{"id":148,"date":"2010-09-18T16:59:25","date_gmt":"2010-09-18T08:59:25","guid":{"rendered":"http:\/\/comzyh.tk\/blog\/?p=148"},"modified":"2015-10-24T16:50:24","modified_gmt":"2015-10-24T08:50:24","slug":"%e7%94%a8%e4%ba%8e%e4%ba%8c%e5%88%86%e5%9b%be%e5%8c%b9%e9%85%8d%e7%9a%84%e5%8c%88%e7%89%99%e5%88%a9%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"https:\/\/comzyh.com\/blog\/archives\/148\/","title":{"rendered":"\u7528\u4e8e\u4e8c\u5206\u56fe\u5339\u914d\u7684\u5308\u7259\u5229\u7b97\u6cd5"},"content":{"rendered":"

\u4e8c\u5206\u56fe\u5339\u914d\u95ee\u9898<\/h2>\n

\u4e8c\u5206\u56fe\u53c8\u79f0\u4f5c\u4e8c\u90e8\u56fe\uff0c\u662f\u56fe\u8bba\u4e2d\u7684\u4e00\u79cd\u7279\u6b8a\u6a21\u578b\u3002 \u8bbeG=(V,E)\u662f\u4e00\u4e2a\u65e0\u5411\u56fe\uff0c\u5982\u679c\u9876\u70b9V\u53ef\u5206\u5272\u4e3a\u4e24\u4e2a\u4e92\u4e0d\u76f8\u4ea4\u7684\u5b50\u96c6(A,B)\uff0c\u5e76\u4e14\u56fe\u4e2d\u7684\u6bcf\u6761\u8fb9\uff08i\uff0cj\uff09\u6240\u5173\u8054\u7684\u4e24\u4e2a\u9876\u70b9i\u548cj\u5206\u522b\u5c5e\u4e8e\u8fd9\u4e24\u4e2a\u4e0d\u540c\u7684\u9876\u70b9\u96c6(i in A,j in B)\uff0c\u5219\u79f0\u56feG\u4e3a\u4e00\u4e2a\u4e8c\u5206\u56fe\u3002<\/p>\n

\u7ed9\u5b9a\u4e00\u4e2a\u4e8c\u5206\u56fe<\/a>G\uff0cM\u4e3aG\u8fb9\u96c6\u7684\u4e00\u4e2a\u5b50\u96c6\uff0c\u5982\u679cM\u6ee1\u8db3\u5f53\u4e2d\u7684\u4efb\u610f\u4e24\u6761\u8fb9\u90fd\u4e0d\u4f9d\u9644\u4e8e\u540c\u4e00\u4e2a\u9876\u70b9\uff0c\u5219\u79f0M\u662f\u4e00\u4e2a\u5339\u914d\u3002<\/p>\n

\u6781\u5927\u5339\u914d(Maximal Matching)\u662f\u6307\u5728\u5f53\u524d\u5df2\u5b8c\u6210\u7684\u5339\u914d\u4e0b,\u65e0\u6cd5\u518d\u901a\u8fc7\u589e\u52a0\u672a\u5b8c\u6210\u5339\u914d\u7684\u8fb9\u7684\u65b9\u5f0f\u6765\u589e\u52a0\u5339\u914d\u7684\u8fb9\u6570\u3002\u6700\u5927\u5339\u914d(maximum matching)\u662f\u6240\u6709\u6781\u5927\u5339\u914d\u5f53\u4e2d\u8fb9\u6570\u6700\u5927\u7684\u4e00\u4e2a\u5339\u914d\u3002\u9009\u62e9\u8fd9\u6837\u7684\u8fb9\u6570\u6700\u5927\u7684\u5b50\u96c6\u79f0\u4e3a\u56fe\u7684\u6700\u5927\u5339\u914d<\/strong>\u95ee\u9898\u3002\uff08\u89c1\u4e0b\u56fe\uff09<\/p>\n\n\n\n
\n
\n
\"\"<\/a>
\u4e8c\u5206\u56fe<\/figcaption><\/figure>\n<\/div>\n
\"\"<\/a>
\u6700\u5927\u4e8c\u5206\u5339\u914d<\/figcaption><\/figure>\n

