n \u4e2a\u7bb1\u5b50\u5b58\u653e\u6709 n \u79cd\u7269\u54c1\uff0c\u8981\u6c42\u786e\u5b9a\u4e00\u79cd\u5206\u7c7b\u65b9\u6848\uff0c\u4f7f\u5f97\u79fb\u52a8\u4ee3\u4ef7\u6700\u5c0f\u3002<\/p>\n
\u6c42\u79fb\u52a8\u4ee3\u4ef7\u6700\u5c0f\u5212\u5f52\u5230\u8ba1\u7b97\u4fdd\u7559\u5728\u539f\u5904\u7684\u7269\u54c1\u6570\u6700\u5927\u3002\u3002\u3002\u7136\u540e\u3002\u3002\u3002
\n<\/p>\n
\r\nconst int N = 150;\r\n\r\nint W[N][N], lx[N], ly[N], p[N];\r\nbool vx[N], vy[N];\r\nint n;\r\n\r\nvoid init(){\r\n\tRD(n); REP_2(i, j, n, n) RD(W[i][j]);\r\n}\r\n\r\n#define w(x, y) (lx[x] + ly[y] - W[x][y])\r\n\r\nbool dfs(int x){\r\n\tvx[x] = true; REP(y, n) if (!vy[y] && !w(x, y)){\r\n vy[y] = true; if(p[y]==-1||dfs(p[y])){\r\n p[y] = x;\r\n return true;\r\n }\r\n\t}\r\n\treturn false;\r\n}\r\n\r\nvoid KM(){\r\n\r\n\tFLC(p, -1); RST(lx, ly);\r\n\r\n\tREP_2(i, j, n, n) checkMax(lx[i], W[i][j]);\r\n\r\n\tREP(x, n){\r\n\t\twhile (true){\r\n\t\t\tRST(vx, vy); if (dfs(x)) break;\r\n\r\n\t\t\tint delta = INF;\r\n\t\t\tREP_2(i, j, n, n) if(vx[i] && !vy[j])\r\n checkMin(delta, w(i, j));\r\n\r\n\t\t\tREP(i, n){\r\n\t\t\t\tif (vx[i]) lx[i] -= delta;\r\n\t\t\t\tif (vy[i]) ly[i] += delta;\r\n\t\t\t}\r\n\t\t}\r\n\t}\r\n}\r\n\r\nvoid print(){\r\n\tint res = 0; REP_2(i, j, n, n) res += W[i][j];\r\n REP(i, n) res -= W[p[i]][i];\r\n\tOT(res);\r\n}\r\n\r\nint main(){\r\n\tinit(); KM();\r\n\tprint();\r\n}\r\n<\/pre>\n\r\nconst int N = 150;\r\n\r\nint W[N][N], lx[N], ly[N], p[N], slack[N];\r\nbool vx[N], vy[N];\r\nint n;\r\n\r\nvoid init(){\r\n\tRD(n); REP_2(i, j, n, n) RD(W[i][j]);\r\n}\r\n\r\n#define w(x, y) (lx[x] + ly[y] - W[x][y])\r\n\r\nbool dfs(int x){\r\n vx[x] = true; REP(y, n) if (!vy[y]){\r\n if (!w(x, y)){\r\n vy[y] = true; if(p[y]==-1||dfs(p[y])){\r\n p[y] = x;\r\n return true;\r\n }\r\n }\r\n else {\r\n checkMin(slack[y], w(x, y));\r\n }\r\n\t}\r\n\treturn false;\r\n}\r\n\r\nvoid KM(){\r\n\r\n\tFLC(p, -1); RST(lx, ly);\r\n\r\n\tREP_2(i, j, n, n) checkMax(lx[i], W[i][j]);\r\n\r\n\tREP(x, n){\r\n\t FLC(slack, 0x7f); while (true){\r\n\t\t\tRST(vx, vy); if (dfs(x)) break;\r\n\r\n\t\t\tint delta = INF;\r\n\t\t\tREP(i, n) if (!vy[i]) checkMin(delta, slack[i]);\r\n\r\n\t\t\tREP(i, n){\r\n\t\t\t\tif (vx[i]) lx[i] -= delta;\r\n\t\t\t\tif (vy[i]) ly[i] += delta; else slack[i] -= delta;\r\n\t\t\t}\r\n\t\t}\r\n\t}\r\n}\r\n\r\nvoid print(){\r\n\tint res = 0; REP_2(i, j, n, n) res += W[i][j];\r\n REP(i, n) res -= W[p[i]][i];\r\n\tOT(res);\r\n}\r\n\r\nint main(){\r\n\tinit(); KM();\r\n\tprint();\r\n}\r\n<\/pre>\n\r\nconst int