{"id":1400,"date":"2025-07-31T22:18:26","date_gmt":"2025-07-31T14:18:26","guid":{"rendered":"http:\/\/heqiwei.cn\/?p=1400"},"modified":"2025-07-31T22:18:27","modified_gmt":"2025-07-31T14:18:27","slug":"%e6%95%b0%e5%ad%a6%e5%bb%ba%e6%a8%a1-%e7%bd%91%e7%bb%9c%e6%9c%80%e5%a4%a7%e6%b5%81%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"https:\/\/heqiwei.cn\/index.php\/2025\/07\/31\/%e6%95%b0%e5%ad%a6%e5%bb%ba%e6%a8%a1-%e7%bd%91%e7%bb%9c%e6%9c%80%e5%a4%a7%e6%b5%81%e9%97%ae%e9%a2%98\/","title":{"rendered":"\u6570\u5b66\u5efa\u6a21\u2014\u2014\u7f51\u7edc\u6700\u5927\u6d41\u95ee\u9898"},"content":{"rendered":"\n

\u6d41\u91cf\u56fe\u7684\u57fa\u672c\u6982\u5ff5<\/h2>\n\n\n\n

\u8bbe\u6709\u5411\u56fe [math] D = (V, A, C)[\/math]<\/p>\n\n\n\n

\"\"<\/div><\/figure>\n\n\n\n

\u5176\u4e2d[math] C_{ij} \\geqslant 0 [\/math] \u4e3a\u5bb9\u91cf\uff0c[math] C_{ij} \\in C [\/math]\uff0c\u901a\u8fc7\u5f27 [math](V_i, V_j)[\/math] \u7684\u6d41\u7684\u6570\u91cf\u79f0\u4e3a\u6d41\u91cf\uff0c\u8bb0\u4f5c [math] x_{ij}[\/math]\uff0c\u6240\u6709\u5f27\u4e0a\u6d41\u91cf\u7684\u96c6\u5408 [math]{x_{ij}}[\/math] \u79f0\u4e3a\u7f51\u7edc [math] D [\/math] \u7684\u4e00\u4e2a\u6d41\uff0c\u6807\u6ce8\u4e86\u6d41\u91cf\u548c\u5bb9\u91cf\u7684\u6709\u5411\u56fe\u79f0\u4e3a\u6d41\u91cf\u56fe\u3002<\/p>\n\n\n\n

    \n
  • \u53d1\u70b9\uff1a\u4ec5\u6709\u51fa\u5f27\u7684\u70b9<\/li>\n\n\n\n
  • \u6536\u70b9\uff1a\u4ec5\u6709\u5165\u5f27\u7684\u70b9<\/li>\n\n\n\n
  • \u4e2d\u95f4\u70b9\uff1a\u9664\u4e86\u53d1\u70b9\u548c\u6536\u70b9\u4e4b\u5916\u7684\u70b9\uff0c\u79f0\u4e3a\u4e2d\u95f4\u70b9<\/li>\n<\/ul>\n\n\n\n

    \u6700\u5927\u6d41\u4e0e\u589e\u5e7f\u94fe<\/h2>\n\n\n\n

    \u5bf9\u4e8e\u6bcf\u4e00\u6761\u5f27[math]
    \\begin {cases}
    \\text {\u524d\u5411\u5f27\uff1a\u627e\u90a3\u4e9b\u8fd8\u53ef\u4ee5\u589e\u52a0\u6d41\u91cf\u7684\u5f27} \\\\
    \\text {\u53cd\u5411\u5f27\uff1a\u627e\u90a3\u4e9b\u53ef\u4ee5\u51cf\u5c11\u6d41\u91cf\u7684\u5f27}
    \\end {cases}
    [\/math]\uff0c\u6ce8\u610f\u5728\u6539\u53d8\u5f27\u540e\u4ecd\u8981\u6ee1\u8db3 [math] 0 \\leqslant x_{ij} \\leqslant C_{ij}[\/math]\u3002<\/p>\n\n\n

    \n
    \"\"<\/div><\/figure>\n<\/div>\n\n\n

    \u82e5\u4ece [math] V_s [\/math] \u589e\u52a0 1 \u4e2a\u5355\u4f4d\uff0c\u5373 [math]\\Delta = 1 [\/math]\uff0c\u89c2\u5bdf\u53ef\u53d1\u73b0\uff0c\u6240\u6709\u7684\u524d\u5411\u5f27\u4e0a\u7684\u6d41\u91cf [math]+1 [\/math]\uff0c\u800c\u6240\u6709\u7684\u53cd\u5411\u5f27\u4e0a\u7684\u6d41\u91cf [math]-1 [\/math]\u3002<\/p>\n\n\n\n

