{"id":100277,"date":"2026-09-04T12:16:59","date_gmt":"2026-09-04T04:16:59","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/100277.html"},"modified":"2026-09-04T12:16:59","modified_gmt":"2026-09-04T04:16:59","slug":"p1671-rigging-the-bovine-election-s-%e3%80%90%e6%b4%9b%e8%b0%b7%e7%ae%97%e6%b3%95%e4%b9%a0%e9%a2%98%e3%80%91","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/100277.html","title":{"rendered":"P1671 Rigging the Bovine Election S \u3010\u6d1b\u8c37\u7b97\u6cd5\u4e60\u9898\u3011"},"content":{"rendered":"<h2>P1671 Rigging the Bovine Election S<\/h2>\n<h3>\u7f51\u9875\u94fe\u63a5<\/h3>\n<p>P1671 Rigging the Bovine Election S <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260904041657-6a9a4639bede1.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>\u9898\u76ee\u63cf\u8ff0<\/h3>\n<p>\u519c\u573a\u88ab\u5212\u5206\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         5 <\/p>\n<p>         \u00d7 <\/p>\n<p>         5 <\/p>\n<p>        5\\\\times 5 <\/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\">5<\/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: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u7684\u683c\u5b50&#xff0c;\u6bcf\u4e2a\u683c\u5b50\u4e2d\u90fd\u6709\u4e00\u5934\u5976\u725b&#xff0c;\u5e76\u4e14\u53ea\u6709\u8377\u65af\u5766&#xff08;\u6807\u8bb0\u4e3a H&#xff09;\u548c\u6770\u897f&#xff08;\u6807\u8bb0\u4e3a J&#xff09;\u4e24\u4e2a\u54c1\u79cd\u3002\u5982\u679c\u4e00\u5934\u5976\u725b\u5728\u53e6\u4e00\u5934\u4e0a\u4e0b\u5de6\u53f3\u56db\u4e2a\u683c\u5b50\u4e2d\u7684\u4efb\u4e00\u683c\u91cc&#xff0c;\u6211\u4eec\u8bf4\u5b83\u4eec\u76f8\u8fde\u3002\u5976\u725b\u8981\u5927\u9009\u4e86\u3002\u73b0\u5728\u6770\u897f\u5976\u725b\u4eec\u60f3\u9009\u62e9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         7 <\/p>\n<p>        7 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span> \u5934\u76f8\u8fde\u7684\u5976\u725b&#xff0c;\u5212\u6210\u4e00\u4e2a\u7ade\u9009\u533a&#xff0c;\u4f7f\u5f97\u5176\u4e2d\u5b83\u4eec\u54c1\u79cd\u7684\u5976\u725b\u6bd4\u8377\u65af\u5766\u7684\u591a\u3002<\/p>\n<p>\u8981\u6c42\u4f60\u7f16\u5199\u4e00\u4e2a\u7a0b\u5e8f\u6c42\u51fa\u65b9\u6848\u603b\u6570\u3002<\/p>\n<h3>\u8f93\u5165\u683c\u5f0f<\/h3>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         5 <\/p>\n<p>        5 <\/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><\/span><\/span><\/span> \u884c&#xff0c;\u8868\u793a\u519c\u573a\u7684\u60c5\u51b5\u3002<\/p>\n<h3>\u8f93\u51fa\u683c\u5f0f<\/h3>\n<p>\u8f93\u51fa\u5212\u533a\u65b9\u6848\u603b\u6570\u3002<\/p>\n<h3>\u8f93\u5165\u8f93\u51fa\u6837\u4f8b #1<\/h3>\n<h4>\u8f93\u5165 #1<\/h4>\n<p>HHHHH<br \/>\nJHJHJ<br \/>\nHHHHH<br \/>\nHJHHJ<br \/>\nHHHHH<\/p>\n<h4>\u8f93\u51fa #1<\/h4>\n<p>2<\/p>\n<h3>\u89e3\u9898\u601d\u8def<\/h3>\n<p>\u672c\u9898\u662f\u7ec4\u5408\u679a\u4e3e &#043; \u8fde\u901a\u6027\u68c0\u67e5\u7684\u641c\u7d22\u9898\u3002\u519c\u573a\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         5 <\/p>\n<p>         \u00d7 <\/p>\n<p>         5 <\/p>\n<p>        5\\\\times5 <\/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\">5<\/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: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u7684\u7f51\u683c&#xff0c;\u5171 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         25 <\/p>\n<p>        25 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">25<\/span><\/span><\/span><\/span><\/span> \u4e2a\u683c\u5b50&#xff0c;\u9700\u8981\u4ece\u4e2d\u9009\u51fa <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         7 <\/p>\n<p>        7 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span> \u4e2a\u683c\u5b50\u7ec4\u6210\u4e00\u4e2a\u7ade\u9009\u533a&#xff0c;\u8981\u6c42\u8fd9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         7 <\/p>\n<p>        7 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span> \u4e2a\u683c\u5b50\u8fde\u901a&#xff0c;\u5e76\u4e14\u5176\u4e2d\u6770\u897f\u5976\u725b&#xff08;J&#xff09;\u7684\u6570\u91cf\u4e0d\u5c11\u4e8e <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>\u3002\u7531\u4e8e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         25 <\/p>\n<p>        25 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">25<\/span><\/span><\/span><\/span><\/span> \u9009 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         7 <\/p>\n<p>        7 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span> \u7684\u7ec4\u5408\u6570\u53ea\u6709 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          C <\/p>\n<p>          25 <\/p>\n<p>          7 <\/p>\n<p>         &#061; <\/p>\n<p>         480700 <\/p>\n<p>        C_{25}^7 &#061; 480700 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0622em;vertical-align: -0.2481em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -2.4519em;margin-left: -0.0715em;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\">25<\/span><\/span><\/span><\/span><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\">7<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2481em\"><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: 0.6444em\"><\/span><span class=\"mord\">480700<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u53ef\u4ee5\u76f4\u63a5\u679a\u4e3e\u6240\u6709\u7ec4\u5408\u5e76\u9010\u4e00\u68c0\u9a8c\u3002<\/p>\n<h5>1. \u95ee\u9898\u7b49\u4ef7\u8f6c\u5316<\/h5>\n<ul>\n<li>\u5c06 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          5 <\/p>\n<p>          \u00d7 <\/p>\n<p>          5 <\/p>\n<p>         5\\\\times5 <\/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\">5<\/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: 0.6444em\"><\/span><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> \u7f51\u683c\u7f16\u53f7\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          1 <\/p>\n<p>          \u223c <\/p>\n<p>          25 <\/p>\n<p>         1\\\\sim25 <\/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=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u223c<\/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\">25<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6bcf\u4e2a\u7f16\u53f7\u5bf9\u5e94\u4e00\u4e2a\u5750\u6807 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          ( <\/p>\n<p>          \u884c <\/p>\n<p>          , <\/p>\n<p>          \u5217 <\/p>\n<p>          ) <\/p>\n<p>         (\u884c,\u5217) <\/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 cjk_fallback\">\u884c<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord cjk_fallback\">\u5217<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          25 <\/p>\n<p>         25 <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">25<\/span><\/span><\/span><\/span><\/span> \u4e2a\u7f16\u53f7\u4e2d\u9009\u51fa <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          7 <\/p>\n<p>         7 <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span> \u4e2a&#xff0c;\u76f8\u5f53\u4e8e\u679a\u4e3e\u6240\u6709 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          7 <\/p>\n<p>         7 <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span> \u4e2a\u4f4d\u7f6e\u7684\u7ec4\u5408\u3002<\/li>\n<li>\u5bf9\u4e8e\u6bcf\u4e2a\u7ec4\u5408&#xff0c;\u9700\u8981\u5224\u65ad&#xff1a;\n<ul>\n<li>\u8fd9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>            7 <\/p>\n<p>           7 <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span> \u4e2a\u683c\u5b50\u662f\u5426\u6784\u6210\u4e00\u4e2a\u8fde\u901a\u5757&#xff08;\u901a\u8fc7\u4e0a\u4e0b\u5de6\u53f3\u76f8\u90bb\u5173\u7cfb&#xff09;&#xff1b;<\/li>\n<li>\u5176\u4e2d\u5b57\u7b26\u4e3a J \u7684\u683c\u5b50\u6570\u91cf\u662f\u5426 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>            \u2265 <\/p>\n<p>            4 <\/p>\n<p>           \\\\ge 4 <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7719em;vertical-align: -0.136em\"><\/span><span class=\"mrel\">\u2265<\/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>\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u6ee1\u8db3\u4e0a\u8ff0\u6761\u4ef6\u7684\u7ec4\u5408\u8ba1\u6570\u5373\u4e3a\u7b54\u6848\u3002<\/li>\n<\/ul>\n<h5>2. \u7b97\u6cd5\u5b9e\u73b0<\/h5>\n<li>\u8f93\u5165\u4e0e\u5efa\u56fe&#xff1a;\u8bfb\u5165 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          5 <\/p>\n<p>          \u00d7 <\/p>\n<p>          5 <\/p>\n<p>         5\\\\times5 <\/p>\n<p>     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     i <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6595em\"><\/span><span class=\"mord mathnormal\">i<\/span><\/span><\/span><\/span><\/span> \u540e&#xff0c;\u5c06\u5176\u6620\u5c04\u4e3a\u5750\u6807 (c[y], d[y])&#xff0c;\u5176\u4e2d\u884c c[y] &#061; (i&#043;4)\/5&#xff0c;\u5217 d[y] &#061; i &#8211; (\u884c-1)*5\u3002<\/li>\n<li>\u5f53 y &#061;&#061; 7 \u65f6&#xff0c;\u8868\u793a\u5df2\u9009\u6ee1 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>            7 <\/p>\n<p>           7 <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span> \u4e2a\u683c\u5b50&#xff0c;\u8fdb\u5165\u68c0\u67e5\u6d41\u7a0b\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u68c0\u67e5\u6d41\u7a0b&#xff1a;\n<ul>\n<li>\u7edf\u8ba1\u8fd9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>            7 <\/p>\n<p>           7 <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span> \u4e2a\u683c\u5b50\u4e2d\u5b57\u7b26\u4e3a J \u7684\u4e2a\u6570 sum\u3002<\/li>\n<li>\u82e5 sum &lt; 4&#xff0c;\u76f4\u63a5\u8df3\u8fc7\u3002<\/li>\n<li>\u5426\u5219\u4ee5\u7b2c\u4e00\u4e2a\u683c\u5b50\u4e3a\u8d77\u70b9&#xff0c;\u4f7f\u7528 dfs1(k) \u4ece\u8be5\u70b9\u51fa\u53d1&#xff0c;\u53ea\u6cbf\u5df2\u9009\u4e2d\u7684\u683c\u5b50\u8fdb\u884c\u4e0a\u4e0b\u5de6\u53f3\u641c\u7d22&#xff0c;\u7edf\u8ba1\u8fde\u901a\u5757\u5927\u5c0f t\u3002<\/li>\n<li>\u82e5 t &#061;&#061; 7&#xff0c;\u8bf4\u660e\u8fd9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>            7 <\/p>\n<p>           7 <\/p>\n<p>       <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span> \u4e2a\u683c\u5b50\u5168\u90e8\u8fde\u901a&#xff0c;\u65b9\u6848\u6570 ans&#043;&#043;\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u8f93\u51fa\u7ed3\u679c&#xff1a;\u8f93\u51fa ans\u3002<\/li>\n<h5>3. \u590d\u6742\u5ea6\u5206\u6790<\/h5>\n<ul>\n<li>\u65f6\u95f4\u590d\u6742\u5ea6&#xff1a;\u679a\u4e3e <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           C <\/p>\n<p>           25 <\/p>\n<p>           7 <\/p>\n<p>          \u2248 <\/p>\n<p>          4.8 <\/p>\n<p>          \u00d7 <\/p>\n<p>           10 <\/p>\n<p>           5 <\/p>\n<p>         C_{25}^7 \\\\approx 4.8\\\\times10^5 <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0622em;vertical-align: -0.2481em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em\"><span class=\"\" style=\"top: -2.4519em;margin-left: -0.0715em;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\">25<\/span><\/span><\/span><\/span><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\">7<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2481em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">4.8<\/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: 0.8141em\"><\/span><span class=\"mord\">1<\/span><span class=\"mord\"><span class=\"mord\">0<\/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\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e2a\u7ec4\u5408&#xff0c;\u6bcf\u4e2a\u7ec4\u5408\u68c0\u67e5\u8fde\u901a\u6027\u6700\u591a\u8bbf\u95ee <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          7 <\/p>\n<p>         7 <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span> \u4e2a\u683c\u5b50\u548c\u5b83\u4eec\u7684 <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\u90bb\u5c45&#xff0c;\u64cd\u4f5c\u6b21\u6570\u5f88\u5c0f&#xff0c;\u603b\u65f6\u95f4\u5b8c\u5168\u5728\u9650\u5236\u5185\u3002<\/li>\n<li>\u7a7a\u95f4\u590d\u6742\u5ea6&#xff1a;\u4ec5\u9700\u5b58\u50a8\u5730\u56fe\u3001\u5f53\u524d\u7ec4\u5408\u7684\u5750\u6807\u6570\u7ec4\u3001\u8bbf\u95ee\u6807\u8bb0\u6570\u7ec4\u7b49&#xff0c;\u5747\u4e3a\u5e38\u6570\u7ea7\u6216 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          O <\/p>\n<p>          ( <\/p>\n<p>          7 <\/p>\n<p>          ) <\/p>\n<p>         O(7) <\/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\">7<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<\/ul>\n<h4>\u603b\u7ed3<\/h4>\n<p>\u5229\u7528 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         25 <\/p>\n<p>        25 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">25<\/span><\/span><\/span><\/span><\/span> \u683c\u9009 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         7 <\/p>\n<p>        7 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span> \u683c\u7ec4\u5408\u6570\u8f83\u5c0f\u7684\u7279\u70b9&#xff0c;\u76f4\u63a5\u679a\u4e3e\u6240\u6709\u53ef\u80fd\u7684\u683c\u5b50\u7ec4\u5408&#xff0c;\u5e76\u901a\u8fc7 DFS \u68c0\u67e5\u8fde\u901a\u6027\u548c\u54c1\u79cd\u6570\u91cf\u6761\u4ef6\u3002\u65b9\u6cd5\u7b80\u5355\u76f4\u89c2&#xff0c;\u8db3\u4ee5\u5728\u65f6\u9650\u5185\u6c42\u51fa\u65b9\u6848\u603b\u6570\u3002<\/p>\n<h3>\u4ee3\u7801\u5185\u5bb9<\/h3>\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><\/p>\n<p><span class=\"token macro property\"><span class=\"token directive-hash\">#<\/span><span class=\"token directive keyword\">define<\/span> <span class=\"token macro-name\">endl<\/span> <span class=\"token char\">&#039;\\\\n&#039;<\/span><\/span><br \/>\n<span class=\"token keyword\">typedef<\/span> <span class=\"token keyword\">long<\/span> <span class=\"token keyword\">long<\/span> ll<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">typedef<\/span> <span class=\"token keyword\">unsigned<\/span> <span class=\"token keyword\">long<\/span> <span class=\"token keyword\">long<\/span> ull<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">typedef<\/span> vector<span class=\"token operator\">&lt;<\/span>vector<span class=\"token operator\">&lt;<\/span>ll<span class=\"token