{"id":75817,"date":"2026-02-13T08:17:26","date_gmt":"2026-02-13T00:17:26","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/75817.html"},"modified":"2026-02-13T08:17:26","modified_gmt":"2026-02-13T00:17:26","slug":"uva-11665-chinese-ink","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/75817.html","title":{"rendered":"UVa 11665 Chinese Ink"},"content":{"rendered":"<h3>\u9898\u76ee\u63cf\u8ff0<\/h3>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Lucca\\\\texttt{Lucca}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">Lucca<\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u4e00\u4e2a\u56db\u5c81\u7684\u5c0f\u5973\u5b69&#xff0c;\u5979\u559c\u6b22\u5728\u7ed8\u56fe\u7eb8\u4e0a\u753b\u591a\u8fb9\u5f62\u3002\u6709\u4e00\u5929&#xff0c;\u5979\u753b\u4e86\u51e0\u4e2a\u591a\u8fb9\u5f62&#xff0c;\u5e76\u4e14\u7528\u9ed1\u8272\u7684\u4e2d\u56fd\u58a8\u6c34\u5c06\u5b83\u4eec\u5168\u90e8\u6d82\u6ee1\u3002\u6d82\u6ee1\u4e4b\u540e&#xff0c;\u5979\u60f3\u77e5\u9053\u56fe\u4e2d\u5230\u5e95\u6709\u591a\u5c11\u4e2a \u9ed1\u8272\u533a\u57df \u3002<br \/>\n\u4e00\u4e2a\u9ed1\u8272\u533a\u57df\u6307\u7684\u662f\u7eb8\u4e0a\u7684\u4e00\u7247\u9ed1\u8272\u70b9\u96c6&#xff0c;\u5176\u4e2d\u4efb\u610f\u4e24\u70b9\u90fd\u53ef\u4ee5\u5728\u8be5\u533a\u57df\u5185\u7528\u4e00\u6761\u8fde\u7eed\u7684\u9ed1\u8272\u8def\u5f84\u76f8\u8fde&#xff08;\u5373\u8fde\u901a\u5757&#xff09;\u3002<br \/>\n\u4f60\u7684\u4efb\u52a1\u5c31\u662f\u5199\u4e00\u4e2a\u7a0b\u5e8f&#xff0c;\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u82e5\u5e72\u4e2a\u7b80\u5355\u591a\u8fb9\u5f62&#xff08;\u8fb9\u754c\u4e0d\u81ea\u4ea4&#xff09;&#xff0c;\u5728\u5c06\u5b83\u4eec\u5168\u90e8\u6d82\u9ed1\u4e4b\u540e&#xff0c;\u7edf\u8ba1\u56fe\u4e2d\u9ed1\u8272\u8fde\u901a\u5757\u7684\u6570\u91cf\u3002<\/p>\n<p>\u8f93\u5165\u683c\u5f0f<br \/>\n\u8f93\u5165\u5305\u542b\u591a\u4e2a\u6d4b\u8bd5\u7528\u4f8b\u3002\u6bcf\u4e2a\u6d4b\u8bd5\u7528\u4f8b\u7684\u683c\u5f0f\u5982\u4e0b&#xff1a;<\/p>\n<ul>\n<li>\u7b2c\u4e00\u884c\u4e00\u4e2a\u6574\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">NN<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><\/span> &#xff08; <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">1\u2264N\u2264401 \\\\le N \\\\le 40<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7804em;vertical-align: -0.136em\"><\/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: 0.109em\">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: 0.6444em\"><\/span><span class=\"mord\">40<\/span><\/span><\/span><\/span><\/span> &#xff09;&#xff0c;\u8868\u793a\u591a\u8fb9\u5f62\u7684\u4e2a\u6570\u3002<\/li>\n<li>\u63a5\u4e0b\u6765 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">NN<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><\/span> \u884c&#xff0c;\u6bcf\u884c\u63cf\u8ff0\u4e00\u4e2a\u591a\u8fb9\u5f62\u3002\u6bcf\u884c\u5305\u542b <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">2\u22c5t2 \\\\cdot t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u22c5<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6151em\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/span> \u4e2a\u6574\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">x1y1x2y2\u2026xtytx_1 y_1 x_2 y_2 \\\\ldots x_t y_t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/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=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/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=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;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 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=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;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 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: 0.1667em\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/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=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2806em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/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><\/span><\/span><\/span> &#xff0c;\u8868\u793a\u591a\u8fb9\u5f62\u8fb9\u754c\u4e0a\u7684\u9876\u70b9\u5750\u6807&#xff08; <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\u2212104\u2264xi,yi\u2264104-10^4 \\\\le x_i, y_i \\\\le 10^4<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9501em;vertical-align: -0.136em\"><\/span><span class=\"mord\">\u2212<\/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\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/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\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/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=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">y<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3117em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.0359em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/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\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/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\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> &#xff0c; <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">3\u2264t\u2264103 \\\\le t \\\\le 10<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7804em;vertical-align: -0.136em\"><\/span><span class=\"mord\">3<\/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\">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: 0.6444em\"><\/span><span class=\"mord\">10<\/span><\/span><\/span><\/span><\/span> &#xff09;\u3002\u591a\u8fb9\u5f62\u7531\u8fd9\u4e9b\u9876\u70b9\u6309\u987a\u5e8f\u8fde\u63a5\u800c\u6210&#xff0c;\u6700\u540e\u4e00\u6761\u8fb9\u8fde\u63a5\u7b2c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">tt<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6151em\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/span> \u4e2a\u9876\u70b9\u548c\u7b2c\u4e00\u4e2a\u9876\u70b9\u3002\u9898\u76ee\u4fdd\u8bc1\u591a\u8fb9\u5f62\u662f\u7b80\u5355\u591a\u8fb9\u5f62&#xff08;\u8fb9\u754c\u4e0d\u81ea\u4ea4&#xff09;\u3002<\/li>\n<li>\u8f93\u5165\u4ee5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">N&#061;0N &#061; 0<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">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\">0<\/span><\/span><\/span><\/span><\/span> \u7ed3\u675f\u3002<\/li>\n<\/ul>\n<p>\u8f93\u51fa\u683c\u5f0f<br \/>\n\u5bf9\u4e8e\u6bcf\u4e2a\u6d4b\u8bd5\u7528\u4f8b&#xff0c;\u8f93\u51fa\u4e00\u884c&#xff0c;\u8868\u793a\u5c06\u6240\u6709\u591a\u8fb9\u5f62\u6d82\u9ed1\u540e\u56fe\u4e2d\u9ed1\u8272\u533a\u57df\u7684\u4e2a\u6570\u3002<\/p>\n<p>\u6837\u4f8b\u8f93\u5165<\/p>\n<p>5<br \/>\n35 29 179 111 19 145 183 22 305 22 305 80 183 80<br \/>\n232 49 361 49 361 178 232 178<br \/>\n137 94 188 156 112 164 79 144<br \/>\n129 143 129 193 79 193<br \/>\n2<br \/>\n20 20 30 20 30 30 20 30<br \/>\n40 40 40 50 50 50 50 40<br \/>\n2<br \/>\n20 20 30 20 30 30 20 30<br \/>\n30 30 40 30 40 40 30 40<br \/>\n3<br \/>\n20 20 40 20 40 40 20 40<br \/>\n50 30 60 20 70 50<br \/>\n60 40 50 30 30 50<br \/>\n0<\/p>\n<p>\u6837\u4f8b\u8f93\u51fa<\/p>\n<p>2<br \/>\n2<br \/>\n1<br \/>\n1<\/p>\n<hr \/>\n<h3>\u9898\u76ee\u5206\u6790<\/h3>\n<h4>\u95ee\u9898\u672c\u8d28<\/h4>\n<p>\u6211\u4eec\u9700\u8981\u7edf\u8ba1\u591a\u4e2a\u591a\u8fb9\u5f62\u5728\u5e73\u9762\u4e0a\u88ab\u6d82\u9ed1\u540e&#xff0c;\u6240\u6709\u9ed1\u8272\u533a\u57df\u5f62\u6210\u7684 \u8fde\u901a\u5757 \u6570\u91cf\u3002<br \/>\n\u5173\u952e\u70b9\u5728\u4e8e&#xff1a;<\/p>\n<li>\u6bcf\u4e2a\u591a\u8fb9\u5f62\u672c\u8eab\u662f \u7b80\u5355\u591a\u8fb9\u5f62 &#xff0c;\u4e0d\u4f1a\u81ea\u4ea4\u3002<\/li>\n<li>\u4f46\u4e0d\u540c\u7684\u591a\u8fb9\u5f62\u4e4b\u95f4\u53ef\u80fd\u5b58\u5728 \u76f8\u4ea4 \u3001 \u5305\u542b \u6216 \u76f8\u79bb \u7684\u5173\u7cfb\u3002<\/li>\n<li>\u5982\u679c\u4e24\u4e2a\u591a\u8fb9\u5f62\u6709\u76f8\u4ea4\u7684\u90e8\u5206&#xff08;\u5305\u62ec\u8fb9\u76f8\u4ea4\u3001\u9876\u70b9\u91cd\u5408&#xff0c;\u6216\u8005\u4e00\u4e2a\u591a\u8fb9\u5f62\u5b8c\u5168\u5305\u542b\u5728\u53e6\u4e00\u4e2a\u591a\u8fb9\u5f62\u5185\u90e8&#xff09;&#xff0c;\u90a3\u4e48\u5b83\u4eec\u6d82\u9ed1\u540e\u4f1a\u5c5e\u4e8e\u540c\u4e00\u4e2a\u8fde\u901a\u5757\u3002<\/li>\n<li>\u56e0\u6b64&#xff0c;\u95ee\u9898\u8f6c\u5316\u4e3a&#xff1a;\u7ed9\u5b9a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">NN<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/span><\/span><\/span><\/span><\/span> \u4e2a\u591a\u8fb9\u5f62&#xff0c;\u5224\u65ad\u5b83\u4eec\u4e4b\u95f4\u7684\u8fde\u901a\u5173\u7cfb&#xff0c;\u7136\u540e\u7edf\u8ba1\u8fde\u901a\u5206\u91cf\u6570\u3002<\/li>\n<h4>\u6838\u5fc3\u96be\u70b9<\/h4>\n<p>\u5982\u4f55\u5224\u65ad\u4e24\u4e2a\u591a\u8fb9\u5f62\u662f\u5426\u8fde\u901a&#xff1f;<br \/>\n\u8fde\u901a\u7684\u5b9a\u4e49\u662f&#xff1a;\u4e24\u4e2a\u591a\u8fb9\u5f62\u5728\u5e73\u9762\u4e0a\u6709\u516c\u5171\u7684\u9ed1\u8272\u533a\u57df\u3002\u8fd9\u53d1\u751f\u5728\u4ee5\u4e0b\u4e24\u79cd\u60c5\u51b5&#xff1a;<\/p>\n<li>\u8fb9\u754c\u76f8\u4ea4 &#xff1a;\u4e24\u4e2a\u591a\u8fb9\u5f62\u7684\u8fb9\u754c\u6709\u4ea4\u70b9&#xff08;\u5305\u62ec\u8fb9\u4e0e\u8fb9\u76f8\u4ea4\u3001\u9876\u70b9\u843d\u5728\u53e6\u4e00\u6761\u8fb9\u4e0a\u3001\u9876\u70b9\u91cd\u5408&#xff09;\u3002<\/li>\n<li>\u5305\u542b\u5173\u7cfb &#xff1a;\u4e00\u4e2a\u591a\u8fb9\u5f62\u5b8c\u5168\u4f4d\u4e8e\u53e6\u4e00\u4e2a\u591a\u8fb9\u5f62\u7684\u5185\u90e8&#xff08;\u5305\u62ec\u8fb9\u754c\u91cd\u5408\u7684\u60c5\u51b5&#xff09;\u3002<\/li>\n<p>\u56e0\u6b64&#xff0c;\u6211\u4eec\u9700\u8981\u5b9e\u73b0\u4e24\u4e2a\u51e0\u4f55\u5224\u65ad&#xff1a;<\/p>\n<ul>\n<li>\u7ebf\u6bb5\u76f8\u4ea4\u5224\u65ad&#xff08;\u5305\u62ec\u7aef\u70b9&#xff09;\u3002<\/li>\n<li>\u70b9\u5728\u591a\u8fb9\u5f62\u5185\u90e8\u5224\u65ad&#xff08;\u5c04\u7ebf\u6cd5&#xff0c;\u5305\u62ec\u70b9\u5728\u8fb9\u754c\u4e0a\u7684\u60c5\u51b5&#xff09;\u3002<\/li>\n<\/ul>\n<h4>\u7b97\u6cd5\u601d\u8def<\/h4>\n<li>\u8bfb\u5165\u6570\u636e &#xff0c;\u5c06\u6bcf\u4e2a\u591a\u8fb9\u5f62\u5b58\u50a8\u4e3a\u70b9\u7684\u5e8f\u5217\u3002<\/li>\n<li>\u4e24\u4e24\u5224\u65ad\u591a\u8fb9\u5f62\u662f\u5426\u8fde\u901a &#xff1a;\n<ul>\n<li>\u68c0\u67e5\u4e24\u4e2a\u591a\u8fb9\u5f62\u7684\u4efb\u610f\u4e24\u6761\u8fb9\u662f\u5426\u76f8\u4ea4&#xff08;\u4f7f\u7528\u7ebf\u6bb5\u76f8\u4ea4\u5224\u65ad&#xff09;\u3002<\/li>\n<li>\u68c0\u67e5\u4e00\u4e2a\u591a\u8fb9\u5f62\u7684\u4efb\u610f\u4e00\u4e2a\u9876\u70b9\u662f\u5426\u5728\u53e6\u4e00\u4e2a\u591a\u8fb9\u5f62\u5185\u90e8&#xff08;\u4f7f\u7528\u5c04\u7ebf\u6cd5&#xff09;\u3002<br \/>\n\u53ea\u8981\u4e0a\u8ff0\u4efb\u4e00\u6761\u4ef6\u6ee1\u8db3&#xff0c;\u5c31\u8ba4\u4e3a\u8fd9\u4e24\u4e2a\u591a\u8fb9\u5f62\u8fde\u901a\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u4f7f\u7528\u5e76\u67e5\u96c6\u5408\u5e76\u8fde\u901a\u7684\u591a\u8fb9\u5f62 &#xff1a;\n<ul>\n<li>\u5c06\u6bcf\u4e2a\u591a\u8fb9\u5f62\u770b\u4f5c\u4e00\u4e2a\u8282\u70b9&#xff0c;\u5982\u679c\u4e24\u4e2a\u591a\u8fb9\u5f62\u8fde\u901a&#xff0c;\u5c31\u5c06\u5b83\u4eec\u5728\u5e76\u67e5\u96c6\u4e2d\u5408\u5e76\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\u7edf\u8ba1\u8fde\u901a\u5206\u91cf &#xff1a;\n<ul>\n<li>\u6700\u7ec8\u5e76\u67e5\u96c6\u4e2d\u4e0d\u540c\u7684\u96c6\u5408\u4e2a\u6570\u5c31\u662f\u9ed1\u8272\u533a\u57df\u7684\u4e2a\u6570\u3002<\/li>\n<\/ul>\n<\/li>\n<h4>\u590d\u6742\u5ea6\u5206\u6790<\/h4>\n<ul>\n<li>\u591a\u8fb9\u5f62\u6570\u91cf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">N\u226440N \\\\le 40<\/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: 0.109em\">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: 0.6444em\"><\/span><span class=\"mord\">40<\/span><\/span><\/span><\/span><\/span> &#xff0c;\u6bcf\u4e2a\u591a\u8fb9\u5f62\u7684\u9876\u70b9\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">t\u226410t \\\\le 10<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7719em;vertical-align: -0.136em\"><\/span><span class=\"mord