\/span><br \/>\n<span class=\"token comment\">\/\/ \u7528\u4e8e\u540e\u7eed\u4ece\u76f4\u5f84\u7aef\u70b9 s \u5f00\u59cb\u6784\u9020\u8def\u5f84<\/span><br \/>\n<span class=\"token keyword\">void<\/span> <span class=\"token function\">pth<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> u<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> prt<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n    fa<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> prt<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">auto<\/span> v <span class=\"token operator\">:<\/span> g<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>v <span class=\"token operator\">&#061;&#061;<\/span> prt<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">continue<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        dep<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> dep<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span>      <span class=\"token comment\">\/\/ \u5b50\u8282\u70b9\u6df1\u5ea6 &#061; \u5f53\u524d\u6df1\u5ea6 &#043; 1<\/span><br \/>\n        <span class=\"token function\">pth<\/span><span class=\"token punctuation\">(<\/span>v<span class=\"token punctuation\">,<\/span> u<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u4ece\u8282\u70b9 u \u51fa\u53d1&#xff08;\u4e0d\u7ecf\u8fc7\u7236\u8282\u70b9 prt&#xff0c;\u4e5f\u4e0d\u7ecf\u8fc7\u7981\u8282\u70b9 ban&#xff09;&#xff0c;<\/span><br \/>\n<span class=\"token comment\">\/\/ \u7edf\u8ba1\u6df1\u5ea6\u6070\u597d\u4e3a tar \u7684\u8282\u70b9\u4e2a\u6570&#xff0c;\u7ed3\u679c\u7d2f\u52a0\u5230 cnt<\/span><br \/>\n<span class=\"token keyword\">void<\/span> <span class=\"token function\">count_dep<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> u<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> prt<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> deep<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> tar<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> ban<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> <span class=\"token operator\">&amp;<\/span>cnt<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>deep <span class=\"token operator\">&#061;&#061;<\/span> tar<span class=\"token punctuation\">)<\/span>               <span class=\"token comment\">\/\/ \u5230\u8fbe\u76ee\u6807\u6df1\u5ea6<\/span><br \/>\n    <span class=\"token punctuation\">{<\/span><br \/>\n        cnt<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">return<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n    <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">auto<\/span> v <span class=\"token operator\">:<\/span> g<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>v <span class=\"token operator\">&#061;&#061;<\/span> prt <span class=\"token operator\">||<\/span> v <span class=\"token operator\">&#061;&#061;<\/span> ban<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">continue<\/span><span class=\"token punctuation\">;<\/span>  <span class=\"token comment\">\/\/ \u4e0d\u8d70\u56de\u5934\u8def&#xff0c;\u4e5f\u4e0d\u8fdb\u5165\u7981\u8282\u70b9<\/span><br \/>\n        <span class=\"token function\">count_dep<\/span><span class=\"token punctuation\">(<\/span>v<span class=\"token punctuation\">,<\/span> u<span class=\"token punctuation\">,<\/span> deep <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> tar<span class=\"token punctuation\">,<\/span> ban<span class=\"token punctuation\">,<\/span> cnt<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token keyword\">signed<\/span> <span class=\"token function\">main<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token comment\">\/\/ freopen(&#034;tree.in&#034;, &#034;r&#034;, stdin);<\/span><br \/>\n    <span class=\"token comment\">\/\/ freopen(&#034;tree.out&#034;, &#034;w&#034;, stdout);<\/span><\/p>\n<p>    ios<span class=\"token double-colon punctuation\">::<\/span><span class=\"token function\">sync_with_stdio<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    cin<span class=\"token punctuation\">.<\/span><span class=\"token function\">tie<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    cout<span class=\"token punctuation\">.<\/span><span class=\"token function\">tie<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>    cin <span class=\"token operator\">&gt;&gt;<\/span> n<span class=\"token punctuation\">;<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u7279\u6b8a\u60c5\u51b5\u7279\u5224&#xff08;\u753b\u56fe\u5373\u53ef\u5f97\u51fa&#xff09;<\/span><br \/>\n    <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>n <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span> cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;3\\\\n&#034;<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span><br \/>\n    <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>n <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span> cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;2\\\\n&#034;<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u8bfb\u5165 n-1 \u6761\u8fb9&#xff0c;\u5efa\u6811<\/span><br \/>\n    <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> u<span class=\"token punctuation\">,<\/span> v<span class=\"token punctuation\">;<\/span><br \/>\n        cin <span class=\"token operator\">&gt;&gt;<\/span> u <span class=\"token operator\">&gt;&gt;<\/span> v<span class=\"token punctuation\">;<\/span><br \/>\n        g<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">push_back<\/span><span class=\"token punctuation\">(<\/span>v<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        g<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">push_back<\/span><span class=\"token punctuation\">(<\/span>u<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u7b2c\u4e00\u6b21 DFS&#xff1a;\u4ece\u4efb\u610f\u70b9 1 \u51fa\u53d1&#xff0c;\u627e\u5230\u6700\u8fdc\u70b9 s&#xff08;\u76f4\u5f84\u7684\u4e00\u4e2a\u7aef\u70b9&#xff09;<\/span><br \/>\n    pair<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">,<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> b <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">dfs1<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> s <span class=\"token operator\">&#061;<\/span> b<span class=\"token punctuation\">.<\/span>second<span class=\"token punctuation\">;<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u4ece s \u51fa\u53d1&#xff0c;\u8bb0\u5f55\u7236\u8282\u70b9\u548c\u6df1\u5ea6<\/span><br \/>\n    dep<span class=\"token punctuation\">[<\/span>s<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token function\">pth<\/span><span class=\"token punctuation\">(<\/span>s<span class=\"token punctuation\">,<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u627e\u5230\u79bb s \u6700\u8fdc\u7684\u70b9 t&#xff08;\u76f4\u5f84\u7684\u53e6\u4e00\u4e2a\u7aef\u70b9&#xff09;<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> t <span class=\"token operator\">&#061;<\/span> s<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>dep<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&gt;<\/span> dep<span class=\"token punctuation\">[<\/span>t<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> t <span class=\"token operator\">&#061;<\/span> i<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> D <span class=\"token operator\">&#061;<\/span> dep<span class=\"token punctuation\">[<\/span>t<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span>               <span class=\"token comment\">\/\/ \u76f4\u5f84\u957f\u5ea6&#xff08;\u8fb9\u6570&#xff09;<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u4ece t \u56de\u6eaf\u5230 s&#xff0c;\u6784\u9020\u76f4\u5f84\u8def\u5f84 path&#xff08;s -&gt; &#8230; -&gt; t&#xff09;<\/span><br \/>\n    vector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> path<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> u <span class=\"token operator\">&#061;<\/span> t<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">while<\/span><span class=\"token punctuation\">(<\/span>u <span class=\"token operator\">!&#061;<\/span> s<span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token punctuation\">{<\/span><br \/>\n        path<span class=\"token punctuation\">.<\/span><span class=\"token function\">push_back<\/span><span class=\"token punctuation\">(<\/span>u<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        u <span class=\"token operator\">&#061;<\/span> fa<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n    path<span class=\"token punctuation\">.<\/span><span class=\"token function\">push_back<\/span><span class=\"token punctuation\">(<\/span>s<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token function\">reverse<\/span><span class=\"token punctuation\">(<\/span>path<span class=\"token punctuation\">.<\/span><span class=\"token function\">begin<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> path<span class=\"token punctuation\">.<\/span><span class=\"token function\">end<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>  <span class=\"token comment\">\/\/ \u73b0\u5728 path[0]&#061;s, path[D]&#061;t<\/span><\/p>\n<p>    <span class=\"token keyword\">int<\/span> ans <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span>                  <span class=\"token comment\">\/\/ \u9ed8\u8ba4\u9700\u8981\u589e\u52a0 1 \u4e2a\u8282\u70b9&#xff08;\u76f4\u5f84\u552f\u4e00\u65f6&#xff09;<\/span><\/p>\n<p>    <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>D <span class=\"token operator\">%<\/span> <span class=\"token number\">2<\/span> <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u76f4\u5f84\u957f\u5ea6\u4e3a\u5076\u6570&#xff1a;\u4e2d\u5fc3\u662f\u4e00\u4e2a\u70b9<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> r <span class=\"token operator\">&#061;<\/span> D <span class=\"token operator\">\/<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> mid <span class=\"token operator\">&#061;<\/span> path<span class=\"token punctuation\">[<\/span>r<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span>        <span class=\"token comment\">\/\/ \u4e2d\u5fc3\u70b9<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> cnt <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u7edf\u8ba1\u4ece\u4e2d\u5fc3\u70b9\u51fa\u53d1&#xff0c;\u8ddd\u79bb\u4e3a r \u7684\u8282\u70b9\u4e2a\u6570<\/span><br \/>\n        <span class=\"token function\">count_dep<\/span><span class=\"token punctuation\">(<\/span>mid<span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> r<span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> cnt<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>cnt <span class=\"token operator\">&gt;<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span> ans <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span>      <span class=\"token comment\">\/\/ \u8d85\u8fc7 2 \u4e2a\u5206\u652f&#xff0c;\u8bf4\u660e\u6709\u591a\u6761\u76f4\u5f84<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n    <span class=\"token keyword\">else<\/span><br \/>\n    <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u76f4\u5f84\u957f\u5ea6\u4e3a\u5947\u6570&#xff1a;\u4e2d\u5fc3\u662f\u4e00\u6761\u8fb9 (u, v)<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> r <span class=\"token operator\">&#061;<\/span> D <span class=\"token operator\">\/<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">;<\/span>            <span class=\"token comment\">\/\/ \u5411\u4e0b\u53d6\u6574<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> u <span class=\"token operator\">&#061;<\/span> path<span class=\"token punctuation\">[<\/span>r<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span>          <span class=\"token comment\">\/\/ \u4e2d\u5fc3\u8fb9\u5de6\u4fa7\u8282\u70b9<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> v <span class=\"token operator\">&#061;<\/span> path<span class=\"token punctuation\">[<\/span>r <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span>      <span class=\"token comment\">\/\/ \u4e2d\u5fc3\u8fb9\u53f3\u4fa7\u8282\u70b9<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> cnt_u <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> cnt_v <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u5206\u522b\u5728 u \u4fa7\u548c v \u4fa7\u7edf\u8ba1\u8ddd\u79bb\u4e3a r \u7684\u8282\u70b9\u4e2a\u6570&#xff08;\u7981\u6b62\u8de8\u8d8a\u4e2d\u5fc3\u8fb9&#xff09;<\/span><br \/>\n        <span class=\"token function\">count_dep<\/span><span class=\"token punctuation\">(<\/span>u<span class=\"token punctuation\">,<\/span> v<span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> r<span class=\"token punctuation\">,<\/span> v<span class=\"token punctuation\">,<\/span> cnt_u<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token function\">count_dep<\/span><span class=\"token punctuation\">(<\/span>v<span class=\"token punctuation\">,<\/span> u<span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> r<span class=\"token punctuation\">,<\/span> u<span class=\"token punctuation\">,<\/span> cnt_v<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>cnt_u <span class=\"token operator\">*<\/span> cnt_v <span class=\"token operator\">&gt;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> ans <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span>  <span class=\"token comment\">\/\/ \u4e24\u4fa7\u4e58\u79ef\u5927\u4e8e 1&#xff0c;\u8bf4\u660e\u6709\u591a\u6761\u76f4\u5f84<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    cout <span class=\"token operator\">&lt;&lt;<\/span> ans <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;\\\\n&#034;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/*<br \/>\n3<br \/>\n1 2<br \/>\n2 3<br \/>\n\u8f93\u51fa 1<\/p>\n<p>4<br \/>\n1 2<br \/>\n2 3<br \/>\n2 4<br \/>\n\u8f93\u51fa 0<\/p>\n<p>8<br \/>\n1 2<br \/>\n1 3<br \/>\n2 5<br \/>\n2 4<br \/>\n5 7<br \/>\n3 6<br \/>\n6 8<br \/>\n\u8f93\u51fa 1<\/p>\n<p>5<br \/>\n1 2<br \/>\n2 3<br \/>\n3 4<br \/>\n4 5<br \/>\n\u8f93\u51fa 1<br \/>\n*\/<\/span><\/p>\n<h4>\u8c03\u8bd5\u5fc3\u5f97<\/h4>\n<h5>1. \u76f4\u5f84\u4e2d\u5fc3\u7684\u6b63\u786e\u5224\u5b9a&#xff08;\u70b9 vs \u8fb9&#xff09;<\/h5>\n<ul>\n<li>\u76f4\u5f84\u957f\u5ea6\u4e3a\u5076\u6570\u65f6&#xff0c;\u4e2d\u5fc3\u662f\u4e00\u4e2a\u70b9&#xff1b;\u4e3a\u5947\u6570\u65f6&#xff0c;\u4e2d\u5fc3\u662f\u4e00\u6761\u8fb9\u3002<\/li>\n<li>\u6240\u6709\u76f4\u5f84\u90fd\u5171\u4eab\u540c\u4e00\u4e2a\u4e2d\u5fc3&#xff0c;\u5fc5\u987b\u6839\u636e\u5947\u5076\u6027\u5206\u522b\u5904\u7406&#xff1a;\n<ul>\n<li>\u5076\u6570&#xff1a;\u4ece\u4e2d\u5fc3\u70b9\u51fa\u53d1&#xff0c;\u7edf\u8ba1\u8ddd\u79bb\u4e3a\u534a\u5f84\u7684\u8282\u70b9\u6570&#xff0c;\u82e5 &gt;2 \u5219\u6709\u591a\u6761\u76f4\u5f84\u3002<\/li>\n<li>\u5947\u6570&#xff1a;\u4ece\u4e2d\u5fc3\u8fb9\u4e24\u4fa7\u5206\u522b\u7edf\u8ba1\u8ddd\u79bb\u4e3a\u534a\u5f84\u7684\u8282\u70b9\u6570&#xff0c;\u82e5\u4e58\u79ef &gt;1 \u5219\u6709\u591a\u6761\u76f4\u5f84\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u9519\u8bef\u505a\u6cd5&#xff1a;\u9009\u5ea6\u6570\u6700\u5927\u7684\u70b9\u6216\u4ece\u76f4\u5f84\u7aef\u70b9\u51fa\u53d1\u7edf\u8ba1\u6700\u957f\u94fe&#xff0c;\u90fd\u65e0\u6cd5\u51c6\u786e\u5224\u65ad\u76f4\u5f84\u6761\u6570\u3002<\/li>\n<\/ul>\n<hr \/>\n<h5>2. \u4e24\u6b21 DFS \u6c42\u76f4\u5f84\u7684\u8fd4\u56de\u503c\u4e0e\u8def\u5f84\u6784\u9020<\/h5>\n<ul>\n<li>\u7b2c\u4e00\u6b21 DFS \u5fc5\u987b\u8fd4\u56de\u6700\u8fdc\u8282\u70b9\u7684\u7f16\u53f7&#xff08;\u800c\u4e0d\u4ec5\u662f\u8ddd\u79bb&#xff09;&#xff0c;\u5426\u5219\u540e\u7eed\u65e0\u6cd5\u4ece\u8be5\u7aef\u70b9\u51fa\u53d1\u3002<\/li>\n<li>\u7b2c\u4e8c\u6b21 DFS \u9700\u8981\u8bb0\u5f55\u6bcf\u4e2a\u8282\u70b9\u7684\u7236\u8282\u70b9\u548c\u6df1\u5ea6&#xff0c;\u4ee5\u4fbf\u4ece\u6700\u8fdc\u70b9\u56de\u6eaf\u6784\u9020\u76f4\u5f84\u8def\u5f84\u3002<\/li>\n<li>\u8def\u5f84\u6784\u9020\u65f6\u6ce8\u610f\u987a\u5e8f&#xff1a;\u4ece\u7aef\u70b9\u56de\u6eaf\u5230\u8d77\u70b9\u540e\u8981 reverse&#xff0c;\u786e\u4fdd path[0] \u662f\u8d77\u70b9&#xff0c;path[D] \u662f\u7ec8\u70b9\u3002<\/li>\n<li>\u4e2d\u5fc3\u5b9a\u4f4d\u4f9d\u8d56\u8def\u5f84\u7d22\u5f15&#xff1a;\u5076\u6570\u53d6 path[D\/2]&#xff0c;\u5947\u6570\u53d6 path[D\/2] \u548c path[D\/2&#043;1]\u3002<\/li>\n<\/ul>\n<hr \/>\n<h4>\u5c0f\u7ed3<\/h4>\n<p>\u591a\u4e8f\u4e86\u8fd9\u9053\u9898&#xff0c;\u4e0d\u7136\u4e00\u76f4\u52302026\u5e74S\u7ec4\u590d\u8d5b\u524d\u6211\u90fd\u4e0d\u4f1a\u53bb\u5b66\u6811\u7684\u76f4\u5f84\u7684\u3002<\/p>\n<hr \/>\n<h3>T2\u70b9\u9488\u5f0f\u6253\u5370\u673a<\/h3>\n<h4>\u9898\u610f\u7b80\u8ff0<\/h4>\n<p>\u4e00\u53f0\u9488\u5f0f\u6253\u5370\u673a\u6709\u4e00\u4e2a\u6253\u5b54\u6a21\u677f&#xff0c;\u662f\u4e00\u4e2a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        n<\/p>\n<p>        \u00d7<\/p>\n<p>        m<\/p>\n<p>        (<\/p>\n<p>        1<\/p>\n<p>        \u2264<\/p>\n<p>        n<\/p>\n<p>        ,<\/p>\n<p>        m<\/p>\n<p>        \u2264<\/p>\n<p>        500<\/p>\n<p>        )<\/p>\n<p>       n\u00d7m(1 \\\\le n,m \\\\le 500)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8304em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">500<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u7684\u77e9\u9635&#xff0c;\u5305\u542b\u20190\u2019\u548c\u20191\u2019&#xff0c;&#039;1\u2019\u8868\u793a\u6a21\u7248\u8be5\u4f4d\u7f6e\u4e0a\u6709\u9488&#xff0c;&#039;0\u2019\u5219\u6ca1\u6709\u3002<\/p>\n<p>\u73b0\u9700\u8981\u5728\u8017\u6750\u4e0a\u6253\u5370\u51fa\u5bf9\u5e94\u7684\u201c\u56fe\u6848\u201d&#xff0c;\u8017\u6750\u662f\u4e00\u4e2a<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>        \u00d7<\/p>\n<p>        b<\/p>\n<p>        (<\/p>\n<p>        1<\/p>\n<p>        \u2264<\/p>\n<p>        a<\/p>\n<p>        ,<\/p>\n<p>        b<\/p>\n<p>        \u2264<\/p>\n<p>        500<\/p>\n<p>        )<\/p>\n<p>       a\u00d7b(1 \\\\le a,b \\\\le 500)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">500<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u7684\u77e9\u9635&#xff0c;\u540c\u6837\u542b\u20190\u2019\u548c\u20191\u2019&#xff0c;&#039;1\u2019\u8868\u793a\u8fd9\u4e2a\u4f4d\u7f6e\u9700\u8981\u4e00\u4e2a\u5b54&#xff0c;&#039;0\u2019\u5219\u4e0d\u9700\u8981\u3002<\/p>\n<p>\u4f60\u53ef\u4ee5\u901a\u8fc7\u79fb\u52a8\u6a21\u7248\u7684\u4f4d\u7f6e\u591a\u6b21\u6309\u538b\u6a21\u677f\u5728\u8017\u6750\u4e0a\u6253\u5b54\u5b9e\u73b0\u76ee\u6807\u3002\u4f46\u662f\u9700\u8981\u6ce8\u610f&#xff1a;<\/p>\n<li>\u6a21\u7248\u548c\u8017\u6750\u5747\u4e0d\u53ef\u65cb\u8f6c&#xff1b;<\/li>\n<li>\u8017\u6750\u6253\u5b54\u540e\u4f1a\u9732\u51fa\u5e95\u677f&#xff0c;\u4e4b\u540e\u8be5\u4f4d\u7f6e\u5c31\u4e0d\u80fd\u518d\u6b21\u88ab\u6253\u5b54&#xff0c;\u5426\u5219\u673a\u5668\u5c06\u635f\u574f\u89c6\u4f5c\u5931\u8d25&#xff1b;<\/li>\n<li>\u6a21\u7248\u4e0a\u7684\u20191\u2019\u4e0d\u80fd\u8d85\u51fa\u8017\u6750\u8fb9\u754c&#xff0c;\u5426\u5219\u673a\u5668\u5c06\u635f\u574f\u89c6\u4f5c\u5931\u8d25&#xff1b;<\/li>\n<p>\u5bf9\u4e8e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        T<\/p>\n<p>        (<\/p>\n<p>        1<\/p>\n<p>        \u2264<\/p>\n<p>        T<\/p>\n<p>        \u2264<\/p>\n<p>        5<\/p>\n<p>        )<\/p>\n<p>       T(1 \\\\le T \\\\le 5)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8193em;vertical-align: -0.136em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">5<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u7ec4\u6d4b\u8bd5\u6570\u636e&#xff0c;\u5224\u65ad\u5e76\u8f93\u51fa&#034;Yes&#034;\u6216&#034;No&#034;\u8868\u793a\u6bcf\u7ec4\u6570\u636e\u4e2d\u7684\u4efb\u52a1\u662f\u5426\u80fd\u5b9e\u73b0\u3002<\/p>\n<p>\u53e6\u5916&#xff0c;\u4fdd\u8bc1\u6240\u6709\u6d4b\u8bd5\u6570\u636e\u4e2d\u20191\u2019\u7684\u4e2a\u6570\u5c0f\u4e8e\u7b49\u4e8e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        5<\/p>\n<p>        e<\/p>\n<p>        6<\/p>\n<p>       5e6<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">5<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord\">6<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<h4>\u8d5b\u65f6\u60f3\u6cd5<\/h4>\n<p>\u522b\u4e50\u4e86&#xff0c;\u8fd9\u9898\u6211A\u4e86&#xff01;<\/p>\n<p>\u600e\u4e48\u8bf4&#xff1f;<\/p>\n<p>\u5bf9\u4e8e\u6a21\u7248\u800c\u8a00&#xff0c;\u8bb0\u5f55\u6a2a\u5411\u4fbf\u5229\u7b2c\u4e00\u4e2a\u20191\u2019\u51fa\u73b0\u7684\u4f4d\u7f6e&#xff0c;\u7136\u540e\u540e\u9762\u904d\u5386\u5230\u7684\u20191\u2019\u7edf\u7edf\u6539\u4e3a\u76f8\u5bf9\u4e8e\u524d\u4e00\u4e2a\u20191\u2019\u7684\u5750\u6807\u504f\u79fb\u91cf&#xff0c;\u4e4b\u540e\u561b\u2026\u2026<\/p>\n<p>\u8fd8\u662f\u4fbf\u5229\u76ee\u6807\u8017\u6750&#xff0c;\u4e00\u65e6\u904d\u5386\u5230\u20191\u2019\u5c31\u6309\u7167\u504f\u79fb\u91cf\u4e00\u6b21\u6253\u5b54\u3002\u5982\u679c\u6bcf\u6b21\u6253\u5b54\u5c06\u20191\u2019\u6539\u6210\u20190\u2019&#xff0c;\u5982\u679c\u51fa\u73b0\u8d85\u51fa\u8017\u6750\u6216\u8005\u4e0d\u8be5\u6253\u5b54\u7684\u60c5\u51b5&#xff0c;\u5c31\u76f4\u63a5\u5224\u5426\u3002<\/p>\n<p>\u6109\u5febAC~<\/p>\n<p>\u6b63\u786e\u6027&#xff1f;\u56e0\u4e3a\u6309\u7167\u6211\u4eec\u7684\u903b\u8f91\u5f53\u5728\u8017\u6750\u4e0a\u904d\u5386\u5230\u4e00\u4e2a\u20191\u2019\u65f6&#xff0c;\u5728\u5979\u524d\u9762\u7684\u20191\u2019\u5df2\u7ecf\u88ab\u6253\u8fc7\u5b54\u53d8\u6210\u20190\u2019\u4e86&#xff0c;\u6240\u4ee5\u53ea\u80fd\u4ece\u5979\u5f00\u59cb\u8ba9\u6a21\u7248\u7b2c\u4e00\u6839\u9488\u6253\u5b54&#xff0c;\u518d\u628a\u540e\u9762\u7684\u82e5\u5e72\u4e2a\u20191\u2019\u4e5f\u6253\u4e86&#xff0c;\u5982\u679c\u540e\u7eed\u6709\u975e\u6cd5\u60c5\u51b5\u5c31\u53ea\u80fd\u7b97\u5b83\u5012\u9709&#xff0c;\u6f0f\u4e86\u4e00\u4e2a\u9488\u773c\u5bfc\u81f4\u4e0d\u80fd\u5b9e\u73b0\u65e2\u5b9a\u76ee\u6807&#xff0c;\u5c31\u76f4\u63a5\u8df3\u51fa\u5faa\u73af\u4e86\u3002<\/p>\n<h4>\u53c2\u8003\u4ee3\u7801<\/h4>\n<p><span