{"id":1090140,"date":"2025-01-08T13:59:59","date_gmt":"2025-01-08T05:59:59","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1090140.html"},"modified":"2025-01-08T14:00:01","modified_gmt":"2025-01-08T06:00:01","slug":"%e5%a6%82%e4%bd%95%e7%94%a8python%e6%b1%82%e5%9b%be%e4%b8%ad%e6%9c%80%e7%9f%ad%e8%b7%af-2","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1090140.html","title":{"rendered":"\u5982\u4f55\u7528python\u6c42\u56fe\u4e2d\u6700\u77ed\u8def"},"content":{"rendered":"

\"\u5982\u4f55\u7528python\u6c42\u56fe\u4e2d\u6700\u77ed\u8def\"<\/p>\n

\u4f7f\u7528Python\u6c42\u56fe\u4e2d\u6700\u77ed\u8def\u5f84\u7684\u65b9\u6cd5\u6709\uff1aDijkstra\u7b97\u6cd5\u3001Bellman-Ford\u7b97\u6cd5\u3001Floyd-Warshall\u7b97\u6cd5\u3002<\/strong> \u5176\u4e2d\uff0cDijkstra\u7b97\u6cd5\u4ee5\u5176\u9ad8\u6548\u6027\u548c\u9002\u7528\u6027\u5e7f\u6cdb\u800c\u88ab\u5e7f\u6cdb\u4f7f\u7528\u3002\u672c\u6587\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528Dijkstra\u7b97\u6cd5\u6c42\u56fe\u4e2d\u6700\u77ed\u8def\u5f84\u3002<\/p>\n<\/p>\n

\u4e00\u3001DIJKSTRA\u7b97\u6cd5<\/p>\n<\/p>\n

Dijkstra\u7b97\u6cd5\u662f\u4e00\u79cd\u8d2a\u5fc3\u7b97\u6cd5\uff0c\u7528\u4e8e\u89e3\u51b3\u4ece\u4e00\u4e2a\u9876\u70b9\u5230\u56fe\u4e2d\u6240\u6709\u5176\u4ed6\u9876\u70b9\u7684\u6700\u77ed\u8def\u5f84\u95ee\u9898\u3002\u5b83\u9002\u7528\u4e8e\u6743\u91cd\u4e3a\u975e\u8d1f\u7684\u56fe\u3002\u4ee5\u4e0b\u662fDijkstra\u7b97\u6cd5\u7684\u8be6\u7ec6\u6b65\u9aa4\uff1a<\/p>\n<\/p>\n

    \n
  1. \u521d\u59cb\u5316<\/strong>\uff1a\u4ece\u8d77\u70b9\u5f00\u59cb\uff0c\u5c06\u8d77\u70b9\u5230\u81ea\u5df1\u7684\u8ddd\u79bb\u8bbe\u4e3a0\uff0c\u5176\u4ed6\u9876\u70b9\u7684\u8ddd\u79bb\u8bbe\u4e3a\u65e0\u7a77\u5927\u3002\u521b\u5efa\u4e00\u4e2a\u4f18\u5148\u7ea7\u961f\u5217\uff0c\u8d77\u70b9\u5165\u961f\u3002<\/li>\n
  2. \u9009\u62e9\u6700\u77ed\u8def\u5f84\u9876\u70b9<\/strong>\uff1a\u4ece\u961f\u5217\u4e2d\u9009\u62e9\u8ddd\u79bb\u6700\u8fd1\u7684\u9876\u70b9\uff0c\u4f5c\u4e3a\u5f53\u524d\u9876\u70b9\u3002<\/li>\n
  3. \u66f4\u65b0\u90bb\u5c45\u9876\u70b9\u7684\u8ddd\u79bb<\/strong>\uff1a\u5bf9\u5f53\u524d\u9876\u70b9\u7684\u6bcf\u4e00\u4e2a\u90bb\u5c45\u9876\u70b9\uff0c\u8ba1\u7b97\u4ece\u5f53\u524d\u9876\u70b9\u7ecf\u8fc7\u8be5\u90bb\u5c45\u9876\u70b9\u7684\u8def\u5f84\u957f\u5ea6\u3002\u5982\u679c\u5c0f\u4e8e\u5df2\u77e5\u7684\u6700\u77ed\u8def\u5f84\uff0c\u5219\u66f4\u65b0\u6700\u77ed\u8def\u5f84\u3002<\/li>\n
