{"id":63010,"date":"2026-01-21T08:05:48","date_gmt":"2026-01-21T00:05:48","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/63010.html"},"modified":"2026-01-21T08:05:48","modified_gmt":"2026-01-21T00:05:48","slug":"uva-11082-matrix-decompressing","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/63010.html","title":{"rendered":"UVa 11082 Matrix Decompressing"},"content":{"rendered":"<h3>\u9898\u76ee\u5927\u610f<\/h3>\n<p>\u7ed9\u5b9a\u4e00\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">R\u00d7CR \\\\times C<\/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: 0.0077em\">R<\/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: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span> \u7684\u6b63\u6574\u6570\u77e9\u9635&#xff0c;\u5df2\u77e5\u5b83\u7684 \u7d2f\u79ef\u884c\u548c \u4e0e \u7d2f\u79ef\u5217\u548c &#xff0c;\u8981\u6c42\u8fd8\u539f\u51fa\u539f\u77e9\u9635\u7684\u6240\u6709 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">R\u00d7CR \\\\times C<\/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: 0.0077em\">R<\/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: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span> \u4e2a\u5143\u7d20\u3002<\/p>\n<p>\u5177\u4f53\u6765\u8bf4&#xff1a;<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RowSum(i)&#061;\u2211j&#061;1CAijRowSum(i) &#061; \\\\sum_{j&#061;1}^{C} A_{ij}<\/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: 0.0077em\">R<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">wS<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">i<\/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: 1.417em;vertical-align: -0.4358em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9812em\"><span class=\"\" style=\"top: -2.4003em;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\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em;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 mathnormal mtight\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4358em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">A<\/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 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CumulativeRowSum(i)&#061;\u2211k&#061;1iRowSum(k)CumulativeRowSum(i) &#061; \\\\sum_{k&#061;1}^{i} RowSum(k)<\/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: 0.0715em\">C<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">wS<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">i<\/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: 1.2643em;vertical-align: -0.2997em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9646em\"><span class=\"\" style=\"top: -2.4003em;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\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em;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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">wS<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ColumnSum(i)&#061;\u2211j&#061;1RAjiColumnSum(i) &#061; \\\\sum_{j&#061;1}^{R} A_{ji}<\/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: 0.0715em\">C<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">mn<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">i<\/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: 1.417em;vertical-align: -0.4358em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9812em\"><span class=\"\" style=\"top: -2.4003em;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\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em;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 mathnormal mtight\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4358em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">A<\/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 mtight\"><span class=\"mord mathnormal mtight\">ji<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CumulativeColumnSum(i)&#061;\u2211k&#061;1iColumnSum(k)CumulativeColumnSum(i) &#061; \\\\sum_{k&#061;1}^{i} ColumnSum(k)<\/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: 0.0715em\">C<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">mn<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">i<\/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: 1.2643em;vertical-align: -0.2997em\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative;top: 0em\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9646em\"><span class=\"\" style=\"top: -2.4003em;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\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em;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 mathnormal mtight\">i<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2997em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">mn<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0315em\">k<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<p>\u9898\u76ee\u4fdd\u8bc1\u81f3\u5c11\u6709\u4e00\u4e2a\u89e3&#xff0c;\u5e76\u4e14\u89c4\u5b9a\u77e9\u9635\u4e2d\u6bcf\u4e2a\u5143\u7d20\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">11<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">2020<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">20<\/span><\/span><\/span><\/span><\/span> \u4e4b\u95f4\u7684\u6574\u6570\u3002<br \/>\n\u82e5\u6709\u591a\u7ec4\u89e3&#xff0c;\u8f93\u51fa\u4efb\u610f\u4e00\u7ec4\u5373\u53ef\u3002<\/p>\n<h3>\u8f93\u5165\u683c\u5f0f<\/h3>\n<p>\u7b2c\u4e00\u884c\u662f\u6d4b\u8bd5\u7528\u4f8b\u6570 <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: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span> \u3002<br \/>\n\u6bcf\u4e2a\u6d4b\u8bd5\u7528\u4f8b\u5305\u542b\u4e09\u884c&#xff1a;<\/p>\n<li>\u4e24\u4e2a\u6574\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RR<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/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><\/span><\/span><\/span><\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RR<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span> \u4e2a\u6574\u6570\u8868\u793a\u7d2f\u79ef\u884c\u548c<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/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><\/span><\/span><\/span> \u4e2a\u6574\u6570\u8868\u793a\u7d2f\u79ef\u5217\u548c<\/li>\n<h3>\u8f93\u51fa\u683c\u5f0f<\/h3>\n<p>\u5bf9\u6bcf\u4e2a\u6d4b\u8bd5\u7528\u4f8b&#xff0c;\u5148\u8f93\u51fa\u4e00\u884c Matrix x&#xff0c;\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">xx<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u662f\u6d4b\u8bd5\u7528\u4f8b\u7f16\u53f7&#xff08;\u4ece 1 \u5f00\u59cb&#xff09;\u3002<br \/>\n\u63a5\u4e0b\u6765\u8f93\u51fa <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RR<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span> \u884c&#xff0c;\u6bcf\u884c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/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><\/span><\/span><\/span> \u4e2a\u6574\u6570\u8868\u793a\u77e9\u9635\u5143\u7d20\u3002<\/p>\n<hr \/>\n<h3>\u89e3\u9898\u601d\u8def<\/h3>\n<h4>1. \u8f6c\u5316\u4e3a\u7f51\u7edc\u6d41\u6a21\u578b<\/h4>\n<p>\u6211\u4eec\u5df2\u77e5\u7684\u662f\u7d2f\u79ef\u548c&#xff0c;\u53ef\u4ee5\u5148\u5c06\u5176\u8f6c\u5316\u4e3a\u884c\u548c\u4e0e\u5217\u548c&#xff1a;<\/p>\n<p>\u8bbe&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">ri&#061;CumulativeRowSum(i)\u2212CumulativeRowSum(i\u22121)cj&#061;CumulativeColumnSum(j)\u2212CumulativeColumnSum(j\u22121)<br \/>\nr_i &#061; CumulativeRowSum(i) &#8211; CumulativeRowSum(i-1)<br \/>\n\\\\\\\\<br \/>\nc_j &#061; CumulativeColumnSum(j) &#8211; CumulativeColumnSum(j-1)<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/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: -0.0278em;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\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">wS<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">wS<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">i<\/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\">1<\/span><span class=\"mclose\">)<\/span><\/span><span class=\"mspace newline\"><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7167em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/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\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">mn<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">mn<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0572em\">j<\/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\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n\u5176\u4e2d <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CumulativeRowSum(0)&#061;0CumulativeRowSum(0) &#061; 0<\/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: 0.0715em\">C<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">wS<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0<\/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: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> &#xff0c; <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CumulativeColumnSum(0)&#061;0CumulativeColumnSum(0) &#061; 0<\/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: 