{"id":2926,"date":"2022-03-15T10:47:47","date_gmt":"2022-03-15T02:47:47","guid":{"rendered":"http:\/\/139.9.1.231\/?p=2926"},"modified":"2022-03-15T10:47:48","modified_gmt":"2022-03-15T02:47:48","slug":"dijkstra","status":"publish","type":"post","link":"http:\/\/139.9.1.231\/index.php\/2022\/03\/15\/dijkstra\/","title":{"rendered":"dijkstra\u7b97\u6cd5\u6c42\u6700\u77ed\u8def\u5f84"},"content":{"rendered":"\n

\u57fa\u672c\u601d\u60f3<\/strong><\/h2>\n\n\n\n

dijkstra\u7684\u7b97\u6cd5\u601d\u60f3<\/code>\u662f\u4ece\u4ee5\u4e0a\u6700\u77ed\u8ddd\u79bb\u6570\u7ec4\u4e2d\u6bcf\u6b21\u9009\u62e9\u4e00\u4e2a\u6700\u8fd1\u7684\u70b9\uff0c\u5c06\u5176\u4f5c\u4e3a\u4e0b\u4e00\u4e2a\u70b9\uff0c\u7136\u540e\u91cd\u65b0\u8ba1\u7b97\u4ece\u8d77\u59cb\u70b9\u7ecf\u8fc7\u8be5\u70b9\u5230\u5176\u4ed6\u6240\u6709\u70b9\u7684\u8ddd\u79bb\uff0c\u66f4\u65b0\u6700\u77ed\u8ddd\u79bb\u6570\u636e\u3002\u5df2\u7ecf\u9009\u53d6\u8fc7\u7684\u70b9\u5c31\u662f\u786e\u5b9a\u4e86\u6700\u77ed\u8def\u5f84\u7684\u70b9\uff0c\u4e0d\u518d\u53c2\u4e0e\u4e0b\u4e00\u6b21\u8ba1\u7b97\u3002<\/p>\n\n\n\n

  1. \u901a\u8fc7Dijkstra\u8ba1\u7b97\u56feG\u4e2d\u7684\u6700\u77ed\u8def\u5f84\u65f6\uff0c\u9700\u8981\u6307\u5b9a\u8d77\u70b9s(\u5373\u4ece\u9876\u70b9s\u5f00\u59cb\u8ba1\u7b97)\u3002<\/li>
  2. \u6b64\u5916\uff0c\u5f15\u8fdb\u4e24\u4e2a\u96c6\u5408S\u548cU\u3002S\u7684\u4f5c\u7528\u662f\u8bb0\u5f55\u5df2\u6c42\u51fa\u6700\u77ed\u8def\u5f84\u7684\u9876\u70b9(\u4ee5\u53ca\u76f8\u5e94\u7684\u6700\u77ed\u8def\u5f84\u957f\u5ea6)\uff0c\u800cU\u5219\u662f\u8bb0\u5f55\u8fd8\u672a\u6c42\u51fa\u6700\u77ed\u8def\u5f84\u7684\u9876\u70b9(\u4ee5\u53ca\u8be5\u9876\u70b9\u5230\u8d77\u70b9s\u7684\u8ddd\u79bb)\u3002<\/li>
  3. \u521d\u59cb\u65f6\uff0cS\u4e2d\u53ea\u6709\u8d77\u70b9s\uff1bU\u4e2d\u662f\u9664s\u4e4b\u5916\u7684\u9876\u70b9\uff0c\u5e76\u4e14U\u4e2d\u9876\u70b9\u7684\u8def\u5f84\u662f\u201d\u8d77\u70b9s\u5230\u8be5\u9876\u70b9\u7684\u8def\u5f84\u201d\u3002\u7136\u540e\uff0c\u4eceU\u4e2d\u627e\u51fa\u8def\u5f84\u6700\u77ed\u7684\u9876\u70b9\uff0c\u5e76\u5c06\u5176\u52a0\u5165\u5230S\u4e2d\uff1b\u63a5\u7740\uff0c\u66f4\u65b0U\u4e2d\u7684\u9876\u70b9\u548c\u9876\u70b9\u5bf9\u5e94\u7684\u8def\u5f84\u3002 \u7136\u540e\uff0c\u518d\u4eceU\u4e2d\u627e\u51fa\u8def\u5f84\u6700\u77ed\u7684\u9876\u70b9\uff0c\u5e76\u5c06\u5176\u52a0\u5165\u5230S\u4e2d\uff1b\u63a5\u7740\uff0c\u66f4\u65b0U\u4e2d\u7684\u9876\u70b9\u548c\u9876\u70b9\u5bf9\u5e94\u7684\u8def\u5f84\u3002 \u2026 \u91cd\u590d\u8be5\u64cd\u4f5c\uff0c\u76f4\u5230\u904d\u5386\u5b8c\u6240\u6709\u9876\u70b9\u3002<\/li><\/ol>\n\n\n\n

