{"id":1084373,"date":"2025-01-08T13:06:41","date_gmt":"2025-01-08T05:06:41","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1084373.html"},"modified":"2025-01-08T13:06:43","modified_gmt":"2025-01-08T05:06:43","slug":"python-%e9%82%bb%e6%8e%a5%e7%9f%a9%e9%98%b5%e5%a6%82%e4%bd%95%e8%ae%a1%e7%ae%97%e5%8f%af%e8%be%be%e7%9f%a9%e9%98%b5-2","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1084373.html","title":{"rendered":"Python \u90bb\u63a5\u77e9\u9635\u5982\u4f55\u8ba1\u7b97\u53ef\u8fbe\u77e9\u9635"},"content":{"rendered":"

\"Python<\/p>\n

\u5728Python\u4e2d\uff0c\u4f7f\u7528\u90bb\u63a5\u77e9\u9635\u6765\u8ba1\u7b97\u53ef\u8fbe\u77e9\u9635\u53ef\u4ee5\u901a\u8fc7\u591a\u79cd\u65b9\u6cd5\u5b9e\u73b0\uff0c\u6700\u4e3b\u8981\u7684\u65b9\u6cd5\u5305\u62ec\uff1a\u4f7f\u7528Floyd-Warshall\u7b97\u6cd5\u3001\u4f7f\u7528\u77e9\u9635\u5e42\u4ee5\u53ca\u4f7f\u7528\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\uff08DFS\uff09\u6216\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22\uff08BFS\uff09\u7b49\u3002<\/strong>\u5176\u4e2d\uff0cFloyd-Warshall\u7b97\u6cd5<\/strong>\u662f\u4e00\u79cd\u7ecf\u5178\u7684\u52a8\u6001\u89c4\u5212\u7b97\u6cd5\uff0c\u7528\u4e8e\u89e3\u51b3\u56fe\u7684\u5168\u5bf9\u5168\u6700\u77ed\u8def\u5f84\u95ee\u9898\uff0c\u5e76\u53ef\u4ee5\u6709\u6548\u5730\u7528\u4e8e\u8ba1\u7b97\u53ef\u8fbe\u77e9\u9635\u3002\u5177\u4f53\u5b9e\u73b0\u65f6\uff0c\u53ef\u4ee5\u901a\u8fc7Python\u7684NumPy\u5e93\u6765\u7b80\u5316\u77e9\u9635\u8fd0\u7b97\u3002\u4e0b\u9762\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u8fd9\u4e9b\u65b9\u6cd5\u3002<\/p>\n<\/p>\n

\u4e00\u3001Floyd-Warshall\u7b97\u6cd5<\/h3>\n<\/p>\n

Floyd-Warshall\u7b97\u6cd5\u662f\u4e00\u79cd\u7528\u4e8e\u8ba1\u7b97\u6240\u6709\u8282\u70b9\u5bf9\u4e4b\u95f4\u7684\u6700\u77ed\u8def\u5f84\u7684\u7b97\u6cd5\uff0c\u8fd9\u4f7f\u5f97\u5b83\u4e5f\u9002\u7528\u4e8e\u8ba1\u7b97\u53ef\u8fbe\u77e9\u9635\u3002\u7b97\u6cd5\u7684\u4e3b\u8981\u601d\u60f3\u662f\u901a\u8fc7\u52a8\u6001\u89c4\u5212\u9010\u6b65\u66f4\u65b0\u8def\u5f84\u4fe1\u606f\uff0c\u6700\u7ec8\u5f97\u5230\u53ef\u8fbe\u77e9\u9635\u3002<\/p>\n<\/p>\n

1\u3001\u7b97\u6cd5\u4ecb\u7ecd<\/h4>\n<\/p>\n

Floyd-Warshall\u7b97\u6cd5\u901a\u8fc7\u4e09\u91cd\u5faa\u73af\u9010\u6b65\u66f4\u65b0\u8def\u5f84\u4fe1\u606f\uff0c\u6838\u5fc3\u601d\u60f3\u662f\u68c0\u67e5\u6bcf\u4e00\u5bf9\u8282\u70b9 (i, j) \u662f\u5426\u901a\u8fc7\u4e2d\u95f4\u8282\u70b9 k \u53ef\u8fbe\u3002\u8bbe\u521d\u59cb\u90bb\u63a5\u77e9\u9635\u4e3a adj_matrix<\/code>\uff0c\u8282\u70b9 i \u5230 j \u7684\u8def\u5f84\u957f\u5ea6\u4e3a adj_matrix[i][j]<\/code>\u3002\u5982\u679c\u5b58\u5728\u4e00\u4e2a\u4e2d\u95f4\u8282\u70b9 k \u4f7f\u5f97\u4ece i \u5230 j \u7684\u8def\u5f84\u6bd4\u76f4\u63a5\u4ece i \u5230 j \u66f4\u77ed\uff0c\u5219\u66f4\u65b0\u8def\u5f84\u957f\u5ea6\u3002<\/p>\n<\/p>\n