\u5982\u56fe\u84dd\u7ebf\u6240\u793a\u662f\u4e00\u79cd\u6700\u5927\u4e8c\u5206\u5339\u914d\u65b9\u6848\uff0c\u5339\u914d\u6570=3
\n\u8b66\u544a\uff1a\u4f7f\u7528IE6\u6d4f\u89c8\u4f1a\u6781\u4e0d\u6b63\u5e38\uff0c\u4e0d\u4fe1\u4f60\u628a\u56fe\u7247\u4e0b\u8f7d\u4e0b\u6765\u7528\u770b\u56fe\u5de5\u5177\u770b\u770b\u3002\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u5982\u679c\u4e00\u4e2a\u5339\u914d\u4e2d\uff0c\u56fe\u4e2d\u7684\u6bcf\u4e2a\u9876\u70b9\u90fd\u548c\u56fe\u4e2d\u67d0\u6761\u8fb9\u76f8\u5173\u8054\uff0c\u5219\u79f0\u6b64\u5339\u914d\u4e3a\u5b8c\u5168\u5339\u914d\uff0c\u4e5f\u79f0\u4f5c\u5b8c\u5907\u5339\u914d\u3002<\/p>\n

\u6c42\u4e8c\u5206\u56fe\u6700\u5927\u5339\u914d\u53ef\u4ee5\u7528\u6700\u5927\u6d41(Maximal Flow)\u6216\u8005\u5308\u7259\u5229\u7b97\u6cd5<\/strong>(Hungarian Algorithm)<\/p>\n

\uff08\u4ee5\u4e0a\u9664\u56fe\u7247\u5747\u6765\u81ea\u767e\u5ea6\u767e\u79d1\uff09<\/p>\n

<\/p>\n

\u5308\u7259\u5229\u7b97\u6cd5<\/h2>\n

\u5148\u8003\u8651\u4e00\u9053\u9898:USACO-4.2.2-stall4<\/a><\/p>\n

\u6c42\u6700\u5927\u5339\u914d\u7684\u4e00\u79cd\u663e\u800c\u6613\u89c1\u7684\u7b97\u6cd5\u662f\uff1a\u5148\u627e\u51fa\u5168\u90e8\u5339\u914d\uff0c\u7136\u540e\u4fdd\u7559\u5339\u914d\u6570\u6700\u591a\u7684\u3002\u4f46\u662f\u8fd9\u4e2a\u7b97\u6cd5\u7684\u590d\u6742\u5ea6\u4e3a\u8fb9\u6570\u7684\u6307\u6570\u7ea7\u51fd\u6570\u3002\u56e0\u6b64\uff0c\u9700\u8981\u5bfb\u6c42\u4e00\u79cd\u66f4\u52a0\u9ad8\u6548\u7684\u7b97\u6cd5\u3002<\/p>\n

\u53ef\u4ee5\u7528\u7f51\u7edc\u6d41\u7684\u6700\u5927\u6d41\u5b9e\u73b0\uff0c\u4e0d\u8fc7\u6700\u5927\u6d41\u6bd4\u8f83\u590d\u6742\uff0c\u4f7f\u7528\u5308\u7259\u5229\u7b97\u6cd5\u7f16\u7a0b\u590d\u6742\u5ea6\u4f4e\u3002<\/p>\n

\u7b97\u6cd5\u6700\u57fa\u672c\u8f6e\u5ed3\uff1a
\n


\n\u7ea2\u7ebf\u4ee3\u8868Find\u51fd\u6570\u7684\u8c03\u7528,\u84dd\u7ebf\u4ee3\u8868\u5df2\u6709\u7684\u914d\u5bf9
\n<\/object>
\n\u67e5\u770b\u6216\u4e0b\u8f7dGIF\u7248\u672c<\/a>
\n
\u6837\u4f8b\u52a8\u753b\u6f14\u793a<\/figcaption><\/figure><\/p>\n
    \n
  1. \u7f6e\u8fb9\u96c6M\u4e3a\u7a7a\uff08\u521d\u59cb\u5316\uff0c\u8c01\u548c\u8c01\u90fd\u6ca1\u8fde\u7740\uff09<\/li>\n
  2. \u9009\u62e9\u4e00\u4e2a\u65b0\u7684\u539f\u70b9\u5bfb\u627e\u589e\u5e7f\u8def<\/li>\n
  3. \u91cd\u590d(2)\u64cd\u4f5c\u76f4\u5230\u627e\u4e0d\u51fa\u589e\u5e7f\u8def\u5f84\u4e3a\u6b62\uff082\uff0c3\u6b65\u9aa4\u6784\u6210\u4e00\u4e2a\u5faa\u73af\uff09<\/li>\n<\/ol>\n