mathnormal\">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: 0.6444em\"><\/span><span class=\"mord\">10<\/span><\/span><\/span><\/span><\/span> \u3002<\/li>\n<li>\u4e24\u4e24\u5224\u65ad\u8fde\u901a\u6027\u9700\u8981 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">O(N2)O(N^2)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">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=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u6b21\u5224\u65ad&#xff0c;\u6bcf\u6b21\u5224\u65ad\u9700\u8981\u68c0\u67e5\u6240\u6709\u8fb9\u5bf9\u548c\u9876\u70b9&#xff0c;\u6700\u574f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">O(t2)O(t^2)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">t<\/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=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> &#xff0c;\u56e0\u6b64\u603b\u590d\u6742\u5ea6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">O(N2t2)O(N^2 t^2)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.0641em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">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\"><span class=\"mord mathnormal\">t<\/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=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> &#xff0c;\u6700\u5927\u7ea6\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">402\u00d7102&#061;16000040^2 \\\\times 10^2 &#061; 160000<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8974em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">4<\/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\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/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\">2<\/span><\/span><\/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\">160000<\/span><\/span><\/span><\/span><\/span> &#xff0c;\u5b8c\u5168\u53ef\u884c\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u89e3\u9898\u601d\u8def\u8be6\u89e3<\/h3>\n<h4>1. \u51e0\u4f55\u57fa\u7840<\/h4>\n<h5>\u53c9\u79ef<\/h5>\n<p>\u7ed9\u5b9a\u4e09\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">P0,P1,P2P_0, P_1, P_2<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/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=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/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=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;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 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><\/span><\/span><\/span> &#xff0c;\u53c9\u79ef <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">cross(P0,P1,P2)&#061;(P1\u2212P0)\u00d7(P2\u2212P0)cross(P_0, P_1, P_2) &#061; (P_1 &#8211; P_0) \\\\times (P_2 &#8211; P_0)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">cross<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/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=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/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=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;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 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=\"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\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/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: 0.2222em\"><\/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\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/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=\"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=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;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 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: 0.2222em\"><\/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\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/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><\/span><\/span><\/span> &#xff0c;\u53ef\u7528\u4e8e\u5224\u65ad\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">P2P_2<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;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 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><\/span><\/span><\/span> \u5728\u5411\u91cf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">P0P1\u2192\\\\overrightarrow{P_0P_1}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.3553em;vertical-align: -0.15em\"><\/span><span class=\"mord accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2053em\"><span class=\"\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/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=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">P<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.1389em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/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><\/span><span class=\"svg-align\" style=\"top: -3.6833em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"height: 0.522em;min-width: 0.888em\"><\/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><\/span><\/span> \u7684\u5de6\u4fa7\u8fd8\u662f\u53f3\u4fa7&#xff0c;\u4ee5\u53ca\u5224\u65ad\u4e09\u70b9\u5171\u7ebf\u3002<\/p>\n<h5>\u7ebf\u6bb5\u76f8\u4ea4\u5224\u65ad<\/h5>\n<p>\u5224\u65ad\u7ebf\u6bb5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ABAB<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CDCD<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><\/span><\/span><\/span><\/span> \u662f\u5426\u76f8\u4ea4&#xff08;\u5305\u62ec\u7aef\u70b9\u76f8\u4ea4&#xff09;&#xff1a;<\/p>\n<li>\u5feb\u901f\u6392\u65a5\u5b9e\u9a8c&#xff1a;\u5982\u679c\u4e24\u4e2a\u7ebf\u6bb5\u6240\u5728\u77e9\u5f62\u4e0d\u76f8\u4ea4&#xff0c;\u5219\u4e0d\u76f8\u4ea4&#xff08;\u53ef\u7701\u7565&#xff0c;\u76f4\u63a5\u4f7f\u7528\u8de8\u7acb\u5b9e\u9a8c&#xff09;\u3002<\/li>\n<li>\u8de8\u7acb\u5b9e\u9a8c&#xff1a;\u5982\u679c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">cross(A,B,C)cross(A, B, C)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">cross<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">cross(A,B,D)cross(A, B, D)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">cross<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5f02\u53f7&#xff0c;\u4e14 