    \u5f53\u6211\u4eec\u80fd\u591f\u627e\u5230\u4e00\u6761\u589e\u5e7f\u94fe\u5c31\u8bf4\u660e\u5f53\u524d\u8fd8\u6709\u4f18\u5316\u7684\u7a7a\u95f4\u3002\u6362\u8a00\u4e4b\uff0c\u53ef\u884c\u6d41[math]x[\/math]\u662f\u6700\u5927\u6d41\u7684\u5145\u5206\u5fc5\u8981<\/strong>\u6761\u4ef6\u662f\uff1a\u4e0d\u5b58\u5728\u4ece[math]V_s[\/math]\u5230[math]V_t[\/math]\u7684\u5173\u4e8e\u6d41[math]x[\/math]\u7684\u4e00\u6761\u589e\u5e7f\u94fe<\/mark>\u3002<\/p>\n\n\n\n

    \u6700\u5927\u6d41\u89e3\u6cd5\u2014\u2014Ford Fulkerson\u7b97\u6cd5<\/h2>\n\n\n\n

    \u4f8b 1. \u67d0\u5730\u533a\u7684\u8f93\u6cb9\u7f51\u7edc\u548c\u73b0\u6709\u7684\u8f93\u6cb9\u8ba1\u5212 (\u521d\u59cb\u6d41) \u5982\u56fe\u6240\u793a\uff0c\u95ee (1) \u73b0\u6709\u7684\u8f93\u6cb9\u91cf\u662f\u591a\u5c11\uff1f(2) \u8f93\u6cb9\u91cf\u662f\u5426\u53ef\u4ee5\u589e\u52a0\uff0c\u82e5\u80fd\u589e\u52a0\uff0c\u8bf7\u7ed9\u51fa\u6700\u5927\u8f93\u6cb9\u91cf\u3002<\/p>\n\n\n

    \n
    \"\"<\/div><\/figure>\n<\/div>\n\n\n

    \u7b97\u6cd5\u601d\u8def\uff1a<\/mark><\/strong><\/p>\n\n\n\n

    \u6211\u4eec\u5bf9\u4e8e\u9664\u53d1\u70b9\u5916\u7684\u4efb\u610f\u4e00\u4e2a\u9876\u70b9 [math] V_j [\/math] \u8bb0\u4f5c\u6807\u53f7 [math](+V_i, \\Delta_j)[\/math]\uff0c\u5728\u8fd9\u91cc\u7528\u2018[math]+[\/math]\u2019\u8868\u793a\u524d\u5411\u5f27\uff0c\u7528\u2018[math]-[\/math]\u2019\u8868\u793a\u53cd\u5411\u5f27\uff0c[math]\\Delta_j [\/math] \u8868\u793a\u6539\u53d8\u91cf\uff0c\u5bf9\u4e8e\u53d1\u70b9 [math] V_s [\/math] \u6211\u4eec\u5219\u76f4\u63a5\u8bb0\u4f5c [math](0, +\\infty)[\/math]\uff0c\u5373\u5047\u5b9a\u4ece\u539f\u70b9\u6709\u6e90\u6e90\u4e0d\u65ad\u7684\u8f93\u5165\u3002<\/p>\n\n\n\n

    \u5bf9\u4e8e\u6240\u7ed9\u7684\u6d41\u91cf\u56fe\uff0c\u6211\u4eec\u5bf9\u9f50\u8fdb\u884c\u5982\u4e0b\u6b65\u9aa4\u7684\u6807\u53f7\u548c\u8c03\u6574\uff1a<\/p>\n\n\n\n