class=\"token macro property\"><span class=\"token directive-hash\">#<\/span><span class=\"token directive keyword\">include<\/span><span class=\"token string\">&lt;bits\/stdc&#043;&#043;.h&gt;<\/span><\/span><br \/>\n<span class=\"token keyword\">using<\/span> <span class=\"token keyword\">namespace<\/span> std<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token macro property\"><span class=\"token directive-hash\">#<\/span><span class=\"token directive keyword\">define<\/span> <span class=\"token macro-name\">int<\/span> <span class=\"token expression\"><span class=\"token keyword\">long<\/span> <span class=\"token keyword\">long<\/span><\/span><\/span><br \/>\n<span class=\"token keyword\">const<\/span> <span class=\"token keyword\">int<\/span> o <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1e5<\/span> <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">22<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token keyword\">char<\/span> u<span class=\"token punctuation\">[<\/span><span class=\"token number\">1002<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1002<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span>   <span class=\"token comment\">\/\/ \u70b9\u9488\u76d8\u77e9\u9635&#xff08;a \u884c b \u5217&#xff09;<\/span><br \/>\n<span class=\"token keyword\">char<\/span> v<span class=\"token punctuation\">[<\/span><span class=\"token number\">1002<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1002<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span>   <span class=\"token comment\">\/\/ \u76ee\u6807\u5185\u5bb9\u77e9\u9635&#xff08;n \u884c m \u5217&#xff09;<\/span><\/p>\n<p><span class=\"token keyword\">signed<\/span> <span class=\"token function\">main<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token comment\">\/\/ freopen(&#034;printer.in&#034;, &#034;r&#034;, stdin);<\/span><br \/>\n    <span class=\"token comment\">\/\/ freopen(&#034;printer.out&#034;, &#034;w&#034;, stdout);<\/span><\/p>\n<p>    ios<span class=\"token double-colon punctuation\">::<\/span><span class=\"token function\">sync_with_stdio<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    cin<span class=\"token punctuation\">.<\/span><span class=\"token function\">tie<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    cout<span class=\"token punctuation\">.<\/span><span class=\"token function\">tie<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>    <span class=\"token keyword\">int<\/span> T<span class=\"token punctuation\">;<\/span><br \/>\n    cin <span class=\"token operator\">&gt;&gt;<\/span> T<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">while<\/span> <span class=\"token punctuation\">(<\/span>T<span class=\"token operator\">&#8212;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> a<span class=\"token punctuation\">,<\/span> b<span class=\"token punctuation\">,<\/span> n<span class=\"token punctuation\">,<\/span> m<span class=\"token punctuation\">;<\/span><br \/>\n        cin <span class=\"token operator\">&gt;&gt;<\/span> a <span class=\"token operator\">&gt;&gt;<\/span> b <span class=\"token operator\">&gt;&gt;<\/span> n <span class=\"token operator\">&gt;&gt;<\/span> m<span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ stp \u5b58\u50a8\u70b9\u9488\u76d8\u4e2d\u6240\u6709 &#039;1&#039; \u7684\u4f4d\u7f6e\u4fe1\u606f<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u7b2c\u4e00\u4e2a\u5143\u7d20\u662f\u7b2c\u4e00\u4e2a &#039;1&#039; \u7684\u7edd\u5bf9\u5750\u6807 (i, j)<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u540e\u7eed\u5143\u7d20\u662f\u6bcf\u4e2a &#039;1&#039; \u76f8\u5bf9\u4e8e\u4e0a\u4e00\u4e2a &#039;1&#039; \u7684\u504f\u79fb\u91cf (dx, dy)<\/span><br \/>\n        vector<span class=\"token operator\">&lt;<\/span>pair<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">,<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;&gt;<\/span> stp<span class=\"token punctuation\">;<\/span><br \/>\n        pair<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">,<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> lst <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span>   <span class=\"token comment\">\/\/ \u4e0a\u4e00\u4e2a &#039;1&#039; \u7684\u5750\u6807<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8bfb\u5165\u70b9\u9488\u76d8<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/span> a<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> j <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&lt;&#061;<\/span> b<span class=\"token punctuation\">;<\/span> j<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token punctuation\">{<\/span><br \/>\n                cin <span class=\"token operator\">&gt;&gt;<\/span> u<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>u<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token char\">&#039;1&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n                <span class=\"token punctuation\">{<\/span><br \/>\n                    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>stp<span class=\"token punctuation\">.<\/span><span class=\"token function\">size<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n                    <span class=\"token punctuation\">{<\/span><br \/>\n                        <span class=\"token comment\">\/\/ \u7b2c\u4e00\u4e2a &#039;1&#039;&#xff0c;\u8bb0\u5f55\u7edd\u5bf9\u5750\u6807<\/span><br \/>\n                        stp<span class=\"token punctuation\">.<\/span><span class=\"token function\">push_back<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">{<\/span>i<span class=\"token punctuation\">,<\/span> j<span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                        lst <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span>i<span class=\"token punctuation\">,<\/span> j<span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                    <span class=\"token punctuation\">}<\/span><br \/>\n                    <span class=\"token keyword\">else<\/span><br \/>\n                    <span class=\"token punctuation\">{<\/span><br \/>\n                        <span class=\"token comment\">\/\/ \u540e\u7eed &#039;1&#039;&#xff0c;\u8bb0\u5f55\u76f8\u5bf9\u4e8e\u4e0a\u4e00\u4e2a &#039;1&#039; \u7684\u504f\u79fb<\/span><br \/>\n                        stp<span class=\"token punctuation\">.<\/span><span class=\"token function\">push_back<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">{<\/span>i <span class=\"token operator\">&#8211;<\/span> lst<span class=\"token punctuation\">.<\/span>first<span class=\"token punctuation\">,<\/span> j <span class=\"token operator\">&#8211;<\/span> lst<span class=\"token punctuation\">.<\/span>second<span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                        lst <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">{<\/span>i<span class=\"token punctuation\">,<\/span> j<span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                    <span class=\"token punctuation\">}<\/span><br \/>\n                <span class=\"token punctuation\">}<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> len <span class=\"token operator\">&#061;<\/span> stp<span class=\"token punctuation\">.<\/span><span class=\"token function\">size<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>   <span class=\"token comment\">\/\/ \u70b9\u9488\u76d8\u4e2d\u9488\u7684\u6570\u91cf<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8bfb\u5165\u76ee\u6807\u5185\u5bb9&#xff0c;\u5e76\u7edf\u8ba1 &#039;1&#039; \u7684\u603b\u6570<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> sum <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> j <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&lt;&#061;<\/span> m<span class=\"token punctuation\">;<\/span> j<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token punctuation\">{<\/span><br \/>\n                cin <span class=\"token operator\">&gt;&gt;<\/span> v<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>v<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token char\">&#039;1&#039;<\/span><span class=\"token punctuation\">)<\/span> sum<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">int<\/span> fg <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span>   <span class=\"token comment\">\/\/ \u6807\u8bb0\u662f\u5426\u5df2\u7ecf\u8f93\u51fa\u8fc7 &#034;No&#034;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u904d\u5386\u76ee\u6807\u77e9\u9635&#xff0c;\u5bfb\u627e\u7b2c\u4e00\u4e2a &#039;1&#039; \u4f5c\u4e3a\u5339\u914d\u7684\u8d77\u70b9<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/span> n<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> j <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&lt;&#061;<\/span> m<span class=\"token punctuation\">;<\/span> j<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            <span class=\"token punctuation\">{<\/span><br \/>\n                <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>v<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token char\">&#039;1&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n                <span class=\"token punctuation\">{<\/span><br \/>\n                    <span class=\"token keyword\">int<\/span> x <span class=\"token operator\">&#061;<\/span> i<span class=\"token punctuation\">,<\/span> y <span class=\"token operator\">&#061;<\/span> j<span class=\"token punctuation\">;<\/span><br \/>\n                    v<span class=\"token punctuation\">[<\/span>x<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>y<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token char\">&#039;0&#039;<\/span><span class=\"token punctuation\">;<\/span>   <span class=\"token comment\">\/\/ \u6682\u65f6\u79fb\u9664\u8fd9\u4e2a\u70b9<\/span><br \/>\n                    sum<span class=\"token operator\">&#8212;<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>                    <span class=\"token comment\">\/\/ \u6839\u636e\u70b9\u9488\u76d8\u7684\u504f\u79fb&#xff0c;\u4f9d\u6b21\u68c0\u67e5\u5176\u4ed6\u9488\u7684\u4f4d\u7f6e<\/span><br \/>\n                    <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> k <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> k <span class=\"token operator\">&lt;<\/span> len<span class=\"token punctuation\">;<\/span> k<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n                    <span class=\"token punctuation\">{<\/span><br \/>\n                        x <span class=\"token operator\">&#043;&#061;<\/span> stp<span class=\"token punctuation\">[<\/span>k<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>first<span class=\"token punctuation\">;<\/span><br \/>\n                        y <span class=\"token operator\">&#043;&#061;<\/span> stp<span class=\"token punctuation\">[<\/span>k<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>second<span class=\"token punctuation\">;<\/span><\/p>\n<p>                        <span class=\"token comment\">\/\/ \u8d8a\u754c\u6216\u8be5\u4f4d\u7f6e\u6ca1\u6709 &#039;1&#039;&#xff0c;\u8bf4\u660e\u5339\u914d\u5931\u8d25<\/span><br \/>\n                        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>x <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">1<\/span> <span class=\"token operator\">||<\/span> x <span class=\"token operator\">&gt;<\/span> n <span class=\"token operator\">||<\/span> y <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">1<\/span> <span class=\"token operator\">||<\/span> y <span class=\"token operator\">&gt;<\/span> m <span class=\"token operator\">||<\/span> v<span class=\"token punctuation\">[<\/span>x<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>y<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token char\">&#039;0&#039;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n                        <span class=\"token punctuation\">{<\/span><br \/>\n                            cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;No\\\\n&#034;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                            fg <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                            <span class=\"token keyword\">break<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                        <span class=\"token punctuation\">}<\/span><\/p>\n<p>                        v<span class=\"token punctuation\">[<\/span>x<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>y<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token char\">&#039;0&#039;<\/span><span class=\"token punctuation\">;<\/span>   <span class=\"token comment\">\/\/ \u79fb\u9664\u5339\u914d\u7684\u70b9<\/span><br \/>\n                        sum<span class=\"token operator\">&#8212;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                    <span class=\"token punctuation\">}<\/span><br \/>\n                    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>fg<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">break<\/span><span class=\"token punctuation\">;<\/span>   <span class=\"token comment\">\/\/ \u5339\u914d\u5931\u8d25&#xff0c;\u8df3\u51fa\u6240\u6709\u5faa\u73af<\/span><\/p>\n<p>                    <span class=\"token comment\">\/\/ \u5982\u679c\u6240\u6709 &#039;1&#039; \u90fd\u88ab\u6070\u597d\u5339\u914d\u5b8c<\/span><br \/>\n                    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>sum<span class=\"token punctuation\">)<\/span><br \/>\n                    <span class=\"token punctuation\">{<\/span><br \/>\n                        cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;Yes\\\\n&#034;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                        <span class=\"token keyword\">continue<\/span><span class=\"token punctuation\">;<\/span>   <span class=\"token comment\">\/\/ \u7ee7\u7eed\u5185\u5c42\u5faa\u73af&#xff0c;\u4f46\u6b64\u65f6\u5df2\u65e0 &#039;1&#039;&#xff0c;\u4f1a\u81ea\u7136\u7ed3\u675f<\/span><br \/>\n                    <span class=\"token punctuation\">}<\/span><br \/>\n                <span class=\"token punctuation\">}<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>fg<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">break<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/*<br \/>\n2<br \/>\n4 2 3 4<br \/>\n10<br \/>\n01<br \/>\n10<br \/>\n00<br \/>\n1100<br \/>\n0110<br \/>\n1100<\/p>\n<p>2 2 2 2<br \/>\n11<br \/>\n11<br \/>\n01<br \/>\n10<\/p>\n<p>Yes<br \/>\nNo<\/p>\n<p>1<br \/>\n4 2 3 4<br \/>\n10<br \/>\n01<br \/>\n10<br \/>\n00<br \/>\n1100<br \/>\n0110<br \/>\n1100<br \/>\n*\/<\/span><\/p>\n<h4>\u5c0f\u7ed3<\/h4>\n<p>\u5f00\u59cb\u770b\u5230\u8fd9\u9053\u9898\u7684\u65f6\u5019\u7ed9\u6211\u5413\u574f\u4e86&#xff0c;\u4ee5\u4e3a\u662f\u4ec0\u4e48\u4ece\u6765\u90fd\u6ca1\u6709\u89c1\u8fc7\u7684\u9ad8\u6df1\u7b97\u6cd5\u3002\u56e0\u4e3a\u9898\u76ee\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5b9e\u5728\u662f\u975e\u5e38\u5403\u7d27&#xff0c;\u4e00\u4e2a\u4e8c\u7ef4\u77e9\u9635\u7684\u9898\u76ee\u9664\u4e86DP\u4e4b\u5916\u6211\u5b9e\u5728\u60f3\u4e0d\u51fa\u4ec0\u4e48\u80fd\u5728<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        O<\/p>\n<p>        (<\/p>\n<p>        n<\/p>\n<p>        l<\/p>\n<p>        o<\/p>\n<p>        g<\/p>\n<p>        n<\/p>\n<p>        )<\/p>\n<p>       O(nlogn)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">g<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u5185\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u7684\u597d\u529e\u6cd5\u3002\u4f46\u662f\u8fd9\u9898\u7528DP\u6709\u592a\u7275\u5f3a\u4e86&#xff0c;\u6a21\u7248\u91cc\u6bcf\u6709\u4e00\u4e2a\u20191\u2019\u5c31\u8981\u7528\u65b9\u7a0b\u8f6c\u79fb\u4e00\u6b21&#xff0c;\u8fd8\u8981\u8003\u8651\u4e71\u4e03\u516b\u7cdf\u7684\u975e\u6cd5\u60c5\u51b5\u3002\u540e\u6765\u662f\u5728\u60f3\u66b4\u529b\u7684\u65f6\u5019\u7a81\u53d1\u5947\u60f3\u7528\u504f\u79fb\u91cf&#xff0c;\u7ed3\u679c\u5c0f\u8d2a\u5fc3\u4e00\u624b\u3001\u65f6\u95f4\u590d\u6742\u5ea6\u4e00\u63a8\u3002\u8036&#xff01;\u6b63\u89e3\u4e0d\u51fa\u6765\u4e86\u5417\u3002<\/p>\n<hr \/>\n<h3>T3 \u6700\u5927\u72ec\u7acb\u96c6<\/h3>\n<h4>\u9898\u610f\u7b80\u8ff0<\/h4>\n<p>\u51fa\u9898\u4eba\u7ec8\u4e8e\u201c\u5c0f\u6c14\u201d\u4e86\u4e00\u56de&#xff0c;\u53ea\u7ed9\u4f60\u4e00\u5f20\u81f3\u591a\u5305\u542b<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        26<\/p>\n<p>       26<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">26<\/span><\/span><\/span><\/span><\/span>\u4e2a\u70b9\u7684\u65e0\u6743\u65e0\u5411\u56fe<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        G<\/p>\n<p>       G<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">G<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6ca1\u6709\u91cd\u8fb9\u6216\u81ea\u73af\u3002<\/p>\n<p>\u867d\u7136\u4f46\u662f&#xff0c;\u8981\u4f60\u6c42\u5f97\u4e1c\u897f\u5f88\u53d8\u6001&#xff1a;<\/p>\n<p>\u2014\u2014\u201c\u5bf9\u4e8e<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        G<\/p>\n<p>       G<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">G<\/span><\/span><\/span><\/span><\/span>\u7684\u70b9\u96c6\u7684\u6bcf\u4e00\u4e2a\u5b50\u96c6\u53ca\u8fd9\u4e2a\u5b50\u70b9\u96c6\u5185\u90e8\u4e4b\u95f4\u7684\u8fde\u8fb9\u6240\u5171\u540c\u7ec4\u6210\u7684\u5b50\u56fe~~&#xff08;\u534e\u590f\u6587\u5b57\u535a\u5927\u7cbe\u6df1&#xff09;~~&#xff0c;\u8bf7\u6c42\u89e3\u51fa\u8be5\u8bf1\u5bfc\u5b50\u56fe(\u524d\u9762\u90a3\u4e00\u957f\u4e32\u8bf4\u7684\u5c31\u662f\u8fd9\u4e2a)\u7684\u6700\u5927\u72ec\u7acb\u96c6\u7684\u5927\u5c0f&#xff0c;\u2014\u2014\u5e76\u4e14&#xff0c;\u5bf9\u4e8e\u8fd9\u4e9b\u72ec\u7acb\u96c6\u7684\u5927\u5c0f\u4e4b\u548c\u3002\u201d<\/p>\n<p>\u4f60\u8fd9\u6b21\u53ef\u80fd\u771f\u7684\u9700\u8981\u66f4\u597d\u7684\u89c2\u611f<\/p>\n<\/p>\n<p>\u4f60\u2014\u2014\u56de\u6765\u5566\u2026\u2026<\/p>\n<h4>\u8d5b\u65f6\u60f3\u6cd5<\/h4>\n<p>\u5929\u54ea&#xff0c;\u8fd9\u662f\u4ec0\u4e48\u4e1c\u897f&#xff01;\u6bcf\u4e2a\u8bf1\u5bfc\u5b50\u56fe\u3001\u6700\u5927\u72ec\u7acb\u96c6\u3001\u5927\u5c0f\u4e4b\u548c\u2026\u2026\u6211\u771f\u7684\u4f1a\u505a\u5417&#xff1f;<\/p>\n<p>\u4e0d\u8fc7\u51fa\u9898\u4eba\u7684\u597d\u610f\u6211\u8fd8\u662f\u8981\u597d\u597d\u9886\u4f1a\u4e00\u4e0b&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         2<\/p>\n<p>         26<\/p>\n<p>       2^{26}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">26<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        6<\/p>\n<p>        e<\/p>\n<p>        7<\/p>\n<p>       6e7<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">6<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u521a\u521a\u597d\u7206<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        512<\/p>\n<p>        M<\/p>\n<p>        B<\/p>\n<p>       512MB<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord\">512<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">M<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><\/span>\u4e0b\u7684long long\u3002\u4e0d\u8fc7int\u80fd\u5f00<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>        e<\/p>\n<p>        7<\/p>\n<p>       1e7<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4ecb\u4e8e\u8fd9\u4e2a\u79c0\u73cd\u6570\u636e\u8303\u56f4\u5b8c\u5168\u53ef\u4ee5\u7528\u72b6\u538bDP\u3002<\/p>\n<p>\u4f46\u662f\u2026\u2026\u600e\u4e48\u8f6c\u79fb\u5462&#xff1f;\u5b8c\u5566&#xff0c;\u65f6\u95f4\u4e0d\u591f&#xff01;\u6211\u8fd8\u662f\u56de\u53bb\u68c0\u67e5\u5427~<\/p>\n<hr \/>\n<h3>\u9644\u5f55<\/h3>\n<\/p>\n<h4>T1\u76f8\u5173\u63a8\u8bba\u8bc1\u660e<\/h4>\n<p>\u8bbe\u6811 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        T<\/p>\n<p>       T<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span> \u7684\u76f4\u5f84\u957f\u5ea6\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span>&#xff08;\u8fb9\u6570&#xff09;\u3002\u53d6\u4e00\u6761\u76f4\u5f84 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>       P<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u7aef\u70b9\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>        ,<\/p>\n<p>        b<\/p>\n<p>       a, b<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8889em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u82e5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e3a\u5076\u6570&#xff0c;\u4ee4 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        c<\/p>\n<p>       c<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span> \u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>       