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">cross(C,D,A)cross(C, D, A)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">cross<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">cross(C,D,B)cross(C, D, B)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">cross<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">D<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0502em\">B<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u5f02\u53f7&#xff0c;\u5219\u7ebf\u6bb5\u76f8\u4ea4\u3002<\/li>\n<li>\u7279\u6b8a\u60c5\u51b5&#xff1a;\u5982\u679c\u53c9\u79ef\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">00<\/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;\u8bf4\u660e\u70b9\u5728\u7ebf\u6bb5\u6240\u5728\u76f4\u7ebf\u4e0a&#xff0c;\u518d\u5224\u65ad\u70b9\u662f\u5426\u5728\u7ebf\u6bb5\u4e0a&#xff08;\u4f7f\u7528\u5750\u6807\u8303\u56f4\u5224\u65ad&#xff09;\u3002<\/li>\n<h5>\u70b9\u5728\u591a\u8fb9\u5f62\u5185\u90e8\u5224\u65ad&#xff08;\u5c04\u7ebf\u6cd5&#xff09;<\/h5>\n<p>\u4ece\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">PP<\/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> \u5411\u53f3\u4f5c\u6c34\u5e73\u5c04\u7ebf&#xff0c;\u7edf\u8ba1\u4e0e\u591a\u8fb9\u5f62\u8fb9\u76f8\u4ea4\u7684\u6b21\u6570&#xff1a;<\/p>\n<ul>\n<li>\u5982\u679c\u4ea4\u70b9\u6570\u4e3a\u5947\u6570&#xff0c;\u70b9\u5728\u5185\u90e8&#xff1b;<\/li>\n<li>\u5982\u679c\u4e3a\u5076\u6570&#xff0c;\u70b9\u5728\u5916\u90e8\u3002<\/li>\n<\/ul>\n<p>\u6ce8\u610f\u8fb9\u754c\u60c5\u51b5&#xff1a;\u5982\u679c\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">PP<\/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> \u5728\u591a\u8fb9\u5f62\u7684\u8fb9\u4e0a&#xff0c;\u76f4\u63a5\u8fd4\u56de\u5728\u5185\u90e8&#xff08;\u56e0\u4e3a\u6d82\u9ed1\u540e\u8fb9\u754c\u4e5f\u662f\u9ed1\u8272&#xff09;\u3002<\/p>\n<h4>2. \u5e76\u67e5\u96c6\u7684\u4f7f\u7528<\/h4>\n<p>\u5c06\u6240\u6709\u591a\u8fb9\u5f62\u7f16\u53f7 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">00<\/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> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">N\u22121N-1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.109em\">N<\/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\">1<\/span><\/span><\/span><\/span><\/span> &#xff0c;\u521d\u59cb\u5316\u6bcf\u4e2a\u591a\u8fb9\u5f62\u4e3a\u4e00\u4e2a\u96c6\u5408\u3002<br \/>\n\u6bcf\u5f53\u53d1\u73b0\u4e24\u4e2a\u591a\u8fb9\u5f62\u8fde\u901a&#xff0c;\u5c31\u5408\u5e76\u5b83\u4eec\u6240\u5728\u7684\u96c6\u5408\u3002<br \/>\n\u6700\u7ec8&#xff0c;\u96c6\u5408\u7684\u6570\u91cf\u5c31\u662f\u8fde\u901a\u5757\u7684\u6570\u91cf\u3002<\/p>\n<h4>3. \u8f93\u5165\u5904\u7406<\/h4>\n<p>\u6bcf\u4e2a\u591a\u8fb9\u5f62\u7684\u8f93\u5165\u662f\u4e00\u884c\u6574\u6570&#xff0c;\u4e2a\u6570\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">2t2t<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/span> &#xff0c;\u4f46 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">tt<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6151em\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/span> \u6ca1\u6709\u663e\u5f0f\u7ed9\u51fa&#xff0c;\u9700\u8981\u901a\u8fc7\u8bfb\u53d6\u6574\u6570\u7684\u4e2a\u6570\u6765\u5224\u65ad\u3002<br \/>\n\u53ef\u4ee5\u4f7f\u7528 while (cin &gt;&gt; val) \u8bfb\u53d6\u76f4\u5230\u6362\u884c\u3002<\/p>\n<hr \/>\n<h3>\u4ee3\u7801\u5b9e\u73b0<\/h3>\n<p><span class=\"token comment\">\/\/ Chinese Ink<\/span><br \/>\n<span class=\"token comment\">\/\/ UVa ID: 11665<\/span><br \/>\n<span class=\"token comment\">\/\/ Verdict: Accepted<\/span><br \/>\n<span class=\"token comment\">\/\/ Submission Date: 2026-01-14<\/span><br \/>\n<span class=\"token comment\">\/\/ UVa Run Time: 0.000s<\/span><br \/>\n<span class=\"token comment\">\/\/<\/span><br \/>\n<span class=\"token comment\">\/\/ \u7248\u6743\u6240\u6709&#xff08;C&#xff09;2026&#xff0c;\u90b1\u79cb\u3002metaphysis # yeah dot net<\/span><\/p>\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 keyword\">struct<\/span> <span class=\"token class-name\">Point<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> x<span class=\"token punctuation\">,<\/span> y<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token function\">Point<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> x <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> y <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">:<\/span> <span class=\"token function\">x<\/span><span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token function\">y<\/span><span class=\"token punctuation\">(<\/span>y<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token keyword\">typedef<\/span> vector<span class=\"token operator\">&lt;<\/span>Point<span class=\"token operator\">&gt;<\/span> Polygon<span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u8ba1\u7b97\u53c9\u79ef (p1-p0) \u00d7 (p2-p0)<\/span><br \/>\n<span class=\"token keyword\">int<\/span> <span class=\"token function\">cross<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">const<\/span> Point<span class=\"token operator\">&amp;<\/span> p0<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">const<\/span> Point<span class=\"token operator\">&amp;<\/span> p1<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">const<\/span> Point<span class=\"token operator\">&amp;<\/span> p2<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> <span class=\"token punctuation\">(<\/span>p1<span class=\"token punctuation\">.<\/span>x <span class=\"token operator\">&#8211;<\/span> p0<span class=\"token punctuation\">.<\/span>x<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> <span class=\"token punctuation\">(<\/span>p2<span class=\"token punctuation\">.