    \u64cd\u4f5c\u6b65\u9aa4<\/strong><\/h2>\n\n\n\n
    1. \u521d\u59cb\u65f6\uff0cS\u53ea\u5305\u542b\u8d77\u70b9s\uff1bU\u5305\u542b\u9664s\u5916\u7684\u5176\u4ed6\u9876\u70b9\uff0c\u4e14U\u4e2d\u9876\u70b9\u7684\u8ddd\u79bb\u4e3a\u201d\u8d77\u70b9s\u5230\u8be5\u9876\u70b9\u7684\u8ddd\u79bb\u201d[\u4f8b\u5982\uff0cU\u4e2d\u9876\u70b9v\u7684\u8ddd\u79bb\u4e3a(s,v)\u7684\u957f\u5ea6\uff0c\u7136\u540es\u548cv\u4e0d\u76f8\u90bb\uff0c\u5219v\u7684\u8ddd\u79bb\u4e3a\u221e]\u3002<\/li>
    2. \u4eceU\u4e2d\u9009\u51fa\u201d\u8ddd\u79bb\u6700\u77ed\u7684\u9876\u70b9k\u201d\uff0c\u5e76\u5c06\u9876\u70b9k\u52a0\u5165\u5230S\u4e2d\uff1b\u540c\u65f6\uff0c\u4eceU\u4e2d\u79fb\u9664\u9876\u70b9k\u3002<\/li>
    3. \u66f4\u65b0U\u4e2d\u5404\u4e2a\u9876\u70b9\u5230\u8d77\u70b9s\u7684\u8ddd\u79bb\u3002\u4e4b\u6240\u4ee5\u66f4\u65b0U\u4e2d\u9876\u70b9\u7684\u8ddd\u79bb\uff0c\u662f\u7531\u4e8e\u4e0a\u4e00\u6b65\u4e2d\u786e\u5b9a\u4e86k\u662f\u6c42\u51fa\u6700\u77ed\u8def\u5f84\u7684\u9876\u70b9\uff0c\u4ece\u800c\u53ef\u4ee5\u5229\u7528k\u6765\u66f4\u65b0\u5176\u5b83\u9876\u70b9\u7684\u8ddd\u79bb\uff1b\u4f8b\u5982\uff0c(s,v)\u7684\u8ddd\u79bb\u53ef\u80fd\u5927\u4e8e(s,k)+(k,v)\u7684\u8ddd\u79bb\u3002<\/li>
    4. \u91cd\u590d\u6b65\u9aa4(2)\u548c(3)\uff0c\u76f4\u5230\u904d\u5386\u5b8c\u6240\u6709\u9876\u70b9\u3002<\/li><\/ol>\n\n\n\n
      \"\"<\/figure>\n\n\n\n

      \u7b2c1\u6b65\uff1a\u521d\u59cb\u5316\u8ddd\u79bb\uff0c\u5176\u5b9e\u6307\u4e0eD\u76f4\u63a5\u8fde\u63a5\u7684\u70b9\u7684\u8ddd\u79bb\u3002dis[c]\u4ee3\u8868D\u5230C\u70b9\u7684\u6700\u77ed\u8ddd\u79bb\uff0c\u56e0\u800c\u521d\u59cbdis[C]=3\uff0cdis[E]=4\uff0cdis[D]=0\uff0c\u5176\u4f59\u4e3a\u65e0\u7a77\u5927\u3002\u8bbe\u7f6e\u96c6\u5408S<\/strong>\u7528\u6765\u8868\u793a\u5df2\u7ecf\u627e\u5230\u7684\u6700\u77ed\u8def\u5f84\u3002\u6b64\u65f6\uff0cS={D}\u3002\u73b0\u5728\u5f97\u5230D\u5230\u5404\u70b9\u8ddd\u79bb{D(0)\uff0cC(3)\uff0cE\uff084\uff09\uff0cF\uff08*\uff09\uff0cG\uff08*\uff09\uff0cB\uff08*\uff09\uff0cA(*)}<\/strong>\uff0c\u5176\u4e2d*\u4ee3\u8868\u672a\u77e5\u6570\u4e5f\u53ef\u4ee5\u8bf4\u662f\u65e0\u7a77\u5927\uff0c\u62ec\u53f7\u91cc\u9762\u7684\u6570\u503c\u4ee3\u8868D\u70b9\u5230\u8be5\u70b9\u7684\u6700\u77ed\u8ddd\u79bb\u3002<\/p>\n\n\n\n