operator\">&gt;&gt;<\/span> vvt<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">typedef<\/span> pair<span class=\"token operator\">&lt;<\/span>ll<span class=\"token punctuation\">,<\/span>ll<span class=\"token operator\">&gt;<\/span> pll<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">const<\/span> ll N<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1e3<\/span><span class=\"token operator\">&#043;<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">const<\/span> ll INF<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1e18<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">const<\/span> ll M<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1e6<\/span><span class=\"token operator\">&#043;<\/span><span class=\"token number\">10<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">const<\/span> ll mod<span class=\"token operator\">&#061;<\/span><span class=\"token number\">1e9<\/span><span class=\"token operator\">&#043;<\/span><span class=\"token number\">7<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token keyword\">const<\/span> ll r<span class=\"token operator\">&#061;<\/span><span class=\"token number\">7<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">const<\/span> ll f<span class=\"token punctuation\">[<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">]<\/span><span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">{<\/span><span class=\"token punctuation\">{<\/span><span class=\"token number\">1<\/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 punctuation\">{<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">,<\/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 number\">0<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">,<\/span><span class=\"token punctuation\">{<\/span><span class=\"token number\">0<\/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><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">char<\/span> mp<span class=\"token punctuation\">[<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\nll ans<span class=\"token punctuation\">,<\/span>t<span class=\"token punctuation\">,<\/span>c<span class=\"token punctuation\">[<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span>d<span class=\"token punctuation\">[<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span>vis<span class=\"token punctuation\">[<\/span><span class=\"token number\">8<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token keyword\">void<\/span> <span class=\"token function\">dfs1<\/span><span class=\"token punctuation\">(<\/span>ll k<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n    vis<span class=\"token punctuation\">[<\/span>k<span class=\"token punctuation\">]<\/span><span class=\"token operator\">&#061;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> t<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span>ll i<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span>i<span class=\"token operator\">&lt;<\/span><span class=\"token number\">4<\/span><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        ll nx<span class=\"token operator\">&#061;<\/span>c<span class=\"token punctuation\">[<\/span>k<span class=\"token punctuation\">]<\/span><span class=\"token operator\">&#043;<\/span>f<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        ll ny<span class=\"token operator\">&#061;<\/span>d<span class=\"token punctuation\">[<\/span>k<span class=\"token punctuation\">]<\/span><span class=\"token operator\">&#043;<\/span>f<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span>ll 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>r<span class=\"token punctuation\">;<\/span>j<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>c<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token operator\">&#061;&#061;<\/span>nx <span class=\"token operator\">&amp;&amp;<\/span> d<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token operator\">&#061;&#061;<\/span>ny <span class=\"token operator\">&amp;&amp;<\/span> <span class=\"token operator\">!