<\/span>y <span class=\"token operator\">&#8211;<\/span> p0<span class=\"token punctuation\">.<\/span>y<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#8211;<\/span> <span class=\"token punctuation\">(<\/span>p2<span class=\"token punctuation\">.<\/span>x <span class=\"token operator\">&#8211;<\/span> p0<span class=\"token punctuation\">.<\/span>x<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> <span class=\"token punctuation\">(<\/span>p1<span class=\"token punctuation\">.<\/span>y <span class=\"token operator\">&#8211;<\/span> p0<span class=\"token punctuation\">.<\/span>y<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u5224\u65ad\u70b9\u662f\u5426\u5728\u7ebf\u6bb5\u4e0a&#xff08;\u5305\u62ec\u7aef\u70b9&#xff09;<\/span><br \/>\n<span class=\"token keyword\">bool<\/span> <span class=\"token function\">onSegment<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">const<\/span> Point<span class=\"token operator\">&amp;<\/span> p<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">const<\/span> Point<span class=\"token operator\">&amp;<\/span> a<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">const<\/span> Point<span class=\"token operator\">&amp;<\/span> b<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token function\">min<\/span><span class=\"token punctuation\">(<\/span>a<span class=\"token punctuation\">.<\/span>x<span class=\"token punctuation\">,<\/span> b<span class=\"token punctuation\">.<\/span>x<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&lt;&#061;<\/span> p<span class=\"token punctuation\">.<\/span>x <span class=\"token operator\">&amp;&amp;<\/span> p<span class=\"token punctuation\">.<\/span>x <span class=\"token operator\">&lt;&#061;<\/span> <span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>a<span class=\"token punctuation\">.<\/span>x<span class=\"token punctuation\">,<\/span> b<span class=\"token punctuation\">.<\/span>x<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&amp;&amp;<\/span><br \/>\n        <span class=\"token function\">min<\/span><span class=\"token punctuation\">(<\/span>a<span class=\"token punctuation\">.<\/span>y<span class=\"token punctuation\">,<\/span> b<span class=\"token punctuation\">.<\/span>y<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&lt;&#061;<\/span> p<span class=\"token punctuation\">.<\/span>y <span class=\"token operator\">&amp;&amp;<\/span> p<span class=\"token punctuation\">.<\/span>y <span class=\"token operator\">&lt;&#061;<\/span> <span class=\"token function\">max<\/span><span class=\"token punctuation\">(<\/span>a<span class=\"token punctuation\">.<\/span>y<span class=\"token punctuation\">,<\/span> b<span class=\"token punctuation\">.<\/span>y<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token function\">cross<\/span><span class=\"token punctuation\">(<\/span>p<span class=\"token punctuation\">,<\/span> a<span class=\"token punctuation\">,<\/span> b<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u5224\u65ad\u7ebf\u6bb5 a-b \u548c c-d \u662f\u5426\u76f8\u4ea4&#xff08;\u5305\u62ec\u7aef\u70b9&#xff09;<\/span><br \/>\n<span class=\"token keyword\">bool<\/span> <span class=\"token function\">segmentsIntersect<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">const<\/span> Point<span class=\"token operator\">&amp;<\/span> a<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">const<\/span> Point<span class=\"token operator\">&amp;<\/span> b<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">const<\/span> Point<span class=\"token operator\">&amp;<\/span> c<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">const<\/span> Point<span class=\"token operator\">&amp;<\/span> d<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> d1 <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">cross<\/span><span class=\"token punctuation\">(<\/span>a<span class=\"token punctuation\">,<\/span> b<span class=\"token punctuation\">,<\/span> c<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> d2 <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">cross<\/span><span class=\"token punctuation\">(<\/span>a<span class=\"token punctuation\">,<\/span> b<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> d3 <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">cross<\/span><span class=\"token punctuation\">(<\/span>c<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">,<\/span> a<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> d4 <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">cross<\/span><span class=\"token punctuation\">(<\/span>c<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">,<\/span> b<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>d1 <span class=\"token operator\">&gt;<\/span> <span class=\"token number\">0<\/span> <span class=\"token operator\">&amp;&amp;<\/span> d2 <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">||<\/span> <span class=\"token punctuation\">(<\/span>d1 <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">0<\/span> <span class=\"token operator\">&amp;&amp;<\/span> d2 <span class=\"token operator\">&gt;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&amp;&amp;<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>d3 <span class=\"token operator\">&gt;<\/span> <span class=\"token number\">0<\/span> <span class=\"token operator\">&amp;&amp;<\/span> d4 <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">||<\/span> <span class=\"token punctuation\">(<\/span>d3 <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">0<\/span> <span class=\"token operator\">&amp;&amp;<\/span> d4 <span class=\"token operator\">&gt;<\/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 keyword\">return<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>d1 <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span> <span class=\"token operator\">&amp;&amp;<\/span> <span class=\"token function\">onSegment<\/span><span class=\"token punctuation\">(<\/span>c<span class=\"token