0.0715em\">C<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0359em\">v<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0197em\">l<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">mn<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mord mathnormal\">u<\/span><span class=\"mord mathnormal\">m<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0<\/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: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> \u3002<\/p>\n<p>\u90a3\u4e48 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">rir_i<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/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: -0.0278em;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><\/span><\/span><\/span> \u5c31\u662f\u7b2c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ii<\/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> \u884c\u7684\u548c&#xff0c; <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">cjc_j<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7167em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/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\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5c31\u662f\u7b2c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">jj<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.854em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span> \u5217\u7684\u548c\u3002<\/p>\n<p>\u95ee\u9898\u8f6c\u5316\u4e3a&#xff1a;\u6784\u9020\u4e00\u4e2a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">R\u00d7CR \\\\times C<\/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: 0.0077em\">R<\/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: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span> \u7684\u6b63\u6574\u6570\u77e9\u9635&#xff0c;\u4f7f\u5f97\u7b2c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ii<\/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> \u884c\u7684\u548c\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">rir_i<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/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: -0.0278em;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><\/span><\/span><\/span> &#xff0c;\u7b2c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">jj<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.854em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span> \u5217\u7684\u548c\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">cjc_j<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7167em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/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\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> &#xff0c;\u4e14\u6bcf\u4e2a\u5143\u7d20\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">[1,20][1, 20]<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">20<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span> \u4e4b\u95f4\u3002<\/p>\n<h4>2. \u5efa\u7acb\u6d41\u91cf\u7f51\u7edc<\/h4>\n<p>\u8fd9\u662f\u4e00\u4e2a\u5178\u578b\u7684 \u4e8c\u5206\u56fe\u5339\u914d \u95ee\u9898&#xff0c;\u53ef\u4ee5\u7528 \u6700\u5927\u6d41 \u89e3\u51b3\u3002<\/p>\n<p>\u6784\u9020\u4e00\u4e2a\u7f51\u7edc&#xff1a;<\/p>\n<ul>\n<li>\u6e90\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SS<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><\/span><\/span><\/span><\/span> \u8fde\u63a5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RR<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span> \u4e2a\u884c\u7ed3\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RiR_i<\/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: 0.0077em\">R<\/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: -0.0077em;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><\/span><\/span><\/span> &#xff0c;\u5bb9\u91cf\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">rir_i<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/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: -0.0278em;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><\/span><\/span><\/span><\/li>\n<li>\u5217\u7ed3\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CjC_j<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/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: 0.3117em\"><span class=\"\" style=\"top: -2.55em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8fde\u63a5\u6c47\u70b9 <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: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span> &#xff0c;\u5bb9\u91cf\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">cjc_j<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7167em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/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\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u6bcf\u4e2a\u884c\u7ed3\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RiR_i<\/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: 0.0077em\">R<\/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: -0.0077em;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><\/span><\/span><\/span> \u8fde\u63a5\u6bcf\u4e2a\u5217\u7ed3\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CjC_j<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/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: 0.3117em\"><span class=\"\" style=\"top: -2.55em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> &#xff0c;\u5bb9\u91cf\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">1919<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">19<\/span><\/span><\/span><\/span><\/span>&#xff08;\u56e0\u4e3a\u5143\u7d20\u6700\u5927\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">2020<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">20<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6700\u5c0f\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">11<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u6240\u4ee5\u6d41\u91cf\u8303\u56f4\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">0\u00a0190~19<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><span class=\"mspace nobreak\">\u00a0<\/span><span class=\"mord\">19<\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5b9e\u9645\u503c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">&#061;&#061;<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.3669em\"><\/span><span class=\"mrel\">&#061;<\/span><\/span><\/span><\/span><\/span>\u6d41\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">&#043;1&#043;1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">&#043;<\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff09;<\/li>\n<\/ul>\n<p>\u8fd9\u6837&#xff0c;\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">SS<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RiR_i<\/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: 0.0077em\">R<\/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: -0.0077em;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><\/span><\/span><\/span> \u7684\u6d41\u91cf\u8868\u793a\u7b2c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ii<\/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> \u884c\u7684\u603b\u5206\u914d\u91cf&#xff0c;\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RiR_i<\/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: 0.0077em\">R<\/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: -0.0077em;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><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CjC_j<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/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: 0.3117em\"><span class=\"\" style=\"top: -2.55em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u6d41\u91cf\u8868\u793a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Aij\u22121A_{ij} &#8211; 1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">A<\/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 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><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: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> &#xff0c;\u4ece <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CjC_j<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/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: 0.3117em\"><span class=\"\" style=\"top: -2.55em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5230 <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: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span> \u7684\u6d41\u91cf\u8868\u793a\u7b2c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">jj<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.854em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><\/span> \u5217\u7684\u603b\u5206\u914d\u91cf\u3002<\/p>\n<h4>3. \u6d41\u91cf\u4e0e\u77e9\u9635\u5143\u7d20\u7684\u5173\u7cfb<\/h4>\n<p>\u8bbe <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">fijf_{ij}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/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: -0.1076em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u8fb9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Ri\u2192CjR_i \\\\to C_j<\/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: 0.0077em\">R<\/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: -0.0077em;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\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/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: 0.3117em\"><span class=\"\" style=\"top: -2.55em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u6d41\u91cf&#xff08; <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">0\u2264fij\u2264190 \\\\le f_{ij} \\\\le 19<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7804em;vertical-align: -0.136em\"><\/span><span class=\"mord\">0<\/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: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/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: -0.1076em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><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: 0.6444em\"><\/span><span class=\"mord\">19<\/span><\/span><\/span><\/span><\/span> &#xff09;&#xff0c;\u5219&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Aij&#061;fij&#043;1<br \/>\nA_{ij} &#061; f_{ij} &#043; 1<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">A<\/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 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><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: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/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: -0.1076em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u56e0\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">fij\u2208[0,19]f_{ij} \\\\in [0, 19]<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/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: -0.1076em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\">0<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">19<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span> &#xff0c;\u6240\u4ee5 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Aij\u2208[1,20]A_{ij} \\\\in [1, 20]<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">A<\/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 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2208<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">20<\/span><span class=\"mclose\">]<\/span><\/span><\/span><\/span><\/span> &#xff0c;\u6ee1\u8db3\u9898\u76ee\u8981\u6c42\u3002<\/p>\n<h4>4. \u6d41\u91cf\u7ea6\u675f<\/h4>\n<p>\u884c\u548c\u7ea6\u675f&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u2211j&#061;1C(fij&#043;1)&#061;ri\u21d2\u2211j&#061;1Cfij&#061;ri\u2212C<br \/>\n\\\\sum_{j&#061;1}^{C} (f_{ij} &#043; 1) &#061; r_i \\\\quad \\\\Rightarrow \\\\quad \\\\sum_{j&#061;1}^{C} f_{ij} &#061; r_i &#8211; C<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 3.2421em;vertical-align: -1.4138em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.8283em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.4138em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/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: -0.1076em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">1<\/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: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/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: -0.0278em;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: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u21d2<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.2421em;vertical-align: -1.4138em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.8283em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.4138em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/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: -0.1076em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><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: 0.7333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/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: -0.0278em;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: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5217\u548c\u7ea6\u675f&#xff1a;<br \/>\n<span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u2211i&#061;1R(fij&#043;1)&#061;cj\u21d2\u2211i&#061;1Rfij&#061;cj\u2212R<br \/>\n\\\\sum_{i&#061;1}^{R} (f_{ij} &#043; 1) &#061; c_j \\\\quad \\\\Rightarrow \\\\quad \\\\sum_{i&#061;1}^{R} f_{ij} &#061; c_j &#8211; R<br \/>\n<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 3.106em;vertical-align: -1.2777em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.8283em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2777em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/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: -0.1076em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord\">1<\/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: 0.7167em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/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\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u21d2<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 3.106em;vertical-align: -1.2777em\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.8283em\"><span class=\"\" style=\"top: -1.8723em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">i<\/span><span class=\"mrel mtight\">&#061;<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.05em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"\"><span class=\"mop op-symbol large-op\">\u2211<\/span><\/span><\/span><span class=\"\" style=\"top: -4.3em;margin-left: 0em\"><span class=\"pstrut\" style=\"height: 3.05em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.2777em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/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: -0.1076em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><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: 0.8694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/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\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><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: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u8fd9\u6837\u6211\u4eec\u5c31\u628a\u539f\u95ee\u9898\u8f6c\u5316\u4e3a\u4e00\u4e2a \u5e26\u4e0b\u754c&#xff08;\u6700\u5c0f\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>&#xff09;\u548c\u4e0a\u754c&#xff08;\u6700\u5927\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">1919<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">19<\/span><\/span><\/span><\/span><\/span>&#xff09;\u7684\u6d41\u5206\u914d\u95ee\u9898 &#xff0c;\u53ef\u4ee5\u7528 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Dinic\\\\texttt{Dinic}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">Dinic<\/span><\/span><\/span><\/span><\/span><\/span> \u7b97\u6cd5 \u6c42\u89e3\u6700\u5927\u6d41\u3002<\/p>\n<hr \/>\n<h3>\u7b97\u6cd5\u6b65\u9aa4<\/h3>\n<li>\u8bfb\u5165 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RR<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/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><\/span><\/span><\/span><\/li>\n<li>\u8ba1\u7b97 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">rir_i<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/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: -0.0278em;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><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">cjc_j<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7167em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/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\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u5efa\u56fe&#xff1a;\n<ul>\n<li>\u6e90\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">S&#061;0S&#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: 0.0576em\">S<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> &#xff0c;\u884c\u7ed3\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">1\u223cR1 \\\\sim R<\/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: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span> &#xff0c;\u5217\u7ed3\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">R&#043;1\u223cR&#043;CR&#043;1 \\\\sim R&#043;C<\/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: 0.0077em\">R<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 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: 0.7667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span> &#xff0c;\u6c47\u70b9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">T&#061;R&#043;C&#043;1T&#061;R&#043;C&#043;1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><span 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: 0.7667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">S\u2192RiS \\\\to R_i<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><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: 0.0077em\">R<\/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: -0.0077em;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><\/span><\/span><\/span> &#xff0c;\u5bb9\u91cf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">ri\u2212Cr_i &#8211; C<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">r<\/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: -0.0278em;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: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span><\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Cj\u2192TC_j \\\\to T<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/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: 0.3117em\"><span class=\"\" style=\"top: -2.55em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span> &#xff0c;\u5bb9\u91cf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">cj\u2212Rc_j &#8211; R<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">c<\/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\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><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: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span><\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Ri\u2192CjR_i \\\\to C_j<\/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: 0.0077em\">R<\/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: -0.0077em;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\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/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: 0.3117em\"><span class=\"\" style=\"top: -2.55em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> &#xff0c;\u5bb9\u91cf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">1919<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">19<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u4e3a\u4e86\u786e\u4fdd\u6d41\u91cf\u53ef\u884c&#xff0c;\u8fd8\u9700\u6dfb\u52a0\u8f85\u52a9\u8fb9 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">S\u2192CjS \\\\to C_j<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">S<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/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: 0.3117em\"><span class=\"\" style=\"top: -2.55em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5bb9\u91cf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">RR<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><\/span><\/span><\/span><\/span> &#xff0c; <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Ri\u2192TR_i \\\\to T<\/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: 0.0077em\">R<\/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: -0.0077em;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\">\u2192<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span> \u5bb9\u91cf <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">CC<\/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><\/span><\/span><\/span> &#xff08;\u8fd9\u662f\u5e38\u89c1\u7684\u6280\u5de7&#xff0c;\u7528\u4e8e\u5904\u7406\u6d41\u91cf\u4e0b\u754c&#xff09;<\/li>\n<\/ul>\n<\/li>\n<li>\u8dd1\u6700\u5927\u6d41<\/li>\n<li>\u6839\u636e\u6b8b\u4f59\u7f51\u7edc\u5f97\u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">fijf_{ij}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/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: -0.1076em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> &#xff0c;\u8ba1\u7b97 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Aij&#061;fij&#043;1A_{ij} &#061; f_{ij} &#043; 1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">A<\/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 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><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: 0.9805em;vertical-align: -0.2861em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right: 0.1076em\">f<\/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: -0.1076em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">ij<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u8f93\u51fa\u77e9\u9635<\/li>\n<hr \/>\n<h3>\u65f6\u95f4\u590d\u6742\u5ea6<\/h3>\n<p>\u9876\u70b9\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">V&#061;R&#043;C&#043;2\u226442V &#061; R &#043; C &#043; 2 \\\\le 42<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><span 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: 0.7667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7667em;vertical-align: -0.0833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7804em;vertical-align: -0.136em\"><\/span><span class=\"mord\">2<\/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\">42<\/span><\/span><\/span><\/span><\/span> &#xff0c;\u8fb9\u6570 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">E&#061;O(R\u00d7C)E &#061; O(R \\\\times C)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0077em\">R<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u3002<br \/>\n<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Dinic\\\\texttt{Dinic}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">Dinic<\/span><\/span><\/span><\/span><\/span><\/span> \u7b97\u6cd5\u5728\u4e8c\u5206\u56fe\u4e0a\u590d\u6742\u5ea6\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">O(VE)O(\\\\sqrt{V}E)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1767em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0278em\">O<\/span><span class=\"mopen\">(<\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.9267em\"><span class=\"svg-align\" style=\"top: -3em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em\"><span class=\"mord mathnormal\" style=\"margin-right: 0.2222em\">V<\/span><\/span><\/span><span class=\"\" style=\"top: -2.8867em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em;height: 1.08em\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.1133em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0576em\">E<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> &#xff0c;\u5b8c\u5168\u53ef\u884c\u3002<\/p>\n<hr \/>\n<h3>\u53c2\u8003\u4ee3\u7801<\/h3>\n<p><span class=\"token comment\">\/\/ Matrix Decompressing<\/span><br \/>\n<span class=\"token comment\">\/\/ UVa ID: 11082<\/span><br \/>\n<span class=\"token comment\">\/\/ Verdict: Accepted<\/span><br \/>\n<span class=\"token comment\">\/\/ Submission Date: 2023-05-31<\/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;2023&#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\">const<\/span> <span class=\"token keyword\">int<\/span> INF <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0x3f3f3f3f<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u5b9a\u4e49\u65e0\u7a77\u5927\u503c<\/span><\/p>\n<p><span class=\"token comment\">\/\/ \u7f51\u7edc\u6d41\u4e2d\u7684\u8fb9\u7ed3\u6784\u4f53<\/span><br \/>\n<span class=\"token keyword\">struct<\/span> <span class=\"token class-name\">arc<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> u<span class=\"token punctuation\">,<\/span> v<span class=\"token punctuation\">;<\/span>           <span class=\"token comment\">\/\/ \u8fb9\u7684\u8d77\u70b9\u548c\u7ec8\u70b9<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> capacity<span class=\"token punctuation\">;<\/span>       <span class=\"token comment\">\/\/ \u8fb9\u7684\u5bb9\u91cf<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> residual<span class=\"token punctuation\">;<\/span>       <span class=\"token comment\">\/\/ \u8fb9\u7684\u5269\u4f59\u5bb9\u91cf<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> next<span class=\"token punctuation\">;<\/span>           <span class=\"token comment\">\/\/ \u4e0b\u4e00\u6761\u8fb9\u7684\u7d22\u5f15&#xff08;\u90bb\u63a5\u8868&#xff09;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token comment\">\/\/ Dinic \u6700\u5927\u6d41\u7b97\u6cd5\u7c7b<\/span><br \/>\n<span class=\"token keyword\">class<\/span> <span class=\"token class-name\">Dinic<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n<span class=\"token keyword\">private<\/span><span class=\"token operator\">:<\/span><br \/>\n    arc <span class=\"token operator\">*<\/span>arcs<span class=\"token punctuation\">;<\/span>          <span class=\"token comment\">\/\/ \u5b58\u50a8\u6240\u6709\u8fb9\u7684\u6570\u7ec4<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> vertices<span class=\"token punctuation\">;<\/span>       <span class=\"token comment\">\/\/ \u9876\u70b9\u603b\u6570<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> source<span class=\"token punctuation\">,<\/span> sink<span class=\"token punctuation\">;<\/span>   <span class=\"token comment\">\/\/ \u6e90\u70b9\u548c\u6c47\u70b9<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> idx<span class=\"token punctuation\">;<\/span>            <span class=\"token comment\">\/\/ \u5f53\u524d\u8fb9\u7684\u7d22\u5f15<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> <span class=\"token operator\">*<\/span>head<span class=\"token punctuation\">;<\/span>          <span class=\"token comment\">\/\/ \u6bcf\u4e2a\u9876\u70b9\u7684\u7b2c\u4e00\u6761\u8fb9\u7d22\u5f15&#xff08;\u90bb\u63a5\u8868\u5934&#xff09;<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> <span class=\"token operator\">*<\/span>dist<span class=\"token punctuation\">;<\/span>          <span class=\"token comment\">\/\/ BFS \u4e2d\u7684\u8ddd\u79bb\u6570\u7ec4<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> <span class=\"token operator\">*<\/span>current<span class=\"token punctuation\">;<\/span>       <span class=\"token comment\">\/\/ \u5f53\u524d\u5f27\u4f18\u5316\u6570\u7ec4<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ BFS \u5206\u5c42&#xff1a;\u6784\u5efa\u5c42\u6b21\u7f51\u7edc<\/span><br \/>\n    <span class=\"token keyword\">bool<\/span> <span class=\"token function\">bfs<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token function\">memset<\/span><span class=\"token punctuation\">(<\/span>dist<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 keyword\">sizeof<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> vertices<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u521d\u59cb\u5316\u6240\u6709\u8ddd\u79bb\u4e3a -1<\/span><br \/>\n        queue<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">int<\/span><span class=\"token operator\">&gt;<\/span> q<span class=\"token punctuation\">;<\/span><br \/>\n        q<span class=\"token punctuation\">.