<\/span>vis<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token function\">dfs1<\/span><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><\/p>\n<p><span class=\"token keyword\">void<\/span> <span class=\"token function\">dfs2<\/span><span class=\"token punctuation\">(<\/span>ll x<span class=\"token punctuation\">,<\/span>ll y<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>y<span class=\"token operator\">&#061;&#061;<\/span>r<span class=\"token operator\">&#043;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><br \/>\n    <span class=\"token punctuation\">{<\/span><br \/>\n        ll sum<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> t<span class=\"token operator\">&#061;<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token function\">memset<\/span><span class=\"token punctuation\">(<\/span>vis<span class=\"token punctuation\">,<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span><span class=\"token keyword\">sizeof<\/span><span class=\"token punctuation\">(<\/span>vis<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span>ll 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>r<span class=\"token punctuation\">;<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>mp<span class=\"token punctuation\">[<\/span>c<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>d<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">]<\/span><span class=\"token operator\">&#061;&#061;<\/span><span class=\"token char\">&#039;J&#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 function\">dfs1<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">if<\/span><span class=\"token punctuation\">(<\/span>sum<span class=\"token operator\">&gt;&#061;<\/span><span class=\"token number\">4<\/span> <span class=\"token operator\">&amp;&amp;<\/span> t<span class=\"token operator\">&#061;&#061;<\/span>r<span class=\"token punctuation\">)<\/span> ans<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\">if<\/span><span class=\"token punctuation\">(<\/span>x<span class=\"token operator\">&gt;<\/span><span class=\"token number\">25<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span>ll i<span class=\"token operator\">&#061;<\/span>x<span class=\"token punctuation\">;<\/span>i<span class=\"token operator\">&lt;&#061;<\/span><span class=\"token number\">25<\/span><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        c<span class=\"token punctuation\">[<\/span>y<span class=\"token punctuation\">]<\/span><span class=\"token operator\">&#061;<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token operator\">&#043;<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">)<\/span><span class=\"token operator\">\/<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        d<span class=\"token punctuation\">[<\/span>y<span class=\"token punctuation\">]<\/span><span class=\"token operator\">&#061;<\/span>i<span class=\"token operator\">&#8211;<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token operator\">&#043;<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">)<\/span><span class=\"token operator\">\/<\/span><span class=\"token number\">5<\/span><span class=\"token operator\">&#8211;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token operator\">*<\/span><span class=\"token number\">5<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token function\">dfs2<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token operator\">&#043;<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span>y<span class=\"token operator\">&#043;<\/span><span class=\"token number\">1<\/span><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\">int<\/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    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> 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><br \/>\n    <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span>ll 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><span class=\"token number\">5<\/span><span class=\"token punctuation\">;<\/span>i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token keyword\">for<\/span><span class=\"token punctuation\">(<\/span>ll 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><span class=\"token number\">5<\/span><span class=\"token punctuation\">;<\/span>j<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            cin<span class=\"token operator\">&gt;&gt;<\/span>mp<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 function\">dfs2<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    cout<span class=\"token operator\">&lt;&lt;<\/span>ans<span class=\"token operator\">&lt;&lt;<\/span>endl<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","protected":false},"excerpt":{"rendered":"<p>P1671 Rigging the Bovine Election S<br \/>\n\u7f51\u9875\u94fe\u63a5<br \/>\nP1671 Rigging the Bovine Election S<br \/>\n\u9898\u76ee\u63cf\u8ff0<br \/>\n\u519c\u573a\u88ab\u5212\u5206\u4e3a  5 \u00d7 5 5\\\\times 5 5\u00d75 \u7684\u683c\u5b50&#xff0c;\u6bcf\u4e2a\u683c\u5b50\u4e2d\u90fd\u6709\u4e00\u5934\u5976\u725b&#xff0c;\u5e76\u4e14\u53ea\u6709\u8377\u65af\u5766&#xff08;\u6807\u8bb0\u4e3a H&#xff09;\u548c\u6770\u897f&#xff08;\u6807\u8bb0\u4e3a 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