    \u6a21\u62df\u6b65\u9aa4\u5982\u53f3\u56fe\u6240\u793a(\u8fc7\u4e8e\u8be6\u7ec6\uff0c\u5927\u725b\u8bf7\u65e0\u89c6)\uff1a<\/p>\n

      \n
    1. \u521d\u59cb\u5316\uff08\u6e05\u7a7a\uff09<\/li>\n
    2. \u4eceA\u6240\u8fde\u63a5\u7684\u70b9\u4e2d\u627e\u5230\u4e00\u4e2a\u672a\u5728\u672c\u6b21\u5faa\u73af\u4e2d\u641c\u7d22\u8fc7\u7684\u70b92\uff0c\u5e76\u5c062\u6807\u8bb0\u4e3a\u641c\u7d22\u8fc7\uff0c\u56e0\u4e3a2\u6ca1\u6709\u88ab\u8fde\u63a5\u8fc7\uff0c\u5339\u914dA2<\/li>\n
    3. \u7ed3\u675f\u4e0a\u6b21\uff0c\u5f00\u59cb\u65b0\u7684\u5faa\u73af\uff0c\u5c06\u6240\u6709\u70b9\u6807\u8bb0\u4e3a\u672a\u641c\u7d22\u8fc7<\/li>\n
    4. \u641c\u7d22B\uff0c\u627e\u5230\u4e00\u4e2a\u672a\u5728\u672c\u6b21\u5faa\u73af\u4e2d\u641c\u7d22\u8fc7\u7684\u70b92\uff0c\u6807\u8bb0\u4e3a\u641c\u7d22\u8fc7<\/li>\n
    5. \u53d1\u73b02\u88ab\u5339\u914d\u8fc7<\/strong>\uff0c\u4ece2\u7684\u7236\u4eb2A\u5bfb\u627e\u589e\u5e7f\u8def<\/strong>\uff0c\u9012\u5f52\u641c\u7d22A{\u4eceA\u6240\u8fde\u63a5\u7684\u70b9\u4e2d\u627e\u5230\u4e00\u4e2a\u672a\u5728\u672c\u6b21\u5faa\u73af\u4e2d\u641c\u7d22\u8fc7\u7684\u70b95\uff081\u5df2\u7ecf<\/strong>\u6807\u8bb0\u4e3a\u7eff\u8272\uff09\uff0c\u5c065\u6807\u8bb0\u4e3a\u641c\u7d22\u8fc7\uff0c\u56e0\u4e3a5\u6ca1\u6709\u88ab\u5339\u914d\u8fc7\uff0c\u5339\u914dA5}\u627e\u5230\u589e\u5e7f\u8def\uff08\u6b64\u5904\u4e3a\u589e\u5e7f\u8def\u7684\u5173\u952e<\/strong>\uff09<\/li>\n
    6. \u7ed3\u675f\u4e0a\u6b21\uff0c\u5f00\u59cb\u65b0\u7684\u5faa\u73af\uff0c\u5c06\u6240\u6709\u70b9\u6807\u8bb0\u4e3a\u672a\u641c\u7d22\u8fc7<\/li>\n
    7. \u641c\u7d22C\uff0c\u627e\u5230\u4e00\u4e2a\u672a\u5728\u672c\u6b21\u5faa\u73af\u4e2d\u641c\u7d22\u8fc7\u7684\u70b91\uff0c\u5e76\u5c061\u6807\u8bb0\u4e3a\u641c\u7d22\u8fc7,\u53d1\u73b01\u672a\u88ab\u5339\u914d\u8fc7\uff0c\u5339\u914dC1<\/li>\n
    8. \u7ed3\u675f\u4e0a\u6b21\uff0c\u5f00\u59cb\u65b0\u7684\u5faa\u73af\uff0c\u5c06\u6240\u6709\u70b9\u6807\u8bb0\u4e3a\u672a\u641c\u7d22\u8fc7<\/li>\n