<\/span><span class=\"token function\">push<\/span><span class=\"token punctuation\">(<\/span>source<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        dist<span class=\"token punctuation\">[<\/span>source<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u6e90\u70b9\u8ddd\u79bb\u8bbe\u4e3a 1&#xff08;\u6216 0&#xff0c;\u8fd9\u91cc\u8bbe\u4e3a 1 \u907f\u514d\u4e0e -1 \u6df7\u6dc6&#xff09;<\/span><\/p>\n<p>        <span class=\"token keyword\">while<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>q<span class=\"token punctuation\">.<\/span><span class=\"token function\">empty<\/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 keyword\">int<\/span> u <span class=\"token operator\">&#061;<\/span> q<span class=\"token punctuation\">.<\/span><span class=\"token function\">front<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> q<span class=\"token punctuation\">.<\/span><span class=\"token function\">pop<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>u <span class=\"token operator\">&#061;&#061;<\/span> sink<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">break<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u5230\u8fbe\u6c47\u70b9<\/span><\/p>\n<p>            <span class=\"token comment\">\/\/ \u904d\u5386 u \u7684\u6240\u6709\u51fa\u8fb9<\/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> head<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token operator\">~<\/span>i<span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&#061;<\/span> arcs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>next<span class=\"token punctuation\">)<\/span><br \/>\n                <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>arcs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>residual <span class=\"token operator\">&gt;<\/span> <span class=\"token number\">0<\/span> <span class=\"token operator\">&amp;&amp;<\/span> dist<span class=\"token punctuation\">[<\/span>arcs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>v<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&lt;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                    <span class=\"token comment\">\/\/ \u5982\u679c\u8fd8\u6709\u5269\u4f59\u5bb9\u91cf\u4e14\u76ee\u6807\u9876\u70b9\u672a\u8bbf\u95ee<\/span><br \/>\n                    dist<span class=\"token punctuation\">[<\/span>arcs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>v<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> dist<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                    q<span class=\"token punctuation\">.<\/span><span class=\"token function\">push<\/span><span class=\"token punctuation\">(<\/span>arcs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>v<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> dist<span class=\"token punctuation\">[<\/span>sink<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&gt;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u8fd4\u56de\u662f\u5426\u80fd\u5230\u8fbe\u6c47\u70b9<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ DFS \u5bfb\u627e\u589e\u5e7f\u8def<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> <span class=\"token function\">dfs<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> u<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> flow<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>u <span class=\"token operator\">&#061;&#061;<\/span> sink<span class=\"token punctuation\">)<\/span> <span class=\"token keyword\">return<\/span> flow<span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u5230\u8fbe\u6c47\u70b9&#xff0c;\u8fd4\u56de\u6d41\u91cf<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u5f53\u524d\u5f27\u4f18\u5316&#xff1a;\u4ece\u4e0a\u6b21\u68c0\u67e5\u5230\u7684\u8fb9\u7ee7\u7eed<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> <span class=\"token operator\">&amp;<\/span>i <span class=\"token operator\">&#061;<\/span> current<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token operator\">~<\/span>i<span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&#061;<\/span> arcs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>next<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n            <span class=\"token keyword\">int<\/span> v <span class=\"token operator\">&#061;<\/span> arcs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>v<span class=\"token punctuation\">,<\/span> r <span class=\"token operator\">&#061;<\/span> arcs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>residual<span class=\"token punctuation\">;<\/span><\/p>\n<p>            <span class=\"token comment\">\/\/ \u786e\u4fdd\u6309\u5c42\u6b21\u7f51\u7edc\u524d\u8fdb\u4e14\u8fd8\u6709\u5269\u4f59\u5bb9\u91cf<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>dist<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;&#061;<\/span> <span class=\"token punctuation\">(<\/span>dist<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&amp;&amp;<\/span> r <span class=\"token operator\">&gt;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                <span class=\"token keyword\">int<\/span> volume <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">dfs<\/span><span class=\"token punctuation\">(<\/span>v<span class=\"token punctuation\">,<\/span> <span class=\"token function\">min<\/span><span class=\"token punctuation\">(<\/span>r<span class=\"token punctuation\">,<\/span> flow<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u9012\u5f52\u5bfb\u627e\u589e\u5e7f\u8def<\/span><br \/>\n                <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>volume <span class=\"token operator\">&gt;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                    <span class=\"token comment\">\/\/ \u66f4\u65b0\u8fb9\u7684\u5269\u4f59\u5bb9\u91cf<\/span><br \/>\n                    arcs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>residual <span class=\"token operator\">-&#061;<\/span> volume<span class=\"token punctuation\">;<\/span><br \/>\n                    arcs<span class=\"token punctuation\">[<\/span>i <span class=\"token operator\">^<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>residual <span class=\"token operator\">&#043;&#061;<\/span> volume<span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u53cd\u5411\u8fb9\u589e\u52a0\u5bb9\u91cf<\/span><br \/>\n                    <span class=\"token keyword\">return<\/span> volume<span class=\"token punctuation\">;<\/span><br \/>\n                <span class=\"token punctuation\">}<\/span><br \/>\n            <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><br \/>\n        <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u6ca1\u6709\u627e\u5230\u589e\u5e7f\u8def<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token keyword\">public<\/span><span class=\"token operator\">:<\/span><br \/>\n    <span class=\"token comment\">\/\/ \u6784\u9020\u51fd\u6570&#xff1a;\u521d\u59cb\u5316\u56fe<\/span><br \/>\n    <span class=\"token function\">Dinic<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> v<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> e<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> s<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> t<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        arcs <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> arc<span class=\"token punctuation\">[<\/span>e<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u5206\u914d\u8fb9\u6570\u7ec4\u7a7a\u95f4<\/span><br \/>\n        vertices <span class=\"token operator\">&#061;<\/span> v<span class=\"token punctuation\">;<\/span><br \/>\n        source <span class=\"token operator\">&#061;<\/span> s<span class=\"token punctuation\">,<\/span> sink <span class=\"token operator\">&#061;<\/span> t<span class=\"token punctuation\">;<\/span><br \/>\n        idx <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        head <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        dist <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        current <span class=\"token operator\">&#061;<\/span> <span class=\"token keyword\">new<\/span> <span class=\"token keyword\">int<\/span><span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token function\">memset<\/span><span class=\"token punctuation\">(<\/span>head<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 