      \n
    1. \u7ed9\u53d1\u70b9 [math] V_s [\/math] \u6807\u53f7 [math](0, +\\infty)[\/math]<\/li>\n\n\n\n
    2. \u53d6\u4e00\u4e2a\u5df2\u6807\u53f7\u7684\u70b9 [math] V_i [\/math]\uff0c\u5bf9\u4e8e [math] V_i [\/math] \u4e00\u5207\u672a\u6807\u53f7\u7684\u90bb\u63a5\u70b9 [math] V_j [\/math] \u6309\u4e0b\u5217\u89c4\u5219\u5904\u7406\n
        \n
      • \u5982\u679c\u6709\u5f27 [math](V_i, V_j) \\in A [\/math] \u4e14 [math] 0 \\leqslant x_{ij} \\leqslant C_{ij}[\/math]\uff0c\u90a3\u4e48\u7ed9 [math] V_j [\/math] \u6807\u53f7 [math](+V_i, \\Delta_j)[\/math]\uff0c\u5176\u4e2d\u589e\u91cf [math]\\Delta_j = \\min \\{C_{ij} – x_{ij}, \\Delta_i\\}[\/math]\u3002<\/li>\n\n\n\n
      • \u5982\u679c\u6709\u5f27 [math](V_j, V_i) \\in A [\/math] \u4e14 [math] 0 \\leqslant x_{ij} \\leqslant C_{ij}[\/math]\uff0c\u90a3\u4e48\u7ed9 [math] V_j [\/math] \u6807\u53f7 [math](-V_i, \\Delta_j)[\/math]\uff0c\u5176\u4e2d\u589e\u91cf [math]\\Delta_j = \\min \\{x_{ij}, \\Delta_i\\}[\/math]\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • \u91cd\u590d\u6b65\u9aa4 2\uff0c\u76f4\u5230 [math] V_t [\/math] \u88ab\u6807\u53f7\u6216\u6807\u53f7\u8fc7\u7a0b\u65e0\u6cd5\u8fdb\u884c\u4e0b\u53bb\u3002\u82e5 [math] V_t [\/math] \u88ab\u6807\u8bb0\uff0c\u5219\u6709\u4e00\u6761\u589e\u5e7f\u94fe\uff0c\u8f6c\u8c03\u6574\u8fc7\u7a0b<\/mark>\uff1b
        \u82e5 [math] V_t [\/math] \u672a\u88ab\u6807\u8bb0\uff0c\u800c\u8fc7\u7a0b\u65e0\u6cd5\u8fdb\u884c\u4e0b\u53bb\uff0c\u8fd9\u65f6\u53ef\u884c\u6d41\u5c31\u662f\u6700\u5927\u6d41\u3002<\/li>\n<\/ol>\n\n\n\n

        \u4e0a\u8ff0\u6b65\u9aa4\u63d0\u5230\u7684\u8c03\u6574\u8fc7\u7a0b<\/mark>\u5982\u4e0b\uff1a<\/p>\n\n\n\n

        \u8bbe\uff1a[math]\\Delta_1 = \\min\\{ C_{ij} – x_{ij}, \\Delta_i \\mid (V_i, V_j) \\in \\text {\u94fe} u \\text {\u7684\u524d\u5411\u5f27} \\}[\/math]
        [math]\\Delta_2 = \\min\\{ x_{ij}, \\Delta_i \\mid (V_j, V_i) \\in \\text {\u94fe} u \\text {\u7684\u540e\u5411\u5f27} \\}[\/math]
        [math]\\Delta = \\min\\{ \\Delta_1, \\Delta_2 \\}[\/math]<\/p>\n\n\n\n

          \n
        1. \u4ee4[math]
          x_{ij} =
          \\begin {cases}
          x_{ij} + \\Delta, & \\text {\u94fe} u \\text {\u7684\u524d\u5411\u5f27} \\\\
          x_{ij} – \\Delta, & \\text {\u94fe} u \\text {\u7684\u540e\u5411\u5f27} \\\\
          x_{ij}, & \\text {\u5f27} \\notin \\text {\u94fe} u
          \\end {cases}
          [\/math]<\/li>\n\n\n\n
        2. \u53bb\u6389\u6240\u6709\u6807\u53f7\uff0c\u56de\u5230\u7b2c\u4e00\u6b65\uff0c\u5bf9\u53ef\u884c\u6d41\u8fdb\u884c\u91cd\u65b0\u6807\u53f7\u3002<\/li>\n<\/ol>\n\n\n\n

          \u5bf9\u4e8e\u672c\u9898\uff0c\u5b9e\u9645\u89e3\u9898\u6b65\u9aa4\u5982\u4e0b\uff1a<\/strong><\/p>\n\n\n\n