    9. \u641c\u7d22D\uff0c\u627e\u5230\u4e00\u4e2a\u672a\u5728\u672c\u6b21\u5faa\u73af\u4e2d\u641c\u7d22\u8fc7\u7684\u70b91\uff0c\u5e76\u5c061\u6807\u8bb0\u4e3a\u641c\u7d22\u8fc7\uff0c\u53d1\u73b01\u88ab\u5339\u914d\u8fc7\uff0c\u9012\u5f52\u641c\u7d221\u7684\u6e90C\u5bfb\u627e\u589e\u5e7f\u8def<\/li>\n
    10. {\u641c\u7d22C\uff0c\u627e\u5230\u4e00\u4e2a\u672a\u5728\u672c\u6b21\u5faa\u73af\u4e2d\u641c\u7d22\u8fc7\u7684\u70b95\uff0c\u6807\u8bb0\u4e3a\u641c\u7d22\u8fc7\uff0c\u53d1\u73b05\u88ab\u5339\u914d\uff0c\u8fdb\u4e00\u6b65\u8fd4\u73b0\u6ca1\u6709\u5176\u4ed6\u53ef\u8fde\u63a5\u70b9\uff0c\u8fd4\u56de\u627e\u4e0d\u5230\u589e\u5e7f\u8def}\u8fd4\u56de\u7b2c9\u6b65<\/li>\n
    11. \u641c\u7d22D\uff0c\u627e\u5230\u4e00\u4e2a\u672a\u5728\u672c\u6b21\u5faa\u73af\u4e2d\u641c\u7d22\u8fc7\u7684\u70b92\uff0c\u53d1\u73b02\u88ab\u5339\u914d\uff0c\u9012\u5f52\u641c\u7d222\u7684\u6e90B\u5bfb\u627e\u589e\u5e7f\u8def<\/li>\n
    12. {\u641c\u7d22B\uff0c\u627e\u5230\u4e00\u4e2a\u672a\u5728\u672c\u6b21\u5faa\u73af\u4e2d\u641c\u7d22\u8fc7\u7684\u70b93\uff0c\u5e76\u5c063\u6807\u8bb0\u4e3a\u641c\u7d22\u8fc7\uff0c\u53d1\u73b03\u672a\u88ab\u5339\u914d\uff0c\u5339\u914dB3\u8fd4\u56de\u627e\u5230}\u65e2\u7136B\u53e6\u5bfb\u65b0\u6b22\uff0c\u5339\u914dD2<\/li>\n
    13. \u7ed3\u675f\u4e0a\u6b21\uff0c\u5f00\u59cb\u65b0\u7684\u5faa\u73af\uff0c\u5c06\u6240\u6709\u70b9\u6807\u8bb0\u4e3a\u672a\u641c\u7d22\u8fc7\uff0c\u9012\u5f52\u641c\u7d22D\u5bfb\u627e\u589e\u5e7f\u8def<\/li>\n
    14. \u641c\u7d22E\uff0c\u627e\u5230\u4e00\u4e2a\u672a\u5728\u672c\u6b21\u5faa\u73af\u4e2d\u641c\u7d22\u8fc7\u7684\u70b92\uff0c\u5e76\u5c062\u6807\u8bb0\u4e3a\u641c\u7d22\u8fc7\uff0c\u53d1\u73b02\u88ab\u5339\u914d\u8fc7\uff0c\u9012\u5f52\u641c\u7d222\u7684\u6e90D\u5bfb\u627e\u589e\u5e7f\u8def<\/li>\n
    15. {\u641c\u7d22D\uff0c\u53d1\u73b01\uff0c5\u5747\u88ab\u5339\u914d\u8fc7\uff0c\u8fd4\u56de\u627e\u4e0d\u5230\u589e\u5e7f\u8def}<\/li>\n
    16. E\u65e0\u5176\u4ed6\u53ef\u8fde\u63a5\u8282\u70b9\uff0c\u653e\u5f03E\uff0cE\u540e\u65e0\u540e\u7eed\u8282\u70b9\uff0c\u5df2\u7ecf\u904d\u5386A-E\uff0c\u7ed3\u675f\u7b97\u6cd5<\/li>\n<\/ol>\n