P<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><\/span><\/span><\/span><\/span> \u7684\u6b63\u4e2d\u95f4\u90a3\u4e2a\u70b9&#xff1b;<\/p>\n<p>\u82e5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u4e3a\u5947\u6570&#xff0c;\u4ee4 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        c<\/p>\n<p>       c<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span> \u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>       P<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><\/span><\/span><\/span><\/span> \u6b63\u4e2d\u95f4\u90a3\u6761\u8fb9\u7684\u4e2d\u70b9&#xff08;\u6211\u4eec\u53ef\u4ee5\u628a\u8fd9\u6761\u8fb9\u770b\u4f5c\u4e00\u4e2a\u201c\u4e2d\u5fc3\u8fb9\u201d&#xff09;\u3002<\/p>\n<p>\u6211\u4eec\u8bc1\u660e&#xff1a;\u4efb\u610f\u53e6\u4e00\u6761\u76f4\u5f84 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        Q<\/p>\n<p>       Q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">Q<\/span><\/span><\/span><\/span><\/span> \u4e5f\u7ecf\u8fc7 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        c<\/p>\n<p>       c<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u5047\u8bbe\u5b58\u5728\u53e6\u4e00\u6761\u76f4\u5f84 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        Q<\/p>\n<p>       Q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">Q<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u7aef\u70b9\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>        ,<\/p>\n<p>        y<\/p>\n<p>       x, y<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4e14 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        Q<\/p>\n<p>       Q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">Q<\/span><\/span><\/span><\/span><\/span> \u4e0d\u7ecf\u8fc7 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        c<\/p>\n<p>       c<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u56e0\u4e3a\u6811\u4e2d\u4efb\u610f\u4e24\u6761\u8def\u5f84\u76f8\u4ea4&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        Q<\/p>\n<p>       Q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">Q<\/span><\/span><\/span><\/span><\/span> \u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>       P<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><\/span><\/span><\/span><\/span> \u5fc5\u6709\u516c\u5171\u90e8\u5206\u3002\u8bbe\u5b83\u4eec\u7684\u4ea4\u96c6\u4e3a\u8def\u5f84 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        R<\/p>\n<p>       R<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4e14 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        R<\/p>\n<p>       R<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span> \u5b8c\u5168\u4f4d\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>       P<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><\/span><\/span><\/span><\/span> \u7684\u4e00\u4fa7&#xff08;\u56e0\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        Q<\/p>\n<p>       Q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">Q<\/span><\/span><\/span><\/span><\/span> \u4e0d\u7ecf\u8fc7 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        c<\/p>\n<p>       c<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002\u4e0d\u59a8\u8bbe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        R<\/p>\n<p>       R<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span> \u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        c<\/p>\n<p>       c<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span> \u8fd9\u4e00\u6bb5\u4e0a\u3002<\/p>\n<p>\u8bbe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        R<\/p>\n<p>       R<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span> \u7684\u4e24\u4e2a\u7aef\u70b9\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        u<\/p>\n<p>        ,<\/p>\n<p>        v<\/p>\n<p>       u, v<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        u<\/p>\n<p>       u<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> \u9760\u8fd1 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span>&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        v<\/p>\n<p>       v<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><\/span> \u9760\u8fd1 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        c<\/p>\n<p>       c<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span>\u3002\u7531\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        Q<\/p>\n<p>       Q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">Q<\/span><\/span><\/span><\/span><\/span> \u662f\u7b80\u5355\u8def\u5f84&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        Q<\/p>\n<p>       Q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">Q<\/span><\/span><\/span><\/span><\/span> \u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        u<\/p>\n<p>       u<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        v<\/p>\n<p>       v<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><\/span> \u5206\u522b\u5411\u4e24\u4fa7\u5ef6\u4f38&#xff0c;\u8bbe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        Q<\/p>\n<p>       Q<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">Q<\/span><\/span><\/span><\/span><\/span> \u7684\u7aef\u70b9\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>       x<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span>&#xff08;\u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        u<\/p>\n<p>       u<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> \u76f8\u8fde&#xff09;\u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        y<\/p>\n<p>       y<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span>&#xff08;\u4e0e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        v<\/p>\n<p>       v<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><\/span> \u76f8\u8fde&#xff09;\u3002<\/p>\n<p>\u4e8e\u662f&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u2223<\/p>\n<p>         x<\/p>\n<p>         \u2212<\/p>\n<p>         y<\/p>\n<p>         \u2223<\/p>\n<p>         &#061;<\/p>\n<p>         \u2223<\/p>\n<p>         x<\/p>\n<p>         \u2212<\/p>\n<p>         u<\/p>\n<p>         \u2223<\/p>\n<p>         &#043;<\/p>\n<p>         \u2223<\/p>\n<p>         u<\/p>\n<p>         \u2212<\/p>\n<p>         v<\/p>\n<p>         \u2223<\/p>\n<p>         &#043;<\/p>\n<p>         \u2223<\/p>\n<p>         v<\/p>\n<p>         \u2212<\/p>\n<p>         y<\/p>\n<p>         \u2223<\/p>\n<p>         &#061;<\/p>\n<p>         D<\/p>\n<p>         (<\/p>\n<p>         \u56e0\u4e3a\u00a0<\/p>\n<p>         Q<\/p>\n<p>         \u00a0\u662f\u76f4\u5f84<\/p>\n<p>         )<\/p>\n<p>         |x-y| &#061; |x-u| &#043; |u-v| &#043; |v-y| &#061; D \\\\quad (\\\\text{\u56e0\u4e3a } Q \\\\text{ \u662f\u76f4\u5f84}) <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord text\"><span class=\"mord cjk_fallback\">\u56e0\u4e3a<\/span><span class=\"mord\">\u00a0<\/span><\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mord text\"><span class=\"mord\">\u00a0<\/span><span class=\"mord cjk_fallback\">\u662f\u76f4\u5f84<\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u800c\u76f4\u5f84 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>       P<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><\/span><\/span><\/span><\/span> \u7684\u957f\u5ea6&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u2223<\/p>\n<p>         a<\/p>\n<p>         \u2212<\/p>\n<p>         b<\/p>\n<p>         \u2223<\/p>\n<p>         &#061;<\/p>\n<p>         \u2223<\/p>\n<p>         a<\/p>\n<p>         \u2212<\/p>\n<p>         u<\/p>\n<p>         \u2223<\/p>\n<p>         &#043;<\/p>\n<p>         \u2223<\/p>\n<p>         u<\/p>\n<p>         \u2212<\/p>\n<p>         v<\/p>\n<p>         \u2223<\/p>\n<p>         &#043;<\/p>\n<p>         \u2223<\/p>\n<p>         v<\/p>\n<p>         \u2212<\/p>\n<p>         b<\/p>\n<p>         \u2223<\/p>\n<p>         &#061;<\/p>\n<p>         D<\/p>\n<p>         |a-b| &#061; |a-u| &#043; |u-v| &#043; |v-b| &#061; D <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u6bd4\u8f83\u4e24\u5f0f&#xff0c;\u5f97\u5230&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u2223<\/p>\n<p>         x<\/p>\n<p>         \u2212<\/p>\n<p>         u<\/p>\n<p>         \u2223<\/p>\n<p>         &#043;<\/p>\n<p>         \u2223<\/p>\n<p>         v<\/p>\n<p>         \u2212<\/p>\n<p>         y<\/p>\n<p>         \u2223<\/p>\n<p>         &#061;<\/p>\n<p>         \u2223<\/p>\n<p>         a<\/p>\n<p>         \u2212<\/p>\n<p>         u<\/p>\n<p>         \u2223<\/p>\n<p>         &#043;<\/p>\n<p>         \u2223<\/p>\n<p>         v<\/p>\n<p>         \u2212<\/p>\n<p>         b<\/p>\n<p>         \u2223<\/p>\n<p>         |x-u| &#043; |v-y| &#061; |a-u| &#043; |v-b| <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u6ce8\u610f&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2223<\/p>\n<p>        x<\/p>\n<p>        \u2212<\/p>\n<p>        u<\/p>\n<p>        \u2223<\/p>\n<p>       |x-u|<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2223<\/p>\n<p>        a<\/p>\n<p>        \u2212<\/p>\n<p>        u<\/p>\n<p>        \u2223<\/p>\n<p>       |a-u|<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span> \u662f\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        u<\/p>\n<p>       u<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> \u51fa\u53d1\u7684\u4e24\u6761\u4e0d\u540c\u5206\u652f\u7684\u957f\u5ea6&#xff1b;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2223<\/p>\n<p>        v<\/p>\n<p>        \u2212<\/p>\n<p>        y<\/p>\n<p>        \u2223<\/p>\n<p>       |v-y|<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2223<\/p>\n<p>        v<\/p>\n<p>        \u2212<\/p>\n<p>        b<\/p>\n<p>        \u2223<\/p>\n<p>       |v-b|<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span> \u662f\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        v<\/p>\n<p>       v<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><\/span> \u51fa\u53d1\u7684\u4e24\u6761\u4e0d\u540c\u5206\u652f\u7684\u957f\u5ea6\u3002<\/p>\n<p>\u5982\u679c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2223<\/p>\n<p>        x<\/p>\n<p>        \u2212<\/p>\n<p>        u<\/p>\n<p>        \u2223<\/p>\n<p>        &gt;<\/p>\n<p>        \u2223<\/p>\n<p>        a<\/p>\n<p>        \u2212<\/p>\n<p>        u<\/p>\n<p>        \u2223<\/p>\n<p>       |x-u| &gt; |a-u|<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u90a3\u4e48 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2223<\/p>\n<p>        x<\/p>\n<p>        \u2212<\/p>\n<p>        y<\/p>\n<p>        \u2223<\/p>\n<p>        &gt;<\/p>\n<p>        \u2223<\/p>\n<p>        a<\/p>\n<p>        \u2212<\/p>\n<p>        u<\/p>\n<p>        \u2223<\/p>\n<p>        &#043;<\/p>\n<p>        \u2223<\/p>\n<p>        u<\/p>\n<p>        \u2212<\/p>\n<p>        v<\/p>\n<p>        \u2223<\/p>\n<p>        &#043;<\/p>\n<p>        \u2223<\/p>\n<p>        v<\/p>\n<p>        \u2212<\/p>\n<p>        b<\/p>\n<p>        \u2223<\/p>\n<p>        &#061;<\/p>\n<p>        D<\/p>\n<p>       |x-y| &gt; |a-u| &#043; |u-v| &#043; |v-b| &#061; D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u77db\u76fe\u3002\u6240\u4ee5\u5fc5\u987b\u6709 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2223<\/p>\n<p>        x<\/p>\n<p>        \u2212<\/p>\n<p>        u<\/p>\n<p>        \u2223<\/p>\n<p>        \u2264<\/p>\n<p>        \u2223<\/p>\n<p>        a<\/p>\n<p>        \u2212<\/p>\n<p>        u<\/p>\n<p>        \u2223<\/p>\n<p>       |x-u| \\\\le |a-u|<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span>\u3002\u540c\u7406 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2223<\/p>\n<p>        v<\/p>\n<p>        \u2212<\/p>\n<p>        y<\/p>\n<p>        \u2223<\/p>\n<p>        \u2264<\/p>\n<p>        \u2223<\/p>\n<p>        v<\/p>\n<p>        \u2212<\/p>\n<p>        b<\/p>\n<p>        \u2223<\/p>\n<p>       |v-y| \\\\le |v-b|<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u4f46\u4e0a\u9762\u7b49\u5f0f\u8981\u6c42\u4e24\u8fb9\u76f8\u7b49&#xff0c;\u56e0\u6b64\u53ea\u80fd\u53d6\u7b49\u53f7&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u2223<\/p>\n<p>         x<\/p>\n<p>         \u2212<\/p>\n<p>         u<\/p>\n<p>         \u2223<\/p>\n<p>         &#061;<\/p>\n<p>         \u2223<\/p>\n<p>         a<\/p>\n<p>         \u2212<\/p>\n<p>         u<\/p>\n<p>         \u2223<\/p>\n<p>         ,<\/p>\n<p>         \u2223<\/p>\n<p>         v<\/p>\n<p>         \u2212<\/p>\n<p>         y<\/p>\n<p>         \u2223<\/p>\n<p>         &#061;<\/p>\n<p>         \u2223<\/p>\n<p>         v<\/p>\n<p>         \u2212<\/p>\n<p>         b<\/p>\n<p>         \u2223<\/p>\n<p>         |x-u| &#061; |a-u|, \\\\quad |v-y| &#061; |v-b| <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord\">\u2223<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u73b0\u5728\u8003\u8651\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>       x<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        b<\/p>\n<p>       b<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span> \u7684\u8ddd\u79bb&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         \u2223<\/p>\n<p>         x<\/p>\n<p>         \u2212<\/p>\n<p>         b<\/p>\n<p>         \u2223<\/p>\n<p>         &#061;<\/p>\n<p>         \u2223<\/p>\n<p>         x<\/p>\n<p>         \u2212<\/p>\n<p>         u<\/p>\n<p>         \u2223<\/p>\n<p>         &#043;<\/p>\n<p>         \u2223<\/p>\n<p>         u<\/p>\n<p>         \u2212<\/p>\n<p>         v<\/p>\n<p>         \u2223<\/p>\n<p>         &#043;<\/p>\n<p>         \u2223<\/p>\n<p>         v<\/p>\n<p>         \u2212<\/p>\n<p>         b<\/p>\n<p>         \u2223<\/p>\n<p>         &#061;<\/p>\n<p>         \u2223<\/p>\n<p>         a<\/p>\n<p>         \u2212<\/p>\n<p>         u<\/p>\n<p>         \u2223<\/p>\n<p>         &#043;<\/p>\n<p>         \u2223<\/p>\n<p>         u<\/p>\n<p>         \u2212<\/p>\n<p>         v<\/p>\n<p>         \u2223<\/p>\n<p>         &#043;<\/p>\n<p>         \u2223<\/p>\n<p>         v<\/p>\n<p>         \u2212<\/p>\n<p>         b<\/p>\n<p>         \u2223<\/p>\n<p>         &#061;<\/p>\n<p>         D<\/p>\n<p>         |x-b| &#061; |x-u| &#043; |u-v| &#043; |v-b| &#061; |a-u| &#043; |u-v| &#043; |v-b| &#061; D <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u6240\u4ee5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>       x<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        b<\/p>\n<p>       b<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span> \u4e5f\u662f\u4e00\u6761\u76f4\u5f84&#xff0c;\u4e14\u5b83\u7ecf\u8fc7 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        c<\/p>\n<p>       c<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span>&#xff08;\u56e0\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        v<\/p>\n<p>       v<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        b<\/p>\n<p>       b<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span> \u7684\u8def\u5f84\u7ecf\u8fc7 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        c<\/p>\n<p>       c<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002<\/p>\n<p>\u540c\u7406&#xff0c;\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        y<\/p>\n<p>       y<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        a<\/p>\n<p>       a<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span><\/span> \u7684\u8ddd\u79bb\u4e5f\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4e5f\u662f\u4e00\u6761\u76f4\u5f84\u3002<\/p>\n<p>\u4f46\u8fd9\u6837\u4e00\u6765&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>       x<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        b<\/p>\n<p>       b<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>       x<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        y<\/p>\n<p>       y<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span> \u90fd\u662f\u957f\u5ea6\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u7684\u76f4\u5f84&#xff0c;\u5b83\u4eec\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>       x<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u51fa\u53d1&#xff0c;\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        u<\/p>\n<p>       u<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">u<\/span><\/span><\/span><\/span><\/span> \u5904\u5206\u53c9\u3002\u7531\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>       x<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        b<\/p>\n<p>       b<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span> \u7ecf\u8fc7 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        c<\/p>\n<p>       c<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u800c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        x<\/p>\n<p>       x<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        y<\/p>\n<p>       y<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span> \u4e0d\u7ecf\u8fc7 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        c<\/p>\n<p>       c<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8fd9\u4f1a\u5bfc\u81f4\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        y<\/p>\n<p>       y<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        b<\/p>\n<p>       b<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span> \u7684\u8ddd\u79bb\u8d85\u8fc7 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4e0e\u76f4\u5f84\u5b9a\u4e49\u77db\u76fe&#xff08;\u5177\u4f53\u8ba1\u7b97&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        \u2223<\/p>\n<p>        y<\/p>\n<p>        \u2212<\/p>\n<p>        b<\/p>\n<p>        \u2223<\/p>\n<p>        &#061;<\/p>\n<p>        \u2223<\/p>\n<p>        y<\/p>\n<p>        \u2212<\/p>\n<p>        v<\/p>\n<p>        \u2223<\/p>\n<p>        &#043;<\/p>\n<p>        \u2223<\/p>\n<p>        v<\/p>\n<p>        \u2212<\/p>\n<p>        u<\/p>\n<p>        \u2223<\/p>\n<p>        &#043;<\/p>\n<p>        \u2223<\/p>\n<p>        u<\/p>\n<p>        \u2212<\/p>\n<p>        x<\/p>\n<p>        \u2223<\/p>\n<p>        &#043;<\/p>\n<p>        \u2223<\/p>\n<p>        x<\/p>\n<p>        \u2212<\/p>\n<p>        u<\/p>\n<p>        \u2223<\/p>\n<p>        &#043;<\/p>\n<p>        \u2223<\/p>\n<p>        u<\/p>\n<p>        \u2212<\/p>\n<p>        v<\/p>\n<p>        \u2223<\/p>\n<p>        &#043;<\/p>\n<p>        \u2223<\/p>\n<p>        v<\/p>\n<p>        \u2212<\/p>\n<p>        b<\/p>\n<p>        \u2223<\/p>\n<p>       |y-b| &#061; |y-v| &#043; |v-u| &#043; |u-x| &#043; |x-u| &#043; |u-v| &#043; |v-b|<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mord\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span> \u4e4b\u7c7b&#xff0c;\u4f1a\u8d85\u8fc7 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        D<\/p>\n<p>       D<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002\u56e0\u6b64\u5047\u8bbe\u4e0d\u6210\u7acb\u3002<\/p>\n<p>\u6240\u4ee5&#xff0c;\u4e0d\u5b58\u5728\u4e0d\u7ecf\u8fc7\u4e2d\u5fc3 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        c<\/p>\n<p>       c<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span> \u7684\u76f4\u5f84\u3002\u6240\u6709\u76f4\u5f84\u90fd\u7ecf\u8fc7 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        c<\/p>\n<p>       c<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u7ed3\u8bba&#xff1a; \u6811\u7684\u6240\u6709\u76f4\u5f84\u90fd\u5171\u4eab\u540c\u4e00\u4e2a\u4e2d\u5fc3&#xff08;\u70b9\u6216\u8fb9&#xff09;\u3002\u8fd9\u4e2a\u4e2d\u5fc3\u5c31\u662f\u76f4\u5f84\u7684\u4e2d\u70b9\u3002<\/p>\n<p>\u8bc1\u6bd5<\/p>\n<hr \/>\n<h4>T3\u9898\u76ee\u76f8\u5173\u201c\u7ffb\u8bd1\u201d<\/h4>\n<h5>\u8bf1\u5bfc\u5b50\u56fe&#xff08;Induced Subgraph&#xff09;<\/h5>\n<p>\u8bf1\u5bfc\u5b50\u56fe&#xff08;Induced Subgraph&#xff09;\u662f\u56fe\u8bba\u4e2d\u7684\u4e00\u4e2a\u6982\u5ff5&#xff0c;\u5b9a\u4e49\u5982\u4e0b&#xff1a;<\/p>\n<p>\u7ed9\u5b9a\u4e00\u4e2a\u56fe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        G<\/p>\n<p>        &#061;<\/p>\n<p>        (<\/p>\n<p>        V<\/p>\n<p>        ,<\/p>\n<p>        E<\/p>\n<p>        )<\/p>\n<p>       G&#061;(V,E)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">G<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u9009\u62e9\u5b83\u7684\u4e00\u4e2a\u9876\u70b9\u5b50\u96c6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        S<\/p>\n<p>        \u2286<\/p>\n<p>        V<\/p>\n<p>       S \\\\subseteq V<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8193em;vertical-align: -0.136em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2286<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><\/span><\/span><\/span><\/span>\u3002\u7531 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        S<\/p>\n<p>       S<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><\/span><\/span><\/span><\/span> \u8bf1\u5bfc\u51fa\u7684\u5b50\u56fe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        G<\/p>\n<p>        [<\/p>\n<p>        S<\/p>\n<p>        ]<\/p>\n<p>       G[S]<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">G<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span> \u5305\u542b&#xff1a;<\/p>\n<ul>\n<li>\u9876\u70b9\u96c6&#xff1a;\u5c31\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         