2\u3001\u5b9e\u73b0\u6b65\u9aa4<\/h4>\n<\/p>\n

\u4ee5\u4e0b\u662f\u4f7f\u7528Python\u548cNumPy\u5e93\u5b9e\u73b0Floyd-Warshall\u7b97\u6cd5\u6765\u8ba1\u7b97\u53ef\u8fbe\u77e9\u9635\u7684\u5177\u4f53\u6b65\u9aa4\uff1a<\/p>\n<\/p>\n

import numpy as np<\/p>\n
def floyd_warshall(adj_matrix):<\/p>\n
    n = len(adj_matrix)<\/p>\n
    reach_matrix = np.copy(adj_matrix)<\/p>\n
    for k in range(n):<\/p>\n
        for i in range(n):<\/p>\n
            for j in range(n):<\/p>\n
                reach_matrix[i][j] = reach_matrix[i][j] or (reach_matrix[i][k] and reach_matrix[k][j])<\/p>\n
    return reach_matrix<\/p>\n
\u793a\u4f8b\u90bb\u63a5\u77e9\u9635\uff080\u8868\u793a\u65e0\u8fde\u63a5\uff0c1\u8868\u793a\u6709\u8fde\u63a5\uff09<\/strong><\/h2>\n
adj_matrix = np.array([<\/p>\n
    [0, 1, 0, 0],<\/p>\n
    [0, 0, 1, 0],<\/p>\n
    [0, 0, 0, 1],<\/p>\n
    [1, 0, 0, 0]<\/p>\n
])<\/p>\n
reach_matrix = floyd_warshall(adj_matrix)<\/p>\n
print("\u53ef\u8fbe\u77e9\u9635:")<\/p>\n
print(reach_matrix)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u590d\u5236\u4e86\u90bb\u63a5\u77e9\u9635 adj_matrix<\/code>\uff0c\u5e76\u901a\u8fc7\u9010\u6b65\u66f4\u65b0\u8def\u5f84\u4fe1\u606f\u6765\u8ba1\u7b97\u53ef\u8fbe\u77e9\u9635 reach_matrix<\/code>\u3002\u6700\u7ec8\u8f93\u51fa\u7684 reach_matrix<\/code> \u5373\u4e3a\u6240\u6709\u8282\u70b9\u5bf9\u4e4b\u95f4\u7684\u53ef\u8fbe\u6027\u4fe1\u606f\u3002<\/p>\n<\/p>\n
\u4e8c\u3001\u77e9\u9635\u5e42<\/h3>\n<\/p>\n
\u4f7f\u7528\u77e9\u9635\u5e42\u7684\u65b9\u6cd5\u8ba1\u7b97\u53ef\u8fbe\u77e9\u9635\u57fa\u4e8e\u4e00\u79cd\u7b80\u5355\u7684\u6570\u5b66\u601d\u60f3\uff1a\u5982\u679c\u4e00\u4e2a\u8282\u70b9\u53ef\u4ee5\u901a\u8fc7 k \u6b65\u4ece\u4e00\u4e2a\u8282\u70b9\u5230\u8fbe\u53e6\u4e00\u4e2a\u8282\u70b9\uff0c\u90a3\u4e48\u5bf9\u5e94\u7684\u90bb\u63a5\u77e9\u9635\u7684 k \u6b21\u5e42\u4e2d\u7684\u5143\u7d20\u5c06\u662f\u975e\u96f6\u7684\u3002<\/p>\n<\/p>\n
1\u3001\u7b97\u6cd5\u4ecb\u7ecd<\/h4>\n<\/p>\n
\u901a\u8fc7\u4e0d\u65ad\u5730\u5c06\u90bb\u63a5\u77e9\u9635\u8fdb\u884c\u5e42\u8fd0\u7b97\uff0c\u76f4\u5230\u8fbe\u5230\u56fe\u4e2d\u6700\u957f\u7684\u8def\u5f84\u957f\u5ea6\uff08\u5373\u8282\u70b9\u6570\u51cf\u4e00\uff09\uff0c\u7136\u540e\u68c0\u67e5\u6bcf\u4e00\u4e2a\u5143\u7d20\u662f\u5426\u4e3a\u975e\u96f6\u3002\u5982\u679c\u67d0\u4e2a\u5143\u7d20\u4e3a\u975e\u96f6\uff0c\u5219\u8868\u793a\u5bf9\u5e94\u7684\u8282\u70b9\u5bf9\u662f\u53ef\u8fbe\u7684\u3002<\/p>\n<\/p>\n
2\u3001\u5b9e\u73b0\u6b65\u9aa4<\/h4>\n<\/p>\n