punctuation\">,<\/span> a<span class=\"token punctuation\">,<\/span> b<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>d2 <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span> <span class=\"token operator\">&amp;&amp;<\/span> <span class=\"token function\">onSegment<\/span><span class=\"token punctuation\">(<\/span>d<span class=\"token punctuation\">,<\/span> a<span class=\"token punctuation\">,<\/span> b<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>d3 <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span> <span class=\"token operator\">&amp;&amp;<\/span> <span class=\"token function\">onSegment<\/span><span class=\"token punctuation\">(<\/span>a<span class=\"token punctuation\">,<\/span> c<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>d4 <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token number\">0<\/span> <span class=\"token operator\">&amp;&amp;<\/span> <span class=\"token function\">onSegment<\/span><span class=\"token punctuation\">(<\/span>b<span class=\"token punctuation\">,<\/span> c<span class=\"token punctuation\">,<\/span> d<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u5c04\u7ebf\u6cd5\u5224\u65ad\u70b9\u662f\u5426\u5728\u591a\u8fb9\u5f62\u5185\u90e8&#xff08;\u5305\u62ec\u8fb9\u754c&#xff09;<\/span><br \/>\n<span class=\"token keyword\">bool<\/span> <span class=\"token function\">pointInPolygon<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">const<\/span> Point<span class=\"token operator\">&amp;<\/span> p<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">const<\/span> Polygon<span class=\"token operator\">&amp;<\/span> poly<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> n <span class=\"token operator\">&#061;<\/span> poly<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 keyword\">bool<\/span> inside <span class=\"token operator\">&#061;<\/span> <span class=\"token boolean\">false<\/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\">0<\/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> <span class=\"token punctuation\">{<\/span><br \/>\n        Point a <span class=\"token operator\">&#061;<\/span> poly<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> b <span class=\"token operator\">&#061;<\/span> poly<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">(<\/span>i <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">%<\/span> n<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token function\">onSegment<\/span><span class=\"token punctuation\">(<\/span>p<span class=\"token punctuation\">,<\/span> a<span class=\"token punctuation\">,<\/span> b<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u5728\u8fb9\u4e0a<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">(<\/span>a<span class=\"token punctuation\">.<\/span>y <span class=\"token operator\">&gt;<\/span> p<span class=\"token punctuation\">.<\/span>y<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">!&#061;<\/span> <span class=\"token punctuation\">(<\/span>b<span class=\"token punctuation\">.<\/span>y <span class=\"token operator\">&gt;<\/span> p<span class=\"token punctuation\">.<\/span>y<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">int<\/span> intersectX <span class=\"token operator\">&#061;<\/span> a<span class=\"token punctuation\">.<\/span>x <span class=\"token operator\">&#043;<\/span> <span class=\"token punctuation\">(<\/span>p<span class=\"token punctuation\">.<\/span>y <span class=\"token operator\">&#8211;<\/span> a<span class=\"token punctuation\">.<\/span>y<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> <span class=\"token punctuation\">(<\/span>b<span class=\"token punctuation\">.<\/span>x <span class=\"token operator\">&#8211;<\/span> a<span class=\"token punctuation\">.<\/span>x<span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token punctuation\">(<\/span>b<span class=\"token punctuation\">.<\/span>y <span class=\"token operator\">&#8211;<\/span> a<span class=\"token punctuation\">.<\/span>y<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>p<span class=\"token punctuation\">.<\/span>x <span class=\"token operator\">&lt;<\/span> intersectX<span class=\"token punctuation\">)<\/span> inside <span class=\"token operator\">&#061;<\/span> <span class=\"token operator\">!<\/span>inside<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\">return<\/span> inside<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u5224\u65ad\u4e24\u4e2a\u591a\u8fb9\u5f62\u662f\u5426\u76f8\u4ea4\u6216\u5305\u542b<\/span><br \/>\n<span class=\"token keyword\">bool<\/span> <span class=\"token function\">polygonsIntersect<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">const<\/span> Polygon<span class=\"token operator\">&amp;<\/span> a<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">const<\/span> Polygon<span class=\"token operator\">&amp;<\/span> b<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> na <span class=\"token operator\">&#061;<\/span> a<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> nb <span class=\"token operator\">&#061;<\/span> b<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 comment\">\/\/ \u8fb9\u76f8\u4ea4\u68c0\u6d4b<\/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\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> na<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><span class=\"token keyword\">int<\/span> j <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&lt;<\/span> nb<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><span class=\"token function\">segmentsIntersect<\/span><span class=\"token punctuation\">(<\/span>a<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> a<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">(<\/span>i <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">%<\/span> na<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> b<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> b<span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">(<\/span>j <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">%<\/span> nb<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token comment\">\/\/ \u5305\u542b\u68c0\u6d4b&#xff1a;a\u7684\u9876\u70b9\u5728b\u5185&#xff0c;\u6216b\u7684\u9876\u70b9\u5728a\u5185<\/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\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> na<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><span class=\"token function\">pointInPolygon<\/span><span class=\"token punctuation\">(<\/span>a<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> b<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token boolean\">true<\/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\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> nb<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><span class=\"token function\">pointInPolygon<\/span><span class=\"token punctuation\">(<\/span>b<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> a<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> <span class=\"token boolean\">true<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">return<\/span> <span class=\"token boolean\">false<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u5e76\u67e5\u96c6<\/span><br \/>\n<span class=\"token keyword\">class<\/span> <span class=\"token class-name\">UnionFind<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">public<\/span><span class=\"token operator\">:<\/span><br \/>\n    vector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> parent<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token function\">UnionFind<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> n<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        parent<span class=\"token punctuation\">.<\/span><span class=\"token function\">resize<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">)<\/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\">0<\/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> parent<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> i<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> <span class=\"token function\">find<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> x<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>parent<span class=\"token punctuation\">[<\/span>x<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">!&#061;<\/span> x<span class=\"token punctuation\">)<\/span> parent<span class=\"token punctuation\">[<\/span>x<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">find<\/span><span class=\"token punctuation\">(<\/span>parent<span class=\"token punctuation\">[<\/span>x<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> parent<span class=\"token punctuation\">[<\/span>x<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n    <span class=\"token keyword\">void<\/span> <span class=\"token function\">unite<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> x<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> y<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> rx <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">find<\/span><span class=\"token punctuation\">(<\/span>x<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">,<\/span> ry <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">find<\/span><span class=\"token punctuation\">(<\/span>y<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>rx <span class=\"token operator\">!&#061;<\/span> ry<span class=\"token punctuation\">)<\/span> parent<span class=\"token punctuation\">[<\/span>rx<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> ry<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> <span class=\"token function\">countComponents<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        unordered_set<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> comps<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\">0<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;<\/span> parent<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> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> comps<span class=\"token punctuation\">.<\/span><span class=\"token function\">insert<\/span><span class=\"token punctuation\">(<\/span><span class=\"token function\">find<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> comps<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 punctuation\">}<\/span><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> <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 boolean\">false<\/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 keyword\">nullptr<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> n<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token keyword\">while<\/span> <span class=\"token punctuation\">(<\/span>cin <span class=\"token operator\">&gt;&gt;<\/span> n <span class=\"token operator\">&amp;&amp;<\/span> n <span class=\"token operator\">!&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        vector<span class=\"token operator\">&lt;<\/span>Polygon<span class=\"token operator\">&gt;<\/span> <span class=\"token function\">polygons<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">)<\/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\">0<\/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> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">int<\/span> t<span class=\"token punctuation\">;<\/span> vector<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> coords<span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token keyword\">int<\/span> val<span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token keyword\">while<\/span> <span class=\"token punctuation\">(<\/span>cin <span class=\"token operator\">&gt;&gt;<\/span> val<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                coords<span class=\"token punctuation\">.