N = 150;\r\n\r\nint W[N][N], lx[N], ly[N], p[N], delta;\r\nbool vx[N], vy[N];\r\nint n;\r\n\r\nvoid init(){\r\n\tRD(n); REP_2(i, j, n, n) RD(W[i][j]);\r\n}\r\n\r\n#define w(x, y) (lx[x] + ly[y] - W[x][y])\r\n\r\nbool dfs(int x){\r\n vx[x] = true; REP(y, n) if (!vy[y]){\r\n if (!w(x, y)){\r\n vy[y] = true; if(p[y]==-1||dfs(p[y])){\r\n p[y] = x;\r\n return true;\r\n }\r\n }\r\n else {\r\n checkMin(delta, w(x, y));\r\n }\r\n\t}\r\n\treturn false;\r\n}\r\n\r\nvoid KM(){\r\n\r\n\tFLC(p, -1); RST(lx, ly);\r\n\r\n\tREP_2(i, j, n, n) checkMax(lx[i], W[i][j]);\r\n\r\n\tREP(x, n){\r\n\t while (true){\r\n\t\t\tRST(vx, vy); delta = INF; if (dfs(x)) break;\r\n\r\n\t\t\tREP(i, n){\r\n\t\t\t\tif (vx[i]) lx[i] -= delta;\r\n\t\t\t\tif (vy[i]) ly[i] += delta;\r\n\t\t\t}\r\n\t\t}\r\n\t}\r\n}\r\n\r\nvoid print(){\r\n\tint res = 0; REP_2(i, j, n, n) res += W[i][j];\r\n REP(i, n) res -= W[p[i]][i];\r\n\tOT(res);\r\n}\r\n\r\nint main(){\r\n\tinit(); KM();\r\n\tprint();\r\n}\r\n<\/pre>\n————–<\/p>\n
\r\nconst int INF = 0x3f3f3f3f;\r\nconst int N = 302;\r\n\r\nint C[N][N], W[N][N];\r\nint Q[512], d[N], p[N], head, tail; bool inQ[N];\r\nint n, s, t, tot, cost;\r\n\r\nvoid init(){\r\n\tRD(n), s = 0, t = 2 * n + 1, tot = 0;\r\n\tint w; REP_1(i, n){\r\n\t C[s][i] = C[i+n][t] = 1;\r\n\t REP_1(j, n){\r\n\t C[i][j+n] = 1, tot += _RD(w);\r\n\t W[i][j+n] = -w, W[j+n][i] = w;\r\n\t }\r\n\t}\r\n}\r\n\r\nbool spfa(){\r\n RST(inQ); FLC(d, 0x3f), d[Q[head = 0] = s] = 0, tail = 1;\r\n while (head < tail){\r\n int u = Q[head++ & 511]; inQ[u] = false;\r\n FOR_1(v, 1, t){\r\n if (C[u][v] && d[v] > d[u] + W[u][v]){\r\n d[v] = d[u] + W[u][v], p[v] = u;\r\n if (!inQ[v]) Q[tail++ & 511] = v, inQ[v] = true;\r\n }\r\n }\r\n }\r\n return d[t] != INF;\r\n}\r\n\r\nvoid addPath(){\r\n int u, v = t; do{\r\n u = p[v], --C[u][v], ++C[v][u],\r\n cost += W[u][v], v = u;\r\n }while(u != s);\r\n}\r\n\r\nvoid solve(){\r\n cost = 0;\r\n while (spfa()) addPath();\r\n}\r\n\r\nint main(){\r\n\tinit(); solve();\r\n\tOT(tot + cost);\r\n}\r\n<\/pre>\n<\/bk><\/p>\n
Further discussion :<\/h3>\n
KM-1\uff08 O(n4) \u5b9e\u73b0\u3002\u3002
\nKM-2 (.. \u6807\u51c6 O(n3) \u5b9e\u73b0\u3002\u3002\u5f15\u5165 \u61d2\u6807\u8bb0(slack label) \u601d\u60f3\u3002\u3002\u3002\u3002\u53c2\u89c1 dd \u8fd9\u7bc7 <\/a>\u3002\u3002 :<\/p>\n“… . \u7ef4\u62a4\u53f3\u8fb9\u7684\u70b9 j \u7684\u6240\u6709\u4e0d\u5728\u5bfc\u51fa\u5b50\u56fe\u7684\u8fb9\u5bf9\u5e94\u7684 lx[i]+ly[j]-w[i][j] \u7684\u6700\u5c0f\u503c……”<\/p><\/blockquote>\n