keyword\">sizeof<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">*<\/span> v<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u521d\u59cb\u5316\u90bb\u63a5\u8868\u5934\u4e3a -1<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u6790\u6784\u51fd\u6570&#xff1a;\u91ca\u653e\u5185\u5b58<\/span><br \/>\n    <span class=\"token operator\">~<\/span><span class=\"token function\">Dinic<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">delete<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> arcs<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">delete<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> head<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">delete<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> dist<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token keyword\">delete<\/span> <span class=\"token punctuation\">[<\/span><span class=\"token punctuation\">]<\/span> current<span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u6dfb\u52a0\u4e00\u6761\u6709\u5411\u8fb9\u53ca\u5176\u53cd\u5411\u8fb9<\/span><br \/>\n    <span class=\"token keyword\">void<\/span> <span class=\"token function\">addArc<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> u<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> v<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> capacity<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u6b63\u5411\u8fb9&#xff1a;u -&gt; v<\/span><br \/>\n        arcs<span class=\"token punctuation\">[<\/span>idx<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span>arc<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span>u<span class=\"token punctuation\">,<\/span> v<span class=\"token punctuation\">,<\/span> capacity<span class=\"token punctuation\">,<\/span> capacity<span class=\"token punctuation\">,<\/span> head<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        head<span class=\"token punctuation\">[<\/span>u<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> idx<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u53cd\u5411\u8fb9&#xff1a;v -&gt; u&#xff0c;\u521d\u59cb\u5bb9\u91cf\u4e3a 0<\/span><br \/>\n        arcs<span class=\"token punctuation\">[<\/span>idx<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token punctuation\">(<\/span>arc<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">{<\/span>v<span class=\"token punctuation\">,<\/span> u<span class=\"token punctuation\">,<\/span> capacity<span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> head<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">}<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        head<span class=\"token punctuation\">[<\/span>v<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> idx<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token comment\">\/\/ \u8ba1\u7b97\u6700\u5927\u6d41\u5e76\u8f93\u51fa\u77e9\u9635<\/span><br \/>\n    <span class=\"token keyword\">int<\/span> <span class=\"token function\">maxFlow<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> r<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">int<\/span> c<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> flow <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ Dinic \u4e3b\u5faa\u73af<\/span><br \/>\n        <span class=\"token keyword\">while<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token function\">bfs<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span> <span class=\"token comment\">\/\/ \u6784\u5efa\u5c42\u6b21\u7f51\u7edc<\/span><br \/>\n            <span class=\"token comment\">\/\/ \u5f53\u524d\u5f27\u4f18\u5316&#xff1a;\u91cd\u7f6e\u5f53\u524d\u5f27\u6570\u7ec4<\/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> vertices<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n                current<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span> head<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>            <span class=\"token comment\">\/\/ \u591a\u6b21 DFS \u5bfb\u627e\u589e\u5e7f\u8def<\/span><br \/>\n            <span class=\"token keyword\">while<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> delta <span class=\"token operator\">&#061;<\/span> <span class=\"token function\">dfs<\/span><span class=\"token punctuation\">(<\/span>source<span class=\"token punctuation\">,<\/span> INF<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n                flow <span class=\"token operator\">&#043;&#061;<\/span> delta<span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u4ece\u6b8b\u4f59\u7f51\u7edc\u4e2d\u63d0\u53d6\u77e9\u9635\u5143\u7d20<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> matrix<span class=\"token punctuation\">[<\/span><span class=\"token number\">32<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span><span class=\"token number\">32<\/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 punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u5b58\u50a8\u7ed3\u679c\u77e9\u9635<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u904d\u5386\u6240\u6709\u8fb9&#xff0c;\u627e\u5230\u8fde\u63a5\u884c\u7ed3\u70b9\u548c\u5217\u7ed3\u70b9\u7684\u8fb9<\/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> idx<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 comment\">\/\/ \u5982\u679c\u8fd9\u6761\u8fb9\u662f\u4ece\u884c\u7ed3\u70b9\u5230\u5217\u7ed3\u70b9<\/span><br \/>\n            <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span> <span class=\"token operator\">&lt;&#061;<\/span> arcs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>u <span class=\"token operator\">&amp;&amp;<\/span> arcs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>u <span class=\"token operator\">&lt;&#061;<\/span> r <span class=\"token operator\">&amp;&amp;<\/span><br \/>\n                r <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span> <span class=\"token operator\">&lt;&#061;<\/span> arcs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>v <span class=\"token operator\">&amp;&amp;<\/span> arcs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>v <span class=\"token operator\">&lt;&#061;<\/span> r <span class=\"token operator\">&#043;<\/span> c<span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                <span class=\"token comment\">\/\/ \u5b9e\u9645\u6d41\u91cf &#061; \u539f\u59cb\u5bb9\u91cf &#8211; \u5269\u4f59\u5bb9\u91cf<\/span><br \/>\n                <span class=\"token comment\">\/\/ \u77e9\u9635\u5143\u7d20 &#061; \u6d41\u91cf &#043; 1&#xff08;\u56e0\u4e3a\u6d41\u91cf\u8868\u793a A[i][j] &#8211; 1&#xff09;<\/span><br \/>\n                matrix<span class=\"token punctuation\">[<\/span>arcs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>u <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">[<\/span>arcs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>v <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span> <span class=\"token operator\">&#8211;<\/span> r<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#061;<\/span><br \/>\n                    arcs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>capacity <span class=\"token operator\">&#8211;<\/span> arcs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">.<\/span>residual <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        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8f93\u51fa\u77e9\u9635<\/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> r<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\">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> c<span class=\"token punctuation\">;<\/span> j<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token punctuation\">{<\/span><br \/>\n                <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>j<span class=\"token punctuation\">)<\/span> cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token char\">&#039; &#039;<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u5143\u7d20\u95f4\u7528\u7a7a\u683c\u5206\u9694<\/span><br \/>\n                cout <span class=\"token operator\">&lt;&lt;<\/span> matrix<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 punctuation\">}<\/span><br \/>\n            cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token char\">&#039;\\\\n&#039;<\/span><span class=\"token punctuation\">;<\/span><br \/>\n        <span class=\"token punctuation\">}<\/span><\/p>\n<p>        <span class=\"token keyword\">return<\/span> flow<span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u8fd4\u56de\u6700\u5927\u6d41\u503c&#xff08;\u672c\u9898\u4e2d\u4e0d\u9700\u8981&#xff09;<\/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 comment\">\/\/ \u5168\u5c40\u6570\u7ec4&#xff1a;\u5b58\u50a8\u7d2f\u79ef\u884c\u548c\u4e0e\u7d2f\u79ef\u5217\u548c<\/span><br \/>\n<span class=\"token keyword\">int<\/span> crs<span class=\"token punctuation\">[<\/span><span class=\"token number\">32<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ Cumulative Row Sums<\/span><br \/>\n<span class=\"token keyword\">int<\/span> ccs<span class=\"token punctuation\">[<\/span><span class=\"token number\">32<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ Cumulative Column Sums<\/span><\/p>\n<p><span class=\"token keyword\">int<\/span> <span class=\"token