S<\/p>\n<p>        S<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><\/span><\/span><\/span><\/span> \u672c\u8eab&#xff1b;<\/li>\n<li>\u8fb9\u96c6&#xff1a;\u539f\u56fe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         G<\/p>\n<p>        G<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">G<\/span><\/span><\/span><\/span><\/span> \u4e2d\u6240\u6709\u4e24\u4e2a\u7aef\u70b9\u90fd\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         S<\/p>\n<p>        S<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><\/span><\/span><\/span><\/span> \u4e2d\u7684\u8fb9\u3002<\/li>\n<\/ul>\n<p>\u5f62\u5f0f\u5316\u5730&#xff1a;<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         G<\/p>\n<p>         [<\/p>\n<p>         S<\/p>\n<p>         ]<\/p>\n<p>         &#061;<\/p>\n<p>         (<\/p>\n<p>         S<\/p>\n<p>         ,<\/p>\n<p>          E<\/p>\n<p>          S<\/p>\n<p>         )<\/p>\n<p>         ,<\/p>\n<p>          E<\/p>\n<p>          S<\/p>\n<p>         &#061;<\/p>\n<p>         {<br \/>\n        \u2009<\/p>\n<p>         (<\/p>\n<p>         u<\/p>\n<p>         ,<\/p>\n<p>         v<\/p>\n<p>         )<\/p>\n<p>         \u2208<\/p>\n<p>         E<\/p>\n<p>         \u2223<\/p>\n<p>         u<\/p>\n<p>         \u2208<\/p>\n<p>         S<\/p>\n<p>         \u00a0\u4e14\u00a0<\/p>\n<p>         v<\/p>\n<p>         \u2208<\/p>\n<p>         S<br \/>\n        \u2009<\/p>\n<p>         }<\/p>\n<p>         G[S] &#061; (S, E_S), \\\\quad E_S &#061; \\\\{\\\\, (u,v) \\\\in E \\\\mid u \\\\in S \\\\text{ \u4e14 } v \\\\in S \\\\,\\\\} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">G<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0576em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0576em\">S<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0576em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0576em\">S<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">{<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2223<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.5782em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7224em;vertical-align: -0.0391em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mord text\"><span class=\"mord\">\u00a0<\/span><span class=\"mord cjk_fallback\">\u4e14<\/span><span class=\"mord\">\u00a0<\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u4e5f\u5c31\u662f\u8bf4&#xff0c;\u8bf1\u5bfc\u5b50\u56fe\u5b8c\u5168\u7531\u9876\u70b9\u5b50\u96c6\u51b3\u5b9a&#xff1a;\u53ea\u8981\u9009\u5b9a\u4e86\u9876\u70b9&#xff0c;\u6240\u6709\u4e24\u7aef\u90fd\u5728\u8fd9\u4e2a\u5b50\u96c6\u91cc\u7684\u8fb9\u90fd\u5fc5\u987b\u4fdd\u7559&#xff0c;\u4e0d\u80fd\u968f\u610f\u5220\u51cf\u3002<\/p>\n<hr \/>\n<h6>\u4e0e\u666e\u901a\u5b50\u56fe\u7684\u533a\u522b<\/h6>\n<ul>\n<li>\u666e\u901a\u5b50\u56fe&#xff1a;\u53ef\u4ee5\u4efb\u610f\u9009\u62e9\u9876\u70b9\u5b50\u96c6\u548c\u8fb9\u5b50\u96c6&#xff0c;\u4e0d\u8981\u6c42\u4fdd\u7559\u6240\u6709\u4e24\u7aef\u5728\u9876\u70b9\u5b50\u96c6\u4e2d\u7684\u8fb9\u3002<\/li>\n<li>\u8bf1\u5bfc\u5b50\u56fe&#xff1a;\u53ea\u7531\u9876\u70b9\u5b50\u96c6\u51b3\u5b9a&#xff0c;\u8fb9\u96c6\u662f\u201c\u5f3a\u5236\u201d\u5305\u542b\u6240\u6709\u4e24\u7aef\u5728\u8be5\u9876\u70b9\u5b50\u96c6\u4e2d\u7684\u539f\u8fb9\u3002<\/li>\n<\/ul>\n<p>\u6240\u4ee5\u8bf1\u5bfc\u5b50\u56fe\u662f\u666e\u901a\u5b50\u56fe\u7684\u4e00\u79cd\u7279\u6b8a\u60c5\u51b5\u3002<\/p>\n<hr \/>\n<h6>\u4e3e\u4e2a\u4f8b\u5b50<\/h6>\n<p>\u539f\u56fe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        G<\/p>\n<p>       G<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">G<\/span><\/span><\/span><\/span><\/span> \u6709\u9876\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>        ,<\/p>\n<p>        2<\/p>\n<p>        ,<\/p>\n<p>        3<\/p>\n<p>       1,2,3<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8389em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">2<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8fb9\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        1<\/p>\n<p>        ,<\/p>\n<p>        2<\/p>\n<p>        )<\/p>\n<p>       (1,2)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">2<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        (<\/p>\n<p>        1<\/p>\n<p>        ,<\/p>\n<p>        3<\/p>\n<p>        )<\/p>\n<p>       (1,3)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">3<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<ul>\n<li>\u9009\u62e9\u9876\u70b9\u5b50\u96c6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         S<\/p>\n<p>         &#061;<\/p>\n<p>         {<\/p>\n<p>         1<\/p>\n<p>         ,<\/p>\n<p>         2<\/p>\n<p>         ,<\/p>\n<p>         3<\/p>\n<p>         }<\/p>\n<p>        S&#061;\\\\{1,2,3\\\\}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">{<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">2<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">3<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8bf1\u5bfc\u5b50\u56fe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         G<\/p>\n<p>         [<\/p>\n<p>         S<\/p>\n<p>         ]<\/p>\n<p>        G[S]<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">G<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span> \u5305\u542b\u6240\u6709\u9876\u70b9\u548c\u6240\u6709\u8fb9\u3002<\/li>\n<li>\u9009\u62e9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         S<\/p>\n<p>         &#061;<\/p>\n<p>         {<\/p>\n<p>         1<\/p>\n<p>         ,<\/p>\n<p>         2<\/p>\n<p>         }<\/p>\n<p>        S&#061;\\\\{1,2\\\\}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">{<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">2<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8bf1\u5bfc\u5b50\u56fe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         G<\/p>\n<p>         [<\/p>\n<p>         S<\/p>\n<p>         ]<\/p>\n<p>        G[S]<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">G<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span> \u5305\u542b\u9876\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         1<\/p>\n<p>         ,<\/p>\n<p>         2<\/p>\n<p>        1,2<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8389em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4ee5\u53ca\u8fb9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         (<\/p>\n<p>         1<\/p>\n<p>         ,<\/p>\n<p>         2<\/p>\n<p>         )<\/p>\n<p>        (1,2)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">2<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002\u8fb9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         (<\/p>\n<p>         1<\/p>\n<p>         ,<\/p>\n<p>         3<\/p>\n<p>         )<\/p>\n<p>        (1,3)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">3<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u4e0d\u5305\u542b&#xff0c;\u56e0\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         3<\/p>\n<p>        3<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span> \u4e0d\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         S<\/p>\n<p>        S<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><\/span><\/span><\/span><\/span> \u4e2d\u3002<\/li>\n<li>\u9009\u62e9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         S<\/p>\n<p>         &#061;<\/p>\n<p>         {<\/p>\n<p>         2<\/p>\n<p>         ,<\/p>\n<p>         3<\/p>\n<p>         }<\/p>\n<p>        S&#061;\\\\{2,3\\\\}<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">{<\/span><span class=\"mord\">2<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">3<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u8bf1\u5bfc\u5b50\u56fe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         G<\/p>\n<p>         [<\/p>\n<p>         S<\/p>\n<p>         ]<\/p>\n<p>        G[S]<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">G<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span> \u5305\u542b\u9876\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         2<\/p>\n<p>         ,<\/p>\n<p>         3<\/p>\n<p>        2,3<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8389em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">2<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4f46\u6ca1\u6709\u8fb9&#xff0c;\u56e0\u4e3a\u539f\u56fe\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         2<\/p>\n<p>        2<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         3<\/p>\n<p>        3<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span> \u4e4b\u95f4\u6ca1\u6709\u8fb9\u3002<\/li>\n<\/ul>\n<p>\u8fd4\u56de\u4f20\u9001\u95e8<\/p>\n<hr \/>\n<h5>\u6700\u5927\u72ec\u7acb\u96c6&#xff08;Maximum Independent Set&#xff09;<\/h5>\n<p>\u6700\u5927\u72ec\u7acb\u96c6&#xff08;Maximum Independent Set&#xff09;\u662f\u56fe\u8bba\u4e2d\u7684\u4e00\u4e2a\u7ecf\u5178\u6982\u5ff5\u3002<\/p>\n<h6>1. \u72ec\u7acb\u96c6&#xff08;Independent Set&#xff09;<\/h6>\n<p>\u7ed9\u5b9a\u4e00\u4e2a\u56fe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        G<\/p>\n<p>        &#061;<\/p>\n<p>        (<\/p>\n<p>        V<\/p>\n<p>        ,<\/p>\n<p>        E<\/p>\n<p>        )<\/p>\n<p>       G&#061;(V,E)<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">G<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4e00\u4e2a\u72ec\u7acb\u96c6\u662f\u9876\u70b9\u96c6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        V<\/p>\n<p>       V<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><\/span><\/span><\/span><\/span> \u7684\u4e00\u4e2a\u5b50\u96c6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        S<\/p>\n<p>       S<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6ee1\u8db3&#xff1a;<\/p>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         S<\/p>\n<p>        S<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><\/span><\/span><\/span><\/span> \u4e2d\u4efb\u610f\u4e24\u4e2a\u9876\u70b9\u4e4b\u95f4\u90fd\u6ca1\u6709\u8fb9\u3002<\/p>\n<p>\u6362\u53e5\u8bdd\u8bf4&#xff0c;\u72ec\u7acb\u96c6\u4e2d\u7684\u9876\u70b9\u4e24\u4e24\u4e92\u4e0d\u76f8\u90bb\u3002<\/p>\n<p>\u4f8b\u5982&#xff0c;\u5bf9\u4e8e\u4e09\u89d2\u5f62&#xff08;\u4e09\u4e2a\u9876\u70b9\u4e24\u4e24\u76f8\u8fde&#xff09;&#xff0c;\u4efb\u610f\u4e24\u4e2a\u9876\u70b9\u90fd\u4e0d\u6784\u6210\u72ec\u7acb\u96c6&#xff0c;\u56e0\u4e3a\u5b83\u4eec\u4e4b\u95f4\u6709\u8fb9&#xff1b;\u4f46\u6bcf\u4e2a\u5355\u72ec\u7684\u9876\u70b9\u6784\u6210\u4e00\u4e2a\u72ec\u7acb\u96c6\u3002<\/p>\n<hr \/>\n<h6>2. \u6700\u5927\u72ec\u7acb\u96c6<\/h6>\n<p>\u6700\u5927\u72ec\u7acb\u96c6\u5c31\u662f\u56fe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        G<\/p>\n<p>       G<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">G<\/span><\/span><\/span><\/span><\/span> \u7684\u6240\u6709\u72ec\u7acb\u96c6\u4e2d&#xff0c;\u5305\u542b\u9876\u70b9\u6570\u6700\u591a\u7684\u90a3\u4e2a\u72ec\u7acb\u96c6\u3002<\/p>\n<ul>\n<li>\u6700\u5927\u72ec\u7acb\u96c6\u7684\u5927\u5c0f\u79f0\u4e3a\u56fe\u7684\u72ec\u7acb\u6570&#xff0c;\u901a\u5e38\u8bb0\u4f5c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         \u03b1<\/p>\n<p>         (<\/p>\n<p>         G<\/p>\n<p>         )<\/p>\n<p>        \\\\alpha(G)<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0037em\">\u03b1<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">G<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>\u6ce8\u610f&#xff1a;\u6700\u5927\u72ec\u7acb\u96c6\u53ef\u80fd\u4e0d\u552f\u4e00&#xff0c;\u4f46\u5927\u5c0f\u662f\u552f\u4e00\u7684\u3002<\/li>\n<\/ul>\n<hr \/>\n<h6>3. \u4e0e\u201c\u6781\u5927\u72ec\u7acb\u96c6\u201d\u7684\u533a\u522b<\/h6>\n<ul>\n<li>\u6781\u5927\u72ec\u7acb\u96c6&#xff08;Maximal Independent Set&#xff09;&#xff1a;\u4e0d\u80fd\u518d\u52a0\u5165\u4efb\u4f55\u9876\u70b9\u800c\u4ecd\u7136\u4fdd\u6301\u72ec\u7acb\u6027\u7684\u72ec\u7acb\u96c6\u3002\u4e5f\u5c31\u662f\u8bf4&#xff0c;\u5bf9\u4e8e\u4e0d\u5728\u96c6\u5408\u4e2d\u7684\u4efb\u610f\u9876\u70b9&#xff0c;\u5b83\u81f3\u5c11\u4e0e\u96c6\u5408\u4e2d\u67d0\u4e2a\u9876\u70b9\u76f8\u90bb\u3002<\/li>\n<li>\u6700\u5927\u72ec\u7acb\u96c6&#xff08;Maximum Independent Set&#xff09;&#xff1a;\u6240\u6709\u72ec\u7acb\u96c6\u4e2d\u9876\u70b9\u6570\u6700\u591a\u7684\u90a3\u4e2a\u3002<\/li>\n<\/ul>\n<p>\u6781\u5927\u72ec\u7acb\u96c6\u4e0d\u4e00\u5b9a\u662f\u6700\u5927\u72ec\u7acb\u96c6\u3002\u4f8b\u5982&#xff0c;\u4e00\u6761\u957f\u5ea6\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        3<\/p>\n<p>       3<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span> \u7684\u8def\u5f84&#xff08;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        4<\/p>\n<p>       4<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">4<\/span><\/span><\/span><\/span><\/span> \u4e2a\u9876\u70b9&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        1<\/p>\n<p>        \u2212<\/p>\n<p>        2<\/p>\n<p>        \u2212<\/p>\n<p>        3<\/p>\n<p>        \u2212<\/p>\n<p>        4<\/p>\n<p>       1-2-3-4<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">2<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">3<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">4<\/span><\/span><\/span><\/span><\/span>&#xff09;&#xff0c;\u96c6\u5408 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        {<\/p>\n<p>        2<\/p>\n<p>        ,<\/p>\n<p>        4<\/p>\n<p>        }<\/p>\n<p>       \\\\{2,4\\\\}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">{<\/span><span class=\"mord\">2<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">4<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span> \u662f\u6781\u5927\u72ec\u7acb\u96c6&#xff0c;\u4f46\u4e0d\u662f\u6700\u5927\u72ec\u7acb\u96c6&#xff1b;\u6700\u5927\u72ec\u7acb\u96c6\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        {<\/p>\n<p>        1<\/p>\n<p>        ,<\/p>\n<p>        3<\/p>\n<p>        }<\/p>\n<p>       \\\\{1,3\\\\}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">{<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">3<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span> \u6216 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        {<\/p>\n<p>        2<\/p>\n<p>        ,<\/p>\n<p>        4<\/p>\n<p>        }<\/p>\n<p>       \\\\{2,4\\\\}<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">{<\/span><span class=\"mord\">2<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">4<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5927\u5c0f\u90fd\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        2<\/p>\n<p>       2<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<h6>4. \u6e29\u99a8\u63d0\u793a<\/h6>\n<p>\u6c42\u89e3\u6700\u5927\u72ec\u7acb\u96c6\u662f NP-hard \u95ee\u9898&#xff1a;<\/p>\n<p>&#xff08;\u5982\u679c\u4f60\u597d\u5947\u5fc3\u6ca1\u90a3\u4e48\u91cd&#xff0c;\u5efa\u8bae\u4f60\u4e0d\u8981\u7ee7\u7eed\u770b\u4e0b\u53bb&#xff0c;\u628a\u5b83\u7406\u89e3\u4e3a\u5f88\u96be\u7684\u95ee\u9898\u5c31\u884c\u4e86&#xff09;<\/p>\n<p>\u2026\u2026<\/p>\n<p>\u2026\u2026<\/p>\n<p>\u2026\u2026<\/p>\n<p>\u2026\u2026<\/p>\n<p>\u2026\u2026<\/p>\n<p>\u2026\u2026<\/p>\n<p>\u597d\u5427&#xff0c;<\/p>\n<h6>NP-hard<\/h6>\n<p>NP-hard \u662f\u8ba1\u7b97\u590d\u6742\u6027\u7406\u8bba\u4e2d\u7684\u4e00\u4e2a\u6982\u5ff5&#xff0c;\u7528\u6765\u63cf\u8ff0\u201c\u81f3\u5c11\u548c NP \u4e2d\u6700\u96be\u7684\u95ee\u9898\u4e00\u6837\u96be\u201d\u7684\u95ee\u9898\u3002<\/p>\n<hr \/>\n<h6>1. \u5148\u7406\u89e3 P \u548c NP<\/h6>\n<ul>\n<li>P \u95ee\u9898&#xff1a;\u53ef\u4ee5\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u89e3\u51b3\u7684\u95ee\u9898\u3002 \u4f8b\u5982&#xff1a;\u6392\u5e8f\u3001\u6700\u77ed\u8def\u3002<\/li>\n<li>NP \u95ee\u9898&#xff1a;\u53ef\u4ee5\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u9a8c\u8bc1\u4e00\u4e2a\u89e3\u662f\u5426\u6b63\u786e\u7684\u95ee\u9898\u3002 \u4f8b\u5982&#xff1a;\u7ed9\u5b9a\u4e00\u4e2a\u56fe\u548c\u4e00\u4e2a\u9876\u70b9\u96c6\u5408&#xff0c;\u95ee\u5b83\u662f\u4e0d\u662f\u72ec\u7acb\u96c6&#xff0c;\u8fd9\u5f88\u5bb9\u6613\u9a8c\u8bc1&#xff1b;\u4f46\u627e\u51fa\u6700\u5927\u7684\u72ec\u7acb\u96c6\u5f88\u96be\u3002<\/li>\n<\/ul>\n<p>\u663e\u7136 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        \u2286<\/p>\n<p>        N<\/p>\n<p>        P<\/p>\n<p>       P \\\\subseteq NP<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8193em;vertical-align: -0.136em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2286<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u4f46 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        P<\/p>\n<p>        &#061;<\/p>\n<p>        N<\/p>\n<p>        P<\/p>\n<p>       P&#061;NP<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><\/span><\/span><\/span><\/span> \u662f\u5426\u6210\u7acb\u81f3\u4eca\u672a\u89e3\u3002<\/p>\n<hr \/>\n<h6>2. NP-hard \u7684\u5b9a\u4e49<\/h6>\n<p>\u4e00\u4e2a\u95ee\u9898 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        H<\/p>\n<p>       H<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0813em\">H<\/span><\/span><\/span><\/span><\/span> \u662f NP-hard \u7684&#xff0c;\u5982\u679c&#xff1a;<\/p>\n<p>\u5bf9\u4e8e\u6240\u6709 NP \u95ee\u9898 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         L<\/p>\n<p>        L<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u90fd\u5b58\u5728\u4e00\u4e2a\u591a\u9879\u5f0f\u65f6\u95f4\u7684\u5f52\u7ea6&#xff0c;\u628a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         L<\/p>\n<p>        L<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">L<\/span><\/span><\/span><\/span><\/span> \u8f6c\u5316\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         H<\/p>\n<p>        H<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0813em\">H<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p>\u4e5f\u5c31\u662f\u8bf4&#xff0c;\u53ea\u8981\u4f60\u80fd\u591a\u9879\u5f0f\u65f6\u95f4\u89e3\u51b3 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        H<\/p>\n<p>       H<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0813em\">H<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5c31\u80fd\u591a\u9879\u5f0f\u65f6\u95f4\u89e3\u51b3\u6240\u6709 NP \u95ee\u9898\u3002\u56e0\u6b64 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>        H<\/p>\n<p>       H<\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0813em\">H<\/span><\/span><\/span><\/span><\/span> \u81f3\u5c11\u548c NP \u4e2d\u6700\u96be\u7684\u95ee\u9898\u4e00\u6837\u96be\u3002<\/p>\n<p>\u6ce8\u610f&#xff1a;<\/p>\n<ul>\n<li>NP-hard \u95ee\u9898\u4e0d\u4e00\u5b9a\u5c5e\u4e8e NP\u3002\u5b83\u53ef\u80fd\u6839\u672c\u65e0\u6cd5\u5728\u591a\u9879\u5f0f\u65f6\u95f4\u5185\u9a8c\u8bc1\u89e3\u3002<\/li>\n<li>\u5982\u679c\u4e00\u4e2a\u95ee\u9898\u65e2\u662f NP-hard&#xff0c;\u53c8\u5c5e\u4e8e NP&#xff0c;\u90a3\u4e48\u5b83\u53eb NP-complete&#xff08;NP \u5b8c\u5168&#xff09;\u3002<\/li>\n<\/ul>\n<hr \/>\n<h6>3. \u6700\u5927\u72ec\u7acb\u96c6\u662f NP-hard<\/h6>\n<ul>\n<li>\u5224\u5b9a\u7248\u672c&#xff1a;\u7ed9\u5b9a\u56fe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>         G<\/p>\n<p>        G<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">G<\/span><\/span><\/span><\/span><\/span> \u548c\u6574\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         k<\/p>\n<p>        k<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u95ee\u662f\u5426\u5b58\u5728\u5927\u5c0f\u81f3\u5c11\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<p>         k<\/p>\n<p>        k<\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><\/span><\/span><\/span><\/span> \u7684\u72ec\u7acb\u96c6\u3002 \u8fd9\u4e2a\u5224\u5b9a\u95ee\u9898\u662f NP-complete \u7684\u3002<\/li>\n<li>\u4f18\u5316\u7248\u672c&#xff1a;\u6c42\u6700\u5927\u72ec\u7acb\u96c6\u7684\u5927\u5c0f\u3002 \u8fd9\u662f NP-hard \u7684\u3002<\/li>\n<\/ul>\n<p>\u6240\u4ee5\u6700\u5927\u72ec\u7acb\u96c6\u6ca1\u6709\u5df2\u77e5\u7684\u591a\u9879\u5f0f\u65f6\u95f4\u7b97\u6cd5\u3002\u5bf9\u4e8e\u4e00\u822c\u56fe&#xff0c;\u901a\u5e38\u53ea\u80fd\u7528\u6307\u6570\u7ea7\u7b97\u6cd5&#xff08;\u5982\u72b6\u538b DP\u3001\u5206\u652f\u9650\u754c\u7b49\u3002\u54ce\u5440&#xff0c;\u597d\u50cf\u5267\u900f\u4e86&#xff09;\u3002<\/p>\n<p>\u2026\u2026\u5c0f\u998b\u732b&#xff01;(\u63a8\u628a\u773c\u955c)<\/p>\n<p>\u73b0\u5728\u603b\u6ee1\u610f\u4e86\u5427&#xff1f;(\u540e\u9762\u4e5f\u6ca1\u4e86)<\/p>\n<hr class=\"footnotes-sep\" \/>\n<li id=\"fn1\" class=\"footnote-item\">\n<p>\u4e0d\u7ecf\u8fc7\u91cd\u590d\u8fb9\u6216\u91cd\u590d\u70b9\u7684\u8def\u5f84 \u21a9\ufe0e<\/p>\n<\/li>\n<li id=\"fn2\" class=\"footnote-item\">\n<p>\u89e3\u91ca\u4e00\u4e0b&#xff0c;\u8fd9\u91cc\u662f\u56e0\u4e3a\u4e00\u68f5\u6811\u81f3\u5c11\u6709\u4e00\u6761\u76f4\u5f84&#xff0c;\u6700\u574f\u60c5\u51b5\u5728\u8fd9\u6761\u76f4\u5f84\u5012\u6570\u7b2c\u4e8c\u4e2a\u70b9\u4e0b\u65b9\u63a5\u4e00\u4e2a\u513f\u5b50\u5c31\u53ef\u4ee5\u4e86 \u21a9\ufe0e<\/p>\n<\/li>\n","protected":false},"excerpt":{"rendered":"<p>2025\u79cb\u5b63\u63d0\u9ad8\u7ec4\u6a21\u62df\u8d5b4\u2014\u2014\u505a\u9898\u968f\u7b14\/\u5957\u5377\u9898\u89e3 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