          \u7b2c\u4e00\u8f6e\u6807\u53f7\uff1a
          <\/strong><\/p>\n\n\n

          \n
          \"\"<\/div><\/figure>\n<\/div>\n\n\n

          \u6b64\u65f6\u6536\u70b9 [math] V_t [\/math] \u88ab\u6807\u53f7\uff0c\u627e\u5230\u4e86\u4e00\u6761\u589e\u5e7f\u94fe\u3002\u5373\u53ef\u884c\u6d41 [math] 3 + 2 + 4 = 9 [\/math] \u4e0d\u662f\u6700\u5927\u6d41\uff0c\u53ef\u589e\u52a0\u7684\u91cf\u4e3a [math]\\min (+\\infty, 1, 1, 1) = 1 [\/math]\uff0c\u589e\u52a0\u540e\u7684\u6d41\u91cf\u4e3a [math] 9 + 1 = 10 [\/math]\u3002\u4e0d\u96be\u53d1\u73b0\u8fd9\u6761\u589e\u5e7f\u94fe\u4e0a\u7684\u5f27\u90fd\u4e3a\u524d\u5411\u5f27\uff0c\u6240\u4ee5\u6700\u7ec8\u4f1a\u4f7f\u5f97\u8be5\u589e\u5e7f\u94fe\u4e0a\u7684\u6bcf\u4e00\u6761\u5f27\u90fd [math]+1 [\/math] \u3002<\/p>\n\n\n\n

          \u7b2c\u4e8c\u8f6e\u6807\u53f7\uff1a<\/strong>
          <\/p>\n\n\n

          \n
          \"\"<\/div><\/figure>\n<\/div>\n\n\n

          \u539f\u6d41\u91cf[math] 4 + 2 + 4 = 10 [\/math]\u3001\u6700\u5c0f\u6539\u53d8\u91cf[math] \\min ( +\\infty, 1, 1, 1) = 1[\/math]\u3001\u589e\u52a0\u540e\u7684\u6d41\u91cf\u4e3a[math] 10 + 1 = 11 [\/math]\u3001\u53c8\u56e0\u4e3a\u524d\u5411\u5f27\uff0c\u6545\u6bcf\u6761\u5f27[math] +1 [\/math]\u3002<\/p>\n\n\n\n

          \u7b2c\u4e09\u8f6e\u6807\u53f7\uff1a<\/strong>
          <\/p>\n\n\n

          \n
          \"\"<\/div><\/figure>\n<\/div>\n\n\n

          \u539f\u6d41\u91cf [math] 4 + 3 + 4 = 11 [\/math]\u3001\u6700\u5c0f\u6539\u53d8\u91cf [math]\\min (+\\infty, 1, 1, 1) = 1 [\/math]\u3001\u589e\u52a0\u540e\u7684\u6d41\u91cf\u4e3a [math] 11 + 1 = 12 [\/math]\u3001\u53c8\u56e0\u4e3a\u524d\u5411\u5f27\uff0c\u6545\u6bcf\u6761\u5f27 [math]+1 [\/math] \u3002<\/p>\n\n\n\n

          \u7b2c\u56db\u8f6e\u6807\u53f7\uff1a<\/strong>
          <\/p>\n\n\n

          \n
          \"\"<\/div><\/figure>\n<\/div>\n\n\n

          \u539f\u6d41\u91cf [math] 4 + 3 + 4 = 12 [\/math]\u3001\u6700\u5c0f\u6539\u53d8\u91cf [math]\\min (+\\infty, 5, 2, 2) = 2 [\/math]\u3001\u589e\u52a0\u540e\u7684\u6d41\u91cf\u4e3a [math] 12 + 2 = 14 [\/math]\u3001\u53c8\u56e0\u4e3a\u524d\u5411\u5f27\uff0c\u6545\u6bcf\u6761\u5f27 [math]+2 [\/math] \u3002<\/p>\n\n\n\n

          \u6700\u7ec8\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u6700\u5927\u6d41\u91cf\u56fe\uff1a
          <\/p>\n\n\n

          \n
          \"\"<\/div><\/figure>\n<\/div>","protected":false},"excerpt":{"rendered":"

          \u6d41\u91cf\u56fe\u7684\u57fa\u672c\u6982\u5ff5 \u8bbe\u6709\u5411\u56fe [math] D = (V, A, C)[\/math] \u5176\u4e2d[math] C_{i […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[19],"tags":[],"class_list":["post-1400","post","type-post","status-publish","format-standard","hentry","category-19"],"_links":{"self":[{"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/posts\/1400","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/comments?post=1400"}],"version-history":[{"count":46,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/posts\/1400\/revisions"}],"predecessor-version":[{"id":1455,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/posts\/1400\/revisions\/1455"}],"wp:attachment":[{"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/media?parent=1400"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/categories?post=1400"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/tags?post=1400"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}