  4. \u91cd\u590d\u6b65\u9aa42\u548c3<\/strong>\uff1a\u76f4\u5230\u4f18\u5148\u7ea7\u961f\u5217\u4e3a\u7a7a\u3002<\/li>\n<\/ol>\n

    import heapq<\/p>\n
    def dijkstra(graph, start):<\/p>\n
        # \u521d\u59cb\u5316<\/p>\n
        pq = [(0, start)]  # (\u8ddd\u79bb, \u8282\u70b9)<\/p>\n
        distances = {node: float('infinity') for node in graph}<\/p>\n
        distances[start] = 0<\/p>\n
        visited = set()<\/p>\n
        while pq:<\/p>\n
            current_distance, current_node = heapq.heappop(pq)<\/p>\n
            # \u5982\u679c\u5f53\u524d\u8282\u70b9\u5df2\u7ecf\u8bbf\u95ee\u8fc7\uff0c\u8df3\u8fc7<\/p>\n
            if current_node in visited:<\/p>\n
                continue<\/p>\n
            visited.add(current_node)<\/p>\n
            # \u66f4\u65b0\u90bb\u5c45\u8282\u70b9\u7684\u8ddd\u79bb<\/p>\n
            for neighbor, weight in graph[current_node].items():<\/p>\n
                distance = current_distance + weight<\/p>\n
                if distance < distances[neighbor]:<\/p>\n
                    distances[neighbor] = distance<\/p>\n
                    heapq.heappush(pq, (distance, neighbor))<\/p>\n
        return distances<\/p>\n
    \u793a\u4f8b\u56fe<\/strong><\/h2>\n
    graph = {<\/p>\n
        'A': {'B': 1, 'C': 4},<\/p>\n
        'B': {'A': 1, 'C': 2, 'D': 5},<\/p>\n
        'C': {'A': 4, 'B': 2, 'D': 1},<\/p>\n
        'D': {'B': 5, 'C': 1}<\/p>\n
    }<\/p>\n
    print(dijkstra(graph, 'A'))<\/p>\n
    <\/code><\/pre>\n<\/p>\n
    Dijkstra\u7b97\u6cd5\u7684\u6838\u5fc3\u5728\u4e8e\u8d2a\u5fc3\u9009\u62e9\u6700\u8fd1\u7684\u9876\u70b9\uff0c\u5e76\u901a\u8fc7\u4f18\u5148\u7ea7\u961f\u5217\u4f18\u5316\u9009\u62e9\u8fc7\u7a0b\u3002<\/strong> \u8fd9\u79cd\u65b9\u6cd5\u4fdd\u8bc1\u4e86\u6bcf\u6b21\u9009\u62e9\u7684\u9876\u70b9\u90fd\u662f\u5f53\u524d\u672a\u5904\u7406\u9876\u70b9\u4e2d\u8ddd\u79bb\u8d77\u70b9\u6700\u8fd1\u7684\u3002<\/p>\n<\/p>\n
    \u4e8c\u3001BELLMAN-FORD\u7b97\u6cd5<\/p>\n<\/p>\n
    Bellman-Ford\u7b97\u6cd5\u7528\u4e8e\u89e3\u51b3\u4ece\u4e00\u4e2a\u9876\u70b9\u5230\u6240\u6709\u5176\u4ed6\u9876\u70b9\u7684\u6700\u77ed\u8def\u5f84\u95ee\u9898\uff0c\u7279\u522b\u9002\u7528\u4e8e\u56fe\u4e2d\u5305\u542b\u8d1f\u6743\u8fb9\u7684\u60c5\u51b5\u3002\u5176\u6838\u5fc3\u601d\u60f3\u662f\u901a\u8fc7\u4e0d\u65ad\u677e\u5f1b\u8fb9\u6765\u9010\u6b65\u627e\u5230\u6700\u77ed\u8def\u5f84\u3002<\/p>\n<\/p>\n