      \u7b2c2\u6b65\uff1a\u4e0d\u8003\u8651\u96c6\u5408S\u4e2d\u7684\u503c\uff0c\u56e0\u4e3adis[C]=3\uff0c\u662f\u5f53\u4e2d\u8ddd\u79bb\u6700\u77ed\u7684\uff0c\u6240\u4ee5\u6b64\u65f6\u66f4\u65b0S\uff0cS={D,C}<\/strong>\u3002\u63a5\u7740\u6211\u4eec\u770b\u4e0eC\u8fde\u63a5\u7684\u70b9\uff0c\u5206\u522b\u6709B\uff0cE\uff0cF\uff0c\u5df2\u7ecf\u5728\u96c6\u5408S\u4e2d\u7684\u4e0d\u770b<\/strong>\uff0cdis[C-B]=10\uff0c\u56e0\u800cdis[B]=dis[C]+10=13\uff0cdis[F]=dis[C]+dis[C-F]=9\uff0cdis[E]=dis[C]+dis[C-E]=3+5=8>4(\u521d\u59cb\u5316\u65f6\u7684dis[E]=4)<\/strong>\u4e0d\u66f4\u65b0\u3002\u6b64\u65f6{D(0)\uff0cC(3)\uff0cE\uff084\uff09\uff0cF\uff089\uff09\uff0cG\uff08*\uff09\uff0cB\uff0813\uff09\uff0cA(*)}\u3002<\/strong><\/p>\n\n\n\n

      \u7b2c3\u6b65\uff1a\u5728\u7b2c2\u6b65\u4e2d\uff0cE\u70b9\u7684\u503c4\u6700\u5c0f\uff0c\u66f4\u65b0S={D\uff0cC\uff0cE}<\/strong>\uff0c\u6b64\u65f6\u770b\u4e0eE\u70b9\u76f4\u63a5\u8fde\u63a5\u7684\u70b9\uff0c\u5206\u522b\u6709F\uff0cG\u3002dis[F]=dis[E]+dis[E-F]=4+2=6\uff08\u6bd4\u539f\u6765\u7684\u503c\u5c0f\uff0c\u5f97\u5230\u66f4\u65b0<\/strong>\uff09\uff0cdis[G]=dis[E]+dis[E-G]=4+8=12\uff08\u66f4\u65b0<\/strong>\uff09\u3002\u6b64\u65f6{D(0)\uff0cC(3)\uff0cE\uff084\uff09\uff0cF\uff086\uff09\uff0cG\uff0812\uff09\uff0cB\uff0813\uff09\uff0cA(*)}<\/strong>\u3002<\/p>\n\n\n\n

      \u7b2c4\u6b65\uff1a\u5728\u7b2c3\u6b65\u4e2d\uff0cF\u70b9\u7684\u503c6\u6700\u5c0f\uff0c\u66f4\u65b0S={D\uff0cC\uff0cE\uff0cF}<\/strong>\uff0c\u6b64\u65f6\u770b\u4e0eF\u70b9\u76f4\u63a5\u8fde\u63a5\u7684\u70b9\uff0c\u5206\u522b\u6709B\uff0cA\uff0cG\u3002dis[B]=dis[F]+dis[F-B]=6+7=13\uff0cdis[A]=dis[F]+dis[F-A]=6+16=22\uff0cdis[G]=dis[F]+dis[F-G]=6+9=15>12\uff08\u4e0d\u66f4\u65b0<\/strong>\uff09\u3002\u6b64\u65f6{D(0)\uff0cC(3)\uff0cE\uff084\uff09\uff0cF\uff086\uff09\uff0cG\uff0812\uff09\uff0cB\uff0813\uff09\uff0cA(22)}.<\/strong><\/p>\n\n\n\n

      \u7b2c5\u6b65\uff1a\u5728\u7b2c4\u6b65\u4e2d\uff0cG\u70b9\u7684\u503c12\u6700\u5c0f\uff0c\u66f4\u65b0S={D\uff0cC\uff0cE\uff0cF\uff0cG}<\/strong>\uff0c\u6b64\u65f6\u770b\u4e0eG\u70b9\u76f4\u63a5\u8fde\u63a5\u7684\u70b9\uff0c\u53ea\u6709A\u3002dis[A]=dis[G]+dis[G-A]=12+14=26>22(\u4e0d\u66f4\u65b0<\/strong>)\u3002{D(0)\uff0cC(3)\uff0cE\uff084\uff09\uff0cF\uff086\uff09\uff0cG\uff0812\uff09\uff0cB\uff0813\uff09\uff0cA(22)}.<\/strong><\/p>\n\n\n\n