KM-3\uff08\u3002\u3002\u81ea\u5df1 yy \u7684\u3002\u3002dfs \u7684\u8fc7\u7a0b\u4e2d\u52a8\u6001\u66f4\u65b0 slack\u3002\u3002\u3002O(n3)<\/del>\u3002\u3002\u3002<\/p>\n—- UPD —-<\/p>\n
.. KM-4 ..<\/a> ( \u975e\u9012\u5f52\u5b9e\u73b0\u3002\u3002\u3002\u3002\u5eb6\u6c11\u5199\u6cd5\u3002\u3002\u3002<\/a>\u3002\u3002\u3002
\n.. KM-5 ..<\/a> ( \u975e\u9012\u5f52\u5b9e\u73b0\u3002\u3002\u3002\u3002TC \u9ad8\u7aef\u72d7\u5199\u6cd5\u3002\u3002<\/a>\u3002\u3002\u3002
\n .. Mincost-Flow-2… <\/a>\uff08\u8d39\u7528\u6d41\u8fde\u7eed\u589e\u5149\u8def\u7b97\u6cd5\u7684 Dijkstra \u5b9e\u73b0\u3002\u3002\u3002\u4e0d\u8fc7\u5728\u8fd9\u9898\u91cc\u662f\u9519\u7684\u3002\u3002\u56e0\u4e3a\u53d6\u8d1f\u503c\u4ee5\u540e\u4ea7\u751f\u4e86\u8d1f\u6743\u73af\u3002\u3002\u3002\u4e0d\u77e5\u9053\u8fd8\u80fd\u4e0d\u80fd\u62a2\u6551\u3002\u3002\uff08\uff1f
\n\u3002\u3002\u6ce8\u610f KM-3 \u6bcf\u6b21\u66f4\u65b0\u53ef\u80fd\u8fbe\u4e0d\u5230\u4e0b\u754c\u3002\uff01\uff01\u3002\uff08\u3002\u3002\u590d\u6742\u5ea6\u4e0d\u80fd\u4fdd\u8bc1 O(n3) \uff1f\u3002\u3002\u3002<\/a><\/p>\nExternal link :<\/h3>\n
http:\/\/acm.timus.ru\/problem.aspx?space=1&num=1076<\/a>
\nhttp:\/\/hi.baidu.com\/fqq11679\/blog\/item\/9c5c22a69c647392d14358bc.html<\/a>
\nhttp:\/\/www.cppblog.com\/MatoNo1\/archive\/2011\/07\/23\/151724.html<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"Brief description : n \u4e2a\u7bb1\u5b50\u5b58\u653e\u6709 n \u79cd\u7269\u54c1\uff0c\u8981\u6c42\u786e\u5b9a\u4e00\u79cd\u5206\u7c7b\u65b9\u6848\uff0c\u4f7f\u5f97\u79fb\u52a8\u4ee3\u4ef7\u6700\u5c0f\u3002 Analyse : \u6c42\u79fb\u52a8\u4ee3\u4ef7\u6700\u5c0f\u5212\u5f52\u5230\u8ba1\u7b97\u4fdd\u7559\u5728\u539f\u5904\u7684\u7269\u54c1\u6570\u6700\u5927\u3002\u3002\u3002\u7136\u540e\u3002\u3002\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[33],"tags":[64,92],"class_list":["post-118","post","type-post","status-publish","format-standard","hentry","category-ural","tag-64","tag-92"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-1U","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/118","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/comments?post=118"}],"version-history":[{"count":1,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/118\/revisions"}],"predecessor-version":[{"id":176,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/118\/revisions\/176"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=118"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=118"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=118"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}