      \n
    1. \u521d\u59cb\u5316<\/strong>\uff1a\u8bbe\u5b9a\u8d77\u70b9\u5230\u81ea\u5df1\u7684\u8ddd\u79bb\u4e3a0\uff0c\u5176\u4ed6\u9876\u70b9\u8ddd\u79bb\u4e3a\u65e0\u7a77\u5927\u3002<\/li>\n
    2. \u677e\u5f1b\u8fb9<\/strong>\uff1a\u91cd\u590dV-1\u6b21\uff08V\u662f\u9876\u70b9\u6570\u91cf\uff09\uff0c\u5bf9\u4e8e\u6bcf\u4e00\u6761\u8fb9(u, v, w)\uff0c\u5982\u679cdist[u] + w < dist[v]\uff0c\u5219\u66f4\u65b0dist[v]\u3002<\/li>\n
    3. \u68c0\u6d4b\u8d1f\u6743\u73af<\/strong>\uff1a\u518d\u8fdb\u884c\u4e00\u6b21\u677e\u5f1b\uff0c\u5982\u679c\u8fd8\u80fd\u66f4\u65b0\u8ddd\u79bb\uff0c\u8bf4\u660e\u5b58\u5728\u8d1f\u6743\u73af\u3002<\/li>\n<\/ol>\n
      def bellman_ford(graph, start):<\/p>\n
          distances = {node: float('infinity') for node in graph}<\/p>\n
          distances[start] = 0<\/p>\n
          for _ in range(len(graph) - 1):<\/p>\n
              for node in graph:<\/p>\n
                  for neighbor, weight in graph[node].items():<\/p>\n
                      if distances[node] + weight < distances[neighbor]:<\/p>\n
                          distances[neighbor] = distances[node] + weight<\/p>\n
          # \u68c0\u6d4b\u8d1f\u6743\u73af<\/p>\n
          for node in graph:<\/p>\n
              for neighbor, weight in graph[node].items():<\/p>\n
                  if distances[node] + weight < distances[neighbor]:<\/p>\n
                      rAI<\/a>se ValueError("Graph contains a negative-weight cycle")<\/p>\n
          return distances<\/p>\n
      \u793a\u4f8b\u56fe<\/strong><\/h2>\n
      graph = {<\/p>\n
          'A': {'B': 1, 'C': 4},<\/p>\n
          'B': {'A': 1, 'C': 2, 'D': 5},<\/p>\n
          'C': {'A': 4, 'B': 2, 'D': 1},<\/p>\n
          'D': {'B': 5, 'C': 1}<\/p>\n
      }<\/p>\n
      print(bellman_ford(graph, 'A'))<\/p>\n
      <\/code><\/pre>\n<\/p>\n
      Bellman-Ford\u7b97\u6cd5\u7684\u4f18\u70b9\u5728\u4e8e\u80fd\u591f\u5904\u7406\u8d1f\u6743\u8fb9\uff0c\u5e76\u4e14\u53ef\u4ee5\u68c0\u6d4b\u8d1f\u6743\u73af\u3002<\/strong> \u7136\u800c\uff0c\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u8f83\u9ad8\uff0c\u4e3aO(VE)\uff0c\u4e0d\u9002\u5408\u8fb9\u5f88\u591a\u7684\u7a20\u5bc6\u56fe\u3002<\/p>\n<\/p>\n
      \u4e09\u3001FLOYD-WARSHALL\u7b97\u6cd5<\/p>\n<\/p>\n