<\/span><span class=\"token function\">push_back<\/span><span class=\"token punctuation\">(<\/span>val<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>cin<span class=\"token punctuation\">.<\/span><span class=\"token function\">peek<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token char\">&#039;\\\\n&#039;<\/span><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            t <span class=\"token operator\">&#061;<\/span> coords<span class=\"token punctuation\">.<\/span><span class=\"token function\">size<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">\/<\/span> <span class=\"token number\">2<\/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> j <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&lt;<\/span> t<span class=\"token punctuation\">;<\/span> j<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> polygons<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span><span class=\"token function\">push_back<\/span><span class=\"token punctuation\">(<\/span><span class=\"token function\">Point<\/span><span class=\"token punctuation\">(<\/span>coords<span class=\"token punctuation\">[<\/span><span class=\"token number\">2<\/span> <span class=\"token operator\">*<\/span> j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> coords<span class=\"token punctuation\">[<\/span><span class=\"token number\">2<\/span> <span class=\"token operator\">*<\/span> j <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 punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><br \/>\n        UnionFind <span class=\"token function\">uf<\/span><span class=\"token punctuation\">(<\/span>n<span class=\"token punctuation\">)<\/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\">0<\/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 keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> j <span class=\"token operator\">&#061;<\/span> i <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&lt;<\/span> n<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><span class=\"token function\">polygonsIntersect<\/span><span class=\"token punctuation\">(<\/span>polygons<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">,<\/span> polygons<span class=\"token punctuation\">[<\/span>j<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> uf<span class=\"token punctuation\">.<\/span><span class=\"token function\">unite<\/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        cout <span class=\"token operator\">&lt;&lt;<\/span> uf<span class=\"token punctuation\">.<\/span><span class=\"token function\">countComponents<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <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 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<hr \/>\n<h3>\u603b\u7ed3<\/h3>\n<p>\u672c\u9898\u662f\u4e00\u9053\u51e0\u4f55 &#043; \u5e76\u67e5\u96c6\u7684\u7efc\u5408\u9898&#xff0c;\u5173\u952e\u5728\u4e8e\u6b63\u786e\u5224\u65ad\u4e24\u4e2a\u591a\u8fb9\u5f62\u662f\u5426\u8fde\u901a&#xff08;\u76f8\u4ea4\u6216\u5305\u542b&#xff09;\u3002<br \/>\n\u5b9e\u73b0\u65f6\u9700\u8981\u6ce8\u610f\u51e0\u4f55\u5224\u65ad\u7684\u7ec6\u8282&#xff0c;\u5c24\u5176\u662f\u8fb9\u754c\u60c5\u51b5\u7684\u5904\u7406&#xff08;\u70b9\u5728\u8fb9\u4e0a\u3001\u7aef\u70b9\u76f8\u4ea4\u7b49&#xff09;\u3002<br \/>\n\u4f7f\u7528\u5e76\u67e5\u96c6\u53ef\u4ee5\u9ad8\u6548\u5730\u5408\u5e76\u8fde\u901a\u7684\u591a\u8fb9\u5f62&#xff0c;\u6700\u7ec8\u5f97\u5230\u8fde\u901a\u5757\u7684\u6570\u91cf\u3002<br \/>\n\u9898\u76ee\u8f93\u5165\u683c\u5f0f\u8f83\u4e3a\u7279\u6b8a&#xff0c;\u9700\u8981\u5c0f\u5fc3\u5904\u7406\u6bcf\u884c\u7684\u9876\u70b9\u5750\u6807\u8bfb\u53d6\u3002<\/p>\n<p>\u901a\u8fc7\u672c\u9898&#xff0c;\u53ef\u4ee5\u52a0\u6df1\u5bf9\u51e0\u4f55\u7b97\u6cd5\u548c\u5e76\u67e5\u96c6\u5e94\u7528\u7684\u7406\u89e3&#xff0c;\u540c\u65f6\u953b\u70bc\u5904\u7406\u590d\u6742\u8f93\u5165\u7684\u80fd\u529b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u9898\u76ee\u63cf\u8ff0<br \/>\nLucca\\\\texttt{Lucca}Lucca \u662f\u4e00\u4e2a\u56db\u5c81\u7684\u5c0f\u5973\u5b69&#xff0c;\u5979\u559c\u6b22\u5728\u7ed8\u56fe\u7eb8\u4e0a\u753b\u591a\u8fb9\u5f62\u3002\u6709\u4e00\u5929&#xff0c;\u5979\u753b\u4e86\u51e0\u4e2a\u591a\u8fb9\u5f62&#xff0c;\u5e76\u4e14\u7528\u9ed1\u8272\u7684\u4e2d\u56fd\u58a8\u6c34\u5c06\u5b83\u4eec\u5168\u90e8\u6d82\u6ee1\u3002\u6d82\u6ee1\u4e4b\u540e&#xff0c;\u5979\u60f3\u77e5\u9053\u56fe\u4e2d\u5230\u5e95\u6709\u591a\u5c11\u4e2a \u9ed1\u8272\u533a\u57df \u3002<br \/>\n\u4e00\u4e2a\u9ed1\u8272\u533a\u57df\u6307\u7684\u662f\u7eb8\u4e0a\u7684\u4e00\u7247\u9ed1\u8272\u70b9\u96c6&#xff0c;\u5176\u4e2d\u4efb\u610f\u4e24\u70b9\u90fd\u53ef\u4ee5\u5728\u8be5\u533a\u57df\u5185\u7528\u4e00\u6761\u8fde\u7eed\u7684\u9ed1\u8272\u8def\u5f84\u76f8\u8fde&#xff08;\u5373\u8fde\u901a\u5757&#xff09;\u3002<br \/>\n\u4f60\u7684\u4efb\u52a1\u5c31\u662f\u5199\u4e00\u4e2a\u7a0b\u5e8f&#xff0c;\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u82e5\u5e72\u4e2a\u7b80\u5355<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[55,427,4405],"topic":[],"class_list":["post-75817","post","type-post","status-publish","format-standard","hentry","category-server","tag-c","tag-427","tag-4405"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>UVa 11665 Chinese Ink - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/75817.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"UVa 11665 Chinese Ink - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u9898\u76ee\u63cf\u8ff0 Lucca\\texttt{Lucca}Lucca \u662f\u4e00\u4e2a\u56db\u5c81\u7684\u5c0f\u5973\u5b69&#xff0c;\u5979\u559c\u6b22\u5728\u7ed8\u56fe\u7eb8\u4e0a\u753b\u591a\u8fb9\u5f62\u3002\u6709\u4e00\u5929&#xff0c;\u5979\u753b\u4e86\u51e0\u4e2a\u591a\u8fb9\u5f62&#xff0c;\u5e76\u4e14\u7528\u9ed1\u8272\u7684\u4e2d\u56fd\u58a8\u6c34\u5c06\u5b83\u4eec\u5168\u90e8\u6d82\u6ee1\u3002\u6d82\u6ee1\u4e4b\u540e&#xff0c;\u5979\u60f3\u77e5\u9053\u56fe\u4e2d\u5230\u5e95\u6709\u591a\u5c11\u4e2a \u9ed1\u8272\u533a\u57df \u3002 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