      \u7b2c6\u6b65\uff1a\u5728\u7b2c5\u6b65\u4e2d\uff0cB\u70b9\u7684\u503c13\u6700\u5c0f\uff0c\u66f4\u65b0S={D\uff0cC\uff0cE\uff0cF\uff0cG\uff0cB}<\/strong>\uff0c\u6b64\u65f6\u770b\u4e0eB\u70b9\u76f4\u63a5\u8fde\u63a5\u7684\u70b9\uff0c\u53ea\u6709A\u3002dis[A]=dis[B]+dis[B-A]=13+12=25>22(\u4e0d\u66f4\u65b0<\/strong>)\u3002{D(0)\uff0cC(3)\uff0cE\uff084\uff09\uff0cF\uff086\uff09\uff0cG\uff0812\uff09\uff0cB\uff0813\uff09\uff0cA(22)}.<\/strong><\/p>\n\n\n\n

      \u7b2c6\u6b65\uff1a\u6700\u540e\u53ea\u5269\u4e0bA\u503c\uff0c\u76f4\u63a5\u8fdb\u5165\u96c6\u5408S={D\uff0cC\uff0cE\uff0cF\uff0cG\uff0cB\uff0cA}<\/strong>\uff0c\u6b64\u65f6\u6240\u6709\u7684\u70b9\u90fd\u5df2\u7ecf\u904d\u5386\u7ed3\u675f\uff0c\u5f97\u5230\u6700\u7ec8\u7ed3\u679c{D(0)\uff0cC(3)\uff0cE\uff084\uff09\uff0cF\uff086\uff09\uff0cG\uff0812\uff09\uff0cB\uff0813\uff09\uff0cA(22)}.<\/strong><\/p>\n\n\n\n

      python\u5b9e\u73b0\uff1a<\/h2>\n\n\n\n

      \u5c06\u4ee5\u4e0a\u7684\u8fc7\u7a0b\u4f7f\u7528python\u6765\u5b9e\u73b0\u3002
      \u9996\u5148\u603b\u7ed3\u4e00\u4e2aDijkstra\u7b97\u6cd5\u7684\u6838\u5fc3\u601d\u60f3\uff0c\u5206\u6210\u4e24\u6b65\u8d70\uff1a<\/p>\n\n\n\n

      1. \u6784\u9020\u4e00\u4e2a\u6700\u77ed\u8def\u5f84\u6570\u7ec4\uff0c\u6bcf\u6b21\u627e\u5230\u6570\u7ec4\u4e2d\u672a\u8bbf\u95ee\u7684\u8282\u70b9\u91cc\u6700\u5c0f\u7684\u70b9<\/li>
      2. \u4ee5\u4e0a\u4e00\u6b65\u7684\u8282\u70b9\u4e3a\u6700\u65b0\u8282\u70b9\uff0c\u66f4\u65b0\u8d77\u59cb\u70b9\u5230\u6240\u6709\u70b9\u7684\u8ddd\u79bb<\/li><\/ol>\n\n\n\n

        \u4f7f\u7528python\u5c31\u662f\u5b9e\u73b0\u8fd9\u4e24\u6b65\u5373\u53ef<\/p>\n\n\n\n