function\">main<\/span><span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> argc<span class=\"token punctuation\">,<\/span> <span class=\"token keyword\">char<\/span> <span class=\"token operator\">*<\/span>argv<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 comment\">\/\/ \u52a0\u901f\u8f93\u5165\u8f93\u51fa<\/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> 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><\/p>\n<p>    <span class=\"token keyword\">int<\/span> T<span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u6d4b\u8bd5\u7528\u4f8b\u6570<\/span><br \/>\n    cin <span class=\"token operator\">&gt;&gt;<\/span> T<span class=\"token punctuation\">;<\/span><\/p>\n<p>    <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> cs <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span> cs <span class=\"token operator\">&lt;<\/span> T<span class=\"token punctuation\">;<\/span> cs<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> R<span class=\"token punctuation\">,<\/span> C<span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u77e9\u9635\u7684\u884c\u6570\u548c\u5217\u6570<\/span><br \/>\n        cin <span class=\"token operator\">&gt;&gt;<\/span> R <span class=\"token operator\">&gt;&gt;<\/span> C<span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u7f51\u7edc\u6d41\u56fe\u7684\u9876\u70b9&#xff1a;0&#061;\u6e90\u70b9&#xff0c;1~R&#061;\u884c\u7ed3\u70b9&#xff0c;R&#043;1~R&#043;C&#061;\u5217\u7ed3\u70b9&#xff0c;R&#043;C&#043;1&#061;\u6c47\u70b9<\/span><br \/>\n        <span class=\"token keyword\">int<\/span> source <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> sink <span class=\"token operator\">&#061;<\/span> R <span class=\"token operator\">&#043;<\/span> C <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u521b\u5efa Dinic \u5bf9\u8c61&#xff08;\u9876\u70b9\u657050\u8db3\u591f&#xff0c;\u8fb9\u657010000\u8db3\u591f&#xff09;<\/span><br \/>\n        Dinic <span class=\"token function\">dinic<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">50<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">10000<\/span><span class=\"token punctuation\">,<\/span> source<span class=\"token punctuation\">,<\/span> sink<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8bfb\u5165\u7d2f\u79ef\u884c\u548c<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/span> R<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            cin <span class=\"token operator\">&gt;&gt;<\/span> crs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8bfb\u5165\u7d2f\u79ef\u5217\u548c<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/span> C<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            cin <span class=\"token operator\">&gt;&gt;<\/span> ccs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8ba1\u7b97\u884c\u548c&#xff1a;r_i &#061; \u7d2f\u79ef\u884c\u548c(i) &#8211; \u7d2f\u79ef\u884c\u548c(i-1)<\/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> R<span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&gt;&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#8212;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            crs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">-&#061;<\/span> crs<span class=\"token punctuation\">[<\/span>i <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8ba1\u7b97\u5217\u548c&#xff1a;c_j &#061; \u7d2f\u79ef\u5217\u548c(j) &#8211; \u7d2f\u79ef\u5217\u548c(j-1)<\/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> C<span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&gt;&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#8212;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            ccs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">-&#061;<\/span> ccs<span class=\"token punctuation\">[<\/span>i <span class=\"token operator\">&#8211;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u5efa\u56fe&#xff1a;\u6dfb\u52a0\u4e3b\u8981\u8fb9<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u6e90\u70b9\u5230\u884c\u7ed3\u70b9&#xff1a;\u5bb9\u91cf\u4e3a\u884c\u548c<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/span> R<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            dinic<span class=\"token punctuation\">.<\/span><span class=\"token function\">addArc<\/span><span class=\"token punctuation\">(<\/span>source<span class=\"token punctuation\">,<\/span> i<span class=\"token punctuation\">,<\/span> crs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u5217\u7ed3\u70b9\u5230\u6c47\u70b9&#xff1a;\u5bb9\u91cf\u4e3a\u5217\u548c<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/span> C<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            dinic<span class=\"token punctuation\">.<\/span><span class=\"token function\">addArc<\/span><span class=\"token punctuation\">(<\/span>R <span class=\"token operator\">&#043;<\/span> i<span class=\"token punctuation\">,<\/span> sink<span class=\"token punctuation\">,<\/span> ccs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u6dfb\u52a0\u8f85\u52a9\u8fb9\u4ee5\u786e\u4fdd\u6d41\u91cf\u53ef\u884c&#xff08;\u5904\u7406\u4e0b\u754c\u7ea6\u675f&#xff09;<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u884c\u7ed3\u70b9\u5230\u6c47\u70b9&#xff1a;\u5bb9\u91cf\u4e3a C&#xff08;\u6bcf\u884c\u6709 C \u4e2a\u5143\u7d20&#xff0c;\u6bcf\u4e2a\u81f3\u5c11\u4e3a 1&#xff09;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/span> R<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            dinic<span class=\"token punctuation\">.<\/span><span class=\"token function\">addArc<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token punctuation\">,<\/span> sink<span class=\"token punctuation\">,<\/span> C<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u6e90\u70b9\u5230\u5217\u7ed3\u70b9&#xff1a;\u5bb9\u91cf\u4e3a R&#xff08;\u6bcf\u5217\u6709 R \u4e2a\u5143\u7d20&#xff0c;\u6bcf\u4e2a\u81f3\u5c11\u4e3a 1&#xff09;<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/span> C<span class=\"token punctuation\">;<\/span> i<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n            dinic<span class=\"token punctuation\">.<\/span><span class=\"token function\">addArc<\/span><span class=\"token punctuation\">(<\/span>source<span class=\"token punctuation\">,<\/span> R <span class=\"token operator\">&#043;<\/span> i<span class=\"token punctuation\">,<\/span> R<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u884c\u7ed3\u70b9\u5230\u5217\u7ed3\u70b9&#xff1a;\u5bb9\u91cf\u4e3a min(19, \u884c\u548c-C)<\/span><br \/>\n        <span class=\"token comment\">\/\/ 19 \u662f\u56e0\u4e3a\u5143\u7d20\u6700\u5927\u4e3a 20&#xff0c;\u6d41\u91cf\u8868\u793a A[i][j]-1&#xff0c;\u6240\u4ee5\u6700\u5927\u6d41\u91cf\u4e3a 19<\/span><br \/>\n        <span class=\"token comment\">\/\/ \u884c\u548c-C \u662f\u56e0\u4e3a\u6bcf\u884c\u6709 C \u4e2a\u5143\u7d20&#xff0c;\u6bcf\u4e2a\u81f3\u5c11\u4e3a 1&#xff0c;\u6240\u4ee5\u53ef\u7528\u4e8e\u5206\u914d\u7684\u6d41\u91cf\u4e3a r_i &#8211; C<\/span><br \/>\n        <span class=\"token keyword\">for<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token keyword\">int<\/span> i <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">;<\/span> i <span class=\"token operator\">&lt;&#061;<\/span> R<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\">1<\/span><span class=\"token punctuation\">;<\/span> j <span class=\"token operator\">&lt;&#061;<\/span> C<span class=\"token punctuation\">;<\/span> j<span class=\"token operator\">&#043;&#043;<\/span><span class=\"token punctuation\">)<\/span><br \/>\n                dinic<span class=\"token punctuation\">.<\/span><span class=\"token function\">addArc<\/span><span class=\"token punctuation\">(<\/span>i<span class=\"token punctuation\">,<\/span> R <span class=\"token operator\">&#043;<\/span> j<span class=\"token punctuation\">,<\/span> <span class=\"token function\">min<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">19<\/span><span class=\"token punctuation\">,<\/span> crs<span class=\"token punctuation\">[<\/span>i<span class=\"token punctuation\">]<\/span> <span class=\"token operator\">&#8211;<\/span> C<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8f93\u51fa\u683c\u5f0f&#xff1a;\u6d4b\u8bd5\u7528\u4f8b\u4e4b\u95f4\u7a7a\u4e00\u884c&#xff08;\u7b2c\u4e00\u4e2a\u9664\u5916&#xff09;<\/span><br \/>\n        <span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>cs<span class=\"token punctuation\">)<\/span><br \/>\n            cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token char\">&#039;\\\\n&#039;<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8f93\u51fa\u6807\u9898<\/span><br \/>\n        cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;Matrix &#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> cs <span class=\"token operator\">&#043;<\/span> <span class=\"token number\">1<\/span> <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token char\">&#039;\\\\n&#039;<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p>        <span class=\"token comment\">\/\/ \u8ba1\u7b97\u6700\u5927\u6d41\u5e76\u8f93\u51fa\u77e9\u9635<\/span><br \/>\n        dinic<span class=\"token punctuation\">.