      Floyd-Warshall\u7b97\u6cd5\u662f\u4e00\u79cd\u52a8\u6001\u89c4\u5212\u7b97\u6cd5\uff0c\u7528\u4e8e\u6c42\u89e3\u6240\u6709\u9876\u70b9\u5bf9\u4e4b\u95f4\u7684\u6700\u77ed\u8def\u5f84\u3002\u5b83\u9002\u7528\u4e8e\u7a20\u5bc6\u56fe\uff0c\u4e14\u80fd\u591f\u5904\u7406\u8d1f\u6743\u8fb9\uff0c\u4f46\u4e0d\u9002\u7528\u4e8e\u8d1f\u6743\u73af\u3002<\/p>\n<\/p>\n
        \n
      1. \u521d\u59cb\u5316<\/strong>\uff1a\u521b\u5efa\u4e00\u4e2a\u8ddd\u79bb\u77e9\u9635dist\uff0cdist[i][j]\u8868\u793a\u9876\u70b9i\u5230\u9876\u70b9j\u7684\u8ddd\u79bb\u3002\u76f4\u63a5\u76f8\u8fde\u7684\u9876\u70b9\u8ddd\u79bb\u4e3a\u8fb9\u6743\u91cd\uff0c\u5176\u4ed6\u4e3a\u65e0\u7a77\u5927\u3002<\/li>\n
      2. \u52a8\u6001\u89c4\u5212<\/strong>\uff1a\u5bf9\u4e8e\u6bcf\u4e00\u5bf9\u9876\u70b9(i, j)\uff0c\u5c1d\u8bd5\u901a\u8fc7\u4e00\u4e2a\u4e2d\u95f4\u9876\u70b9k\uff0c\u66f4\u65b0dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j])\u3002<\/li>\n<\/ol>\n
        def floyd_warshall(graph):<\/p>\n
            nodes = list(graph.keys())<\/p>\n
            dist = {node: {node: float('infinity') for node in nodes} for node in nodes}<\/p>\n
            for node in nodes:<\/p>\n
                dist[node][node] = 0<\/p>\n
                for neighbor, weight in graph[node].items():<\/p>\n
                    dist[node][neighbor] = weight<\/p>\n
            for k in nodes:<\/p>\n
                for i in nodes:<\/p>\n
                    for j in nodes:<\/p>\n
                        dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j])<\/p>\n
            return dist<\/p>\n
        \u793a\u4f8b\u56fe<\/strong><\/h2>\n
        graph = {<\/p>\n
            'A': {'B': 1, 'C': 4},<\/p>\n
            'B': {'A': 1, 'C': 2, 'D': 5},<\/p>\n
            'C': {'A': 4, 'B': 2, 'D': 1},<\/p>\n
            'D': {'B': 5, 'C': 1}<\/p>\n
        }<\/p>\n
        print(floyd_warshall(graph))<\/p>\n
        <\/code><\/pre>\n<\/p>\n
        Floyd-Warshall\u7b97\u6cd5\u7684\u4f18\u52bf\u5728\u4e8e\u7b80\u5355\u76f4\u89c2\uff0c\u80fd\u591f\u5904\u7406\u6240\u6709\u9876\u70b9\u5bf9\u4e4b\u95f4\u7684\u6700\u77ed\u8def\u5f84\u95ee\u9898\u3002<\/strong> \u7136\u800c\uff0c\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(V^3)\uff0c\u5bf9\u4e8e\u9876\u70b9\u5f88\u591a\u7684\u56fe\uff0c\u8ba1\u7b97\u91cf\u8f83\u5927\u3002<\/p>\n<\/p>\n
        \u56db\u3001\u7ed3\u8bba<\/p>\n<\/p>\n