      \u9644\u672c\u4f53\u9898\u89e3CODE\uff1a<\/p>\n

      \r\n\/*\r\nID:\r\nPROG: stall4\r\nLANG: C++\r\n*\/\r\n#include \r\n#include \r\n#include \r\n#include \r\n#define cin fin\r\n#define cout fout\r\n#define din cin\r\n#define dout cout\r\nusing namespace std;\r\nifstream fin (\"stall4.in\" );\r\nofstream fout(\"stall4.out\");\r\nint tab[201][201];\/\/\u90bb\u63a5\u77e9\u9635,\u4e0d\u662f\u771f\u6b63\u610f\u4e49\u7684\u90bb\u63a5\u77e9\u9635,\u7b2c\u4e00\u7ef4\u5bf9\u5e94\u725b,\u7b2c\u4e8c\u7ef4\u5bf9\u5e94\u725b\u68da\r\nint state[201],result[201];\/\/stata:\u662f\u5426\u88ab\u641c\u7d22\u8fc7;result:\u67d0\u725b\u680f\u5bf9\u5e94\u7684\u725b\r\nint n,m;\r\nint ans;\/\/\u627e\u5230\u591a\u5c11\u5339\u914d\r\n\r\nint find(int x){\/\/ \u5308\u7259\u5229\u7b97\u6cd5\r\n    int i;\r\n    for (i=1;i<=m;i++){\r\n        if (tab[x][i]==1 && !state[i]){\r\n           state[i]=1;\/\/\u6807\u8bb0\u4e3a\u641c\u7d22\u8fc7\r\n           if (result[i]==0\/\/\u672a\u88ab\u5339\u914d\u8fc7\r\n\t\t   || find(result[i])){\/\/\u80fd\u627e\u5230\u4e00\u6761\u589e\u5e7f\u8def\r\n              result[i]=x;\/\/\u5339\u914di,x\r\n              return 1;\/\/\u80fd\u627e\u5230\u65b0\u7684\u5339\u914d\r\n              }\r\n           }\r\n        }\r\n    return 0;\r\n    }\r\nint main(){\r\n    int i,j;\r\n    int n1,t;\r\n    cin >> n >> m;\r\n    memset(tab,0,sizeof(tab));\r\n    for (i=1;i<=n;i++){\r\n        cin >> n1;\r\n        for (j=1;j<=n1;j++){\r\n            cin >> t;\r\n            tab[i][t]=1;\r\n            }\r\n        }\r\n    for (i=1;i<=n;i++){\r\n        memset(state,0,sizeof(state));\/\/\u6e05\u7a7a\u662f\u5426\u641c\u7d22\u8fc7\u6570\u7ec4\r\n        if (find(i)) ans++;\/\/\u627e\u5230\u65b0\u7684\u5339\u914d\r\n        }\/\/\u5b8c\u6210\u540e Result[i]\u4fdd\u5b58\u7740\u7b2ci\u4e2a\u725b\u680f\u5bf9\u5e94\u7684\u5976\u725b\uff0c\u672c\u9898\u4e0d\u7528\u8f93\u51fa\uff0c\u5176\u4ed6\u9898\u6709\u53ef\u80fd\u7528\r\n    cout << ans<< endl;\r\n    \/\/system(\"pause\");\r\n    return 0;\r\n    fin.close();\r\n    fout.close();\r\n    }\r\n<\/pre>\n
      \u53e6\u5916,\u6700\u5c0f\u70b9\u96c6\u8986\u76d6\u95ee\u9898\u5176\u5b9e\u76f8\u5f53\u4e8e\u4e8c\u5206\u56fe\u6700\u5927\u5339\u914d\u95ee\u9898,\u8bc1\u660e\u89c1Matrix67 \u535a\u5ba2\u4e8c\u5206\u56fe\u6700\u5927\u5339\u914d\u7684König\u5b9a\u7406\u53ca\u5176\u8bc1\u660e<\/a><\/p>\n
      \u4f8b\u9898:POJ3041<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
      \u53e6\u5916,\u6700\u5c0f\u70b9\u96c6\u8986\u76d6\u95ee\u9898\u5176\u5b9e\u76f8\u5f53\u4e8e\u4e8c\u5206\u56fe\u6700\u5927\u5339\u914d\u95ee\u9898,\u8bc1\u660e\u89c1Matrix67 \u535a\u5ba2\u4e8c\u5206\u56fe\u6700\u5927\u5339\u914d\u7684König\u5b9a\u7406\u53ca\u5176\u8bc1\u660e<\/a><\/p>\n
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