<\/span><span class=\"token function\">maxFlow<\/span><span class=\"token punctuation\">(<\/span>R<span class=\"token punctuation\">,<\/span> C<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\n    <span class=\"token punctuation\">}<\/span><\/p>\n<p>    <span class=\"token keyword\">return<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<hr \/>\n<h3>\u4ee3\u7801\u5173\u952e\u70b9\u89e3\u91ca<\/h3>\n<h4>1. \u7f51\u7edc\u6d41\u5efa\u6a21\u6280\u5de7<\/h4>\n<p>\u4ee3\u7801\u4e2d\u4f7f\u7528\u4e86\u591a\u79cd\u6280\u5de7\u6765\u786e\u4fdd\u6d41\u91cf\u7684\u6b63\u786e\u6027&#xff1a;<\/p>\n<ul>\n<li>\u53cd\u5411\u8fb9&#xff1a;\u6bcf\u6761\u6b63\u5411\u8fb9\u90fd\u6709\u4e00\u6761\u5bf9\u5e94\u7684\u53cd\u5411\u8fb9&#xff0c;\u7528\u4e8e\u5b9e\u73b0\u6d41\u91cf\u7684\u8c03\u6574\u3002<\/li>\n<li>\u5c42\u6b21\u7f51\u7edc&#xff1a;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">BFS\\\\texttt{BFS}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">BFS<\/span><\/span><\/span><\/span><\/span><\/span> \u6784\u5efa\u8ddd\u79bb\u6807\u53f7&#xff0c;\u786e\u4fdd <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">DFS\\\\texttt{DFS}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">DFS<\/span><\/span><\/span><\/span><\/span><\/span> \u6309\u7167\u6700\u77ed\u8def\u5f84\u589e\u5e7f\u3002<\/li>\n<li>\u5f53\u524d\u5f27\u4f18\u5316&#xff1a;\u907f\u514d\u91cd\u590d\u68c0\u67e5\u5df2\u7ecf\u65e0\u6cd5\u589e\u5e7f\u7684\u8fb9&#xff0c;\u63d0\u9ad8\u6548\u7387\u3002<\/li>\n<li>\u8f85\u52a9\u8fb9&#xff1a;\u6dfb\u52a0 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">S\u2212&gt;CjS-&gt;C_j<\/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: 0.0576em\">S<\/span><span class=\"mord\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.9694em;vertical-align: -0.2861em\"><\/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: 0.3117em\"><span class=\"\" style=\"top: -2.55em;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 mathnormal mtight\" style=\"margin-right: 0.0572em\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.2861em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Ri\u2212&gt;TR_i-&gt;T<\/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: 0.0077em\">R<\/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: -0.0077em;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=\"mord\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.1389em\">T<\/span><\/span><\/span><\/span><\/span> \u8fb9\u6765\u5904\u7406\u5143\u7d20\u7684\u4e0b\u754c\u7ea6\u675f&#xff08;\u6bcf\u4e2a\u5143\u7d20\u81f3\u5c11\u4e3a <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">11<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>&#xff09;\u3002<\/li>\n<\/ul>\n<h4>2. \u77e9\u9635\u5143\u7d20\u7684\u63d0\u53d6<\/h4>\n<p>\u77e9\u9635\u5143\u7d20\u7684\u8ba1\u7b97\u516c\u5f0f\u4e3a&#xff1a;<\/p>\n<p>A[i][j] &#061; \u539f\u59cb\u5bb9\u91cf &#8211; \u5269\u4f59\u5bb9\u91cf &#043; 1<\/p>\n<p>\u8fd9\u662f\u56e0\u4e3a&#xff1a;<\/p>\n<ul>\n<li>\u539f\u59cb\u5bb9\u91cf&#xff1a;\u8868\u793a\u5141\u8bb8\u7684\u6700\u5927\u6d41\u91cf&#xff08;\u5373 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">A[i][j]\u22121A[i][j]-1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mclose\">]<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"mclose\">]<\/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> \u7684\u6700\u5927\u503c&#xff09;<\/li>\n<li>\u5269\u4f59\u5bb9\u91cf&#xff1a;\u8868\u793a\u8fd8\u672a\u4f7f\u7528\u7684\u6d41\u91cf<\/li>\n<li>\u5b9e\u9645\u6d41\u91cf &#061; \u539f\u59cb\u5bb9\u91cf &#8211; \u5269\u4f59\u5bb9\u91cf&#xff1a;\u8868\u793a\u5b9e\u9645\u4f7f\u7528\u7684\u6d41\u91cf&#xff08;\u5373 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">A[i][j]\u22121A[i][j]-1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mclose\">]<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0572em\">j<\/span><span class=\"mclose\">]<\/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>&#xff09;<\/li>\n<li>&#043;1&#xff1a;\u6062\u590d\u4e3a\u5b9e\u9645\u7684\u77e9\u9635\u5143\u7d20\u503c<\/li>\n<\/ul>\n<h4>3. \u8fb9\u754c\u60c5\u51b5\u5904\u7406<\/h4>\n<ul>\n<li>\u5f53 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">crs[i]\u2212Ccrs[i] &#8211; C<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">crs<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mclose\">]<\/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: 0.6833em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><\/span><\/span><\/span><\/span> \u53ef\u80fd\u4e3a\u8d1f\u6570\u65f6&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">min(19,crs[i]\u2212C)min(19, crs[i] &#8211; C)<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">min<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">19<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">crs<\/span><span class=\"mopen\">[<\/span><span class=\"mord mathnormal\">i<\/span><span class=\"mclose\">]<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\" style=\"margin-right: 0.0715em\">C<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u786e\u4fdd\u5bb9\u91cf\u975e\u8d1f\u3002<\/li>\n<li>\u9898\u76ee\u4fdd\u8bc1\u81f3\u5c11\u6709\u4e00\u4e2a\u89e3&#xff0c;\u6240\u4ee5\u6700\u5927\u6d41\u4e00\u5b9a\u80fd\u627e\u5230\u53ef\u884c\u89e3\u3002<\/li>\n<li>\u77e9\u9635\u5927\u5c0f\u9650\u5236\u5728 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">20\u00d72020\u00d720<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">20<\/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\">20<\/span><\/span><\/span><\/span><\/span> \u4ee5\u5185&#xff0c;\u56e0\u6b64\u6570\u7ec4\u5927\u5c0f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">3232<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">32<\/span><\/span><\/span><\/span><\/span> \u8db3\u591f\u4f7f\u7528\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u603b\u7ed3<\/h3>\n<p>\u672c\u9898\u7684\u5173\u952e\u5728\u4e8e&#xff1a;<\/p>\n<li>\u5c06\u7d2f\u79ef\u548c\u8f6c\u5316\u4e3a\u884c\u548c\u4e0e\u5217\u548c<\/li>\n<li>\u5efa\u7acb\u6d41\u91cf\u7f51\u7edc&#xff0c;\u5c06\u77e9\u9635\u5143\u7d20\u8868\u793a\u4e3a\u6d41\u91cf<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">&#043;1&#043;1<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.7278em;vertical-align: -0.0833em\"><\/span><span class=\"mord\">&#043;<\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/li>\n<li>\u5229\u7528 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">Dinic\\\\texttt{Dinic}<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6111em\"><\/span><span class=\"mord text\"><span class=\"mord texttt\">Dinic<\/span><\/span><\/span><\/span><\/span><\/span> \u7b97\u6cd5\u6c42\u89e3\u5e26\u4e0a\u4e0b\u754c\u7684\u6d41\u5206\u914d\u95ee\u9898<\/li>\n<li>\u8f93\u51fa\u65f6\u6ce8\u610f\u77e9\u9635\u5143\u7d20\u7684\u53d6\u503c\u8303\u56f4\u662f <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">11<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span> \u5230 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">2020<\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">20<\/span><\/span><\/span><\/span><\/span><\/li>\n<p>\u8fd9\u9053\u9898\u5f88\u597d\u5730\u5c55\u793a\u4e86\u5982\u4f55\u5c06\u77e9\u9635\u6784\u9020\u95ee\u9898\u8f6c\u5316\u4e3a\u7f51\u7edc\u6d41\u95ee\u9898&#xff0c;\u662f\u7ec3\u4e60 \u6700\u5927\u6d41\u5efa\u6a21 \u7684\u7ecf\u5178\u9898\u76ee\u3002\u901a\u8fc7\u6dfb\u52a0\u8be6\u7ec6\u7684\u4e2d\u6587\u6ce8\u91ca&#xff0c;\u5e0c\u671b\u80fd\u5e2e\u52a9\u8bfb\u8005\u66f4\u597d\u5730\u7406\u89e3\u7f51\u7edc\u6d41\u7b97\u6cd5\u7684\u5b9e\u73b0\u7ec6\u8282\u548c\u5efa\u6a21\u6280\u5de7\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u9898\u76ee\u5927\u610f<br \/>\n\u7ed9\u5b9a\u4e00\u4e2a R\u00d7CR \\\\times CR\u00d7C \u7684\u6b63\u6574\u6570\u77e9\u9635&#xff0c;\u5df2\u77e5\u5b83\u7684 \u7d2f\u79ef\u884c\u548c \u4e0e \u7d2f\u79ef\u5217\u548c &#xff0c;\u8981\u6c42\u8fd8\u539f\u51fa\u539f\u77e9\u9635\u7684\u6240\u6709 R\u00d7CR \\\\times CR\u00d7C \u4e2a\u5143\u7d20\u3002<br \/>\n\u5177\u4f53\u6765\u8bf4&#xff1a;<br \/>\nRowSum(i)\u2211j1CAijRowSum(i)  \\\\sum_{j1}^{C} A_{ij}RowSum(i)\u2211j1C\u200bAij\u200bCumulativeRowSum(i)\u2211k1iRowSum(k)CumulativeRowSum(i)  \\\\sum_{k1}<\/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-63010","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 11082 Matrix Decompressing - \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\/63010.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"UVa 11082 Matrix Decompressing - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u9898\u76ee\u5927\u610f \u7ed9\u5b9a\u4e00\u4e2a R\u00d7CR \\times CR\u00d7C \u7684\u6b63\u6574\u6570\u77e9\u9635&#xff0c;\u5df2\u77e5\u5b83\u7684 \u7d2f\u79ef\u884c\u548c \u4e0e \u7d2f\u79ef\u5217\u548c &#xff0c;\u8981\u6c42\u8fd8\u539f\u51fa\u539f\u77e9\u9635\u7684\u6240\u6709 R\u00d7CR \\times CR\u00d7C \u4e2a\u5143\u7d20\u3002 \u5177\u4f53\u6765\u8bf4&#xff1a; RowSum(i)\u2211j1CAijRowSum(i) \\sum_{j1}^{C} A_{ij}RowSum(i)\u2211j1C\u200bAij\u200bCumulativeRowSum(i)\u2211k1iRowSum(k)CumulativeRowSum(i) \\sum_{k1}\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/63010.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta 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