        \n\r\nMAX= float('inf')\r\n\r\nmatrix = [\r\n    [0,10,MAX,4,MAX,MAX],\r\n    [10,0,8,2,6,MAX],\r\n    [MAX,8,10,15,1,5],\r\n    [4,2,15,0,6,MAX],\r\n    [MAX,6,1,6,0,12],\r\n    [MAX,MAX,5,MAX,12,0]\r\n    ]\r\n\r\n\r\ndef dijkstra(matrix, start_node):\r\n    \r\n    #\u77e9\u9635\u4e00\u7ef4\u6570\u7ec4\u7684\u957f\u5ea6\uff0c\u5373\u8282\u70b9\u7684\u4e2a\u6570\r\n    matrix_length = len(matrix)\r\n\r\n    #\u8bbf\u95ee\u8fc7\u7684\u8282\u70b9\u6570\u7ec4\r\n    used_node = [False] * matrix_length\r\n\r\n    #\u6700\u77ed\u8def\u5f84\u8ddd\u79bb\u6570\u7ec4\r\n    distance = [MAX] * matrix_length\r\n\r\n    #\u521d\u59cb\u5316\uff0c\u5c06\u8d77\u59cb\u8282\u70b9\u7684\u6700\u77ed\u8def\u5f84\u4fee\u6539\u62100\r\n    distance[start_node] = 0\r\n    \r\n    #\u5c06\u8bbf\u95ee\u8282\u70b9\u4e2d\u672a\u8bbf\u95ee\u7684\u4e2a\u6570\u4f5c\u4e3a\u5faa\u73af\u503c\uff0c\u5176\u5b9e\u4e5f\u53ef\u4ee5\u7528\u4e2a\u70b9\u957f\u5ea6\u4ee3\u66ff\u3002\r\n    while used_node.count(False):\r\n        min_value = float('inf')\r\n        min_value_index = 999\r\n        \r\n        #\u5728\u6700\u77ed\u8def\u5f84\u8282\u70b9\u4e2d\u627e\u5230\u6700\u5c0f\u503c\uff0c\u5df2\u7ecf\u8bbf\u95ee\u8fc7\u7684\u4e0d\u5728\u53c2\u4e0e\u5faa\u73af\u3002\r\n        #\u5f97\u5230\u6700\u5c0f\u503c\u4e0b\u6807\uff0c\u6bcf\u5faa\u73af\u4e00\u6b21\u80af\u5b9a\u6709\u4e00\u4e2a\u6700\u5c0f\u503c\r\n        for index in range(matrix_length):\r\n            if not used_node[index] and distance[index] < min_value:\r\n                min_value = distance[index]\r\n                min_value_index = index\r\n        \r\n        #\u5c06\u8bbf\u95ee\u8282\u70b9\u6570\u7ec4\u5bf9\u5e94\u7684\u503c\u4fee\u6539\u6210True\uff0c\u6807\u5fd7\u5176\u5df2\u7ecf\u8bbf\u95ee\u8fc7\u4e86\r\n        used_node[min_value_index] = True\r\n\r\n        #\u66f4\u65b0distance\u6570\u7ec4\u3002\r\n        #\u4ee5B\u70b9\u4e3a\u4f8b\uff1adistance[x] \u8d77\u59cb\u70b9\u8fbe\u5230B\u70b9\u7684\u8ddd\u79bb\uff0c\r\n        #distance[min_value_index] + matrix[min_value_index][index] \u662f\u8d77\u59cb\u70b9\u7ecf\u8fc7\u67d0\u70b9\u8fbe\u5230B\u70b9\u7684\u8ddd\u79bb\uff0c\u6bd4\u8f83\u4e24\u4e2a\u503c\uff0c\u53d6\u8f83\u5c0f\u7684\u90a3\u4e2a\u3002\r\n        for index in range(matrix_length):\r\n            distance[index] = min(distance[index], distance[min_value_index] + matrix[min_value_index][index])\r\n\r\n    return distance\r\n\r\n\r\n\r\n\r\nstart_node = int(input('\u8bf7\u8f93\u5165\u8d77\u59cb\u8282\u70b9:'))\r\nresult = dijkstra(matrix,start_node)\r\nprint('\u8d77\u59cb\u8282\u70b9\u5230\u5176\u4ed6\u70b9\u8ddd\u79bb\uff1a%s' % result)<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
        \u57fa\u672c\u601d\u60f3 dijkstra\u7684\u7b97\u6cd5\u601d\u60f3\u662f\u4ece\u4ee5\u4e0a\u6700\u77ed\u8ddd\u79bb\u6570\u7ec4\u4e2d\u6bcf\u6b21\u9009\u62e9\u4e00\u4e2a\u6700\u8fd1\u7684\u70b9\uff0c\u5c06\u5176\u4f5c\u4e3a\u4e0b\u4e00\u4e2a\u70b9\uff0c\u7136\u540e\u91cd\u65b0\u8ba1\u7b97 … \u7ee7\u7eed\u9605\u8bfbdijkstra\u7b97\u6cd5\u6c42\u6700\u77ed\u8def\u5f84<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[6,8],"tags":[],"_links":{"self":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/2926"}],"collection":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/comments?post=2926"}],"version-history":[{"count":7,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/2926\/revisions"}],"predecessor-version":[{"id":2934,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/2926\/revisions\/2934"}],"wp:attachment":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/media?parent=2926"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/categories?post=2926"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/tags?post=2926"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}