        \u5728\u4f7f\u7528Python\u6c42\u56fe\u4e2d\u6700\u77ed\u8def\u5f84\u65f6\uff0c\u9009\u62e9\u5408\u9002\u7684\u7b97\u6cd5\u81f3\u5173\u91cd\u8981\u3002Dijkstra\u7b97\u6cd5\u9002\u7528\u4e8e\u65e0\u8d1f\u6743\u8fb9\u7684\u56fe\uff0cBellman-Ford\u7b97\u6cd5\u9002\u7528\u4e8e\u5305\u542b\u8d1f\u6743\u8fb9\u7684\u56fe\uff0cFloyd-Warshall\u7b97\u6cd5\u9002\u7528\u4e8e\u7a20\u5bc6\u56fe\u7684\u5168\u5c40\u6700\u77ed\u8def\u5f84\u95ee\u9898\u3002<\/strong> \u6839\u636e\u5177\u4f53\u95ee\u9898\u7684\u7279\u70b9\u9009\u62e9\u5408\u9002\u7684\u7b97\u6cd5\uff0c\u80fd\u591f\u6709\u6548\u63d0\u9ad8\u6c42\u89e3\u6548\u7387\u3002<\/p>\n<\/p>\n
        \u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
         \u5728Python\u4e2d\uff0c\u5982\u4f55\u4f7f\u7528\u56fe\u8bba\u5e93\u6765\u6c42\u89e3\u6700\u77ed\u8def\u5f84\u95ee\u9898\uff1f<\/strong><\/p>\n
        Python\u4e2d\u6709\u591a\u4e2a\u56fe\u8bba\u5e93\u53ef\u4ee5\u7528\u4e8e\u6c42\u89e3\u6700\u77ed\u8def\u5f84\u95ee\u9898\uff0c\u6bd4\u5982NetworkX\u548cGraph-tool\u3002\u4f7f\u7528NetworkX\u5e93\uff0c\u53ef\u4ee5\u8f7b\u677e\u5730\u6784\u5efa\u56fe\u5f62\u5e76\u4f7f\u7528\u5185\u7f6e\u7684\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\uff08\u5982Dijkstra\u7b97\u6cd5\u6216Bellman-Ford\u7b97\u6cd5\uff09\u6765\u627e\u5230\u6700\u77ed\u8def\u5f84\u3002\u9996\u5148\uff0c\u9700\u8981\u5b89\u88c5NetworkX\u5e93\uff0c\u7136\u540e\u5b9a\u4e49\u56fe\u7684\u7ed3\u6784\uff0c\u6700\u540e\u8c03\u7528\u76f8\u5e94\u7684\u51fd\u6570\u6765\u8ba1\u7b97\u6700\u77ed\u8def\u5f84\u3002<\/p>\n
        \u5728\u6c42\u89e3\u6700\u77ed\u8def\u5f84\u65f6\uff0c\u5982\u4f55\u9009\u62e9\u5408\u9002\u7684\u7b97\u6cd5\uff1f<\/strong><\/p>\n
        \u9009\u62e9\u5408\u9002\u7684\u7b97\u6cd5\u53d6\u51b3\u4e8e\u56fe\u7684\u7279\u6027\u548c\u5177\u4f53\u9700\u6c42\u3002\u4f8b\u5982\uff0c\u5982\u679c\u56fe\u662f\u7a20\u5bc6\u7684\uff0c\u53ef\u4ee5\u8003\u8651\u4f7f\u7528Floyd-Warshall\u7b97\u6cd5\uff0c\u800c\u5bf9\u4e8e\u7a00\u758f\u56fe\uff0cDijkstra\u7b97\u6cd5\u901a\u5e38\u66f4\u9ad8\u6548\u3002\u5982\u679c\u56fe\u4e2d\u6709\u8d1f\u6743\u8fb9\uff0c\u53ef\u4ee5\u4f7f\u7528Bellman-Ford\u7b97\u6cd5\u3002\u4e86\u89e3\u8fd9\u4e9b\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u548c\u9002\u7528\u573a\u666f\uff0c\u53ef\u4ee5\u5e2e\u52a9\u4f60\u505a\u51fa\u66f4\u4f18\u7684\u9009\u62e9\u3002<\/p>\n
        \u5982\u4f55\u5728Python\u4e2d\u53ef\u89c6\u5316\u6700\u77ed\u8def\u5f84\u7684\u7ed3\u679c\uff1f<\/strong><\/p>\n
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