\u4ee5\u4e0b\u662f\u4f7f\u7528Python\u548cNumPy\u5e93\u5b9e\u73b0\u77e9\u9635\u5e42\u65b9\u6cd5\u6765\u8ba1\u7b97\u53ef\u8fbe\u77e9\u9635\u7684\u5177\u4f53\u6b65\u9aa4\uff1a<\/p>\n<\/p>\n
import numpy as np<\/p>\n
def matrix_power_reachability(adj_matrix):<\/p>\n
    n = len(adj_matrix)<\/p>\n
    reach_matrix = np.copy(adj_matrix)<\/p>\n
    power_matrix = np.copy(adj_matrix)<\/p>\n
    for _ in range(1, n):<\/p>\n
        power_matrix = np.dot(power_matrix, adj_matrix)<\/p>\n
        reach_matrix = np.logical_or(reach_matrix, power_matrix)<\/p>\n
    return reach_matrix.astype(int)<\/p>\n
\u793a\u4f8b\u90bb\u63a5\u77e9\u9635\uff080\u8868\u793a\u65e0\u8fde\u63a5\uff0c1\u8868\u793a\u6709\u8fde\u63a5\uff09<\/strong><\/h2>\n
adj_matrix = np.array([<\/p>\n
    [0, 1, 0, 0],<\/p>\n
    [0, 0, 1, 0],<\/p>\n
    [0, 0, 0, 1],<\/p>\n
    [1, 0, 0, 0]<\/p>\n
])<\/p>\n
reach_matrix = matrix_power_reachability(adj_matrix)<\/p>\n
print("\u53ef\u8fbe\u77e9\u9635:")<\/p>\n
print(reach_matrix)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u901a\u8fc7\u9010\u6b65\u8ba1\u7b97\u90bb\u63a5\u77e9\u9635\u7684\u5e42\uff0c\u5e76\u5bf9\u6bcf\u4e00\u6b65\u7684\u7ed3\u679c\u8fdb\u884c\u903b\u8f91\u6216\u8fd0\u7b97\uff0c\u6700\u7ec8\u5f97\u5230\u53ef\u8fbe\u77e9\u9635 reach_matrix<\/code>\u3002<\/p>\n<\/p>\n
\u4e09\u3001\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\uff08DFS\uff09\u548c\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22\uff08BFS\uff09<\/h3>\n<\/p>\n
\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\uff08DFS\uff09\u548c\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22\uff08BFS\uff09\u662f\u4e24\u79cd\u7ecf\u5178\u7684\u56fe\u904d\u5386\u7b97\u6cd5\uff0c\u53ef\u4ee5\u7528\u6765\u8ba1\u7b97\u4ece\u6bcf\u4e2a\u8282\u70b9\u51fa\u53d1\u7684\u53ef\u8fbe\u6027\u4fe1\u606f\uff0c\u4ece\u800c\u6784\u5efa\u53ef\u8fbe\u77e9\u9635\u3002<\/p>\n<\/p>\n
1\u3001DFS\u7b97\u6cd5\u4ecb\u7ecd<\/h4>\n<\/p>\n
DFS\u662f\u4e00\u79cd\u5229\u7528\u6808\u7ed3\u6784\u7684\u56fe\u904d\u5386\u7b97\u6cd5\uff0c\u901a\u8fc7\u9012\u5f52\u6216\u663e\u5f0f\u6808\u5b9e\u73b0\u3002\u5b83\u4ece\u4e00\u4e2a\u8d77\u59cb\u8282\u70b9\u5f00\u59cb\uff0c\u6cbf\u7740\u672a\u8bbf\u95ee\u8fc7\u7684\u8282\u70b9\u4e0d\u65ad\u6df1\u5165\uff0c\u76f4\u5230\u65e0\u6cd5\u7ee7\u7eed\u4e3a\u6b62\uff0c\u7136\u540e\u56de\u6eaf\u5230\u4e0a\u4e00\u4e2a\u8282\u70b9\u7ee7\u7eed\u641c\u7d22\u3002<\/p>\n<\/p>\n
2\u3001BFS\u7b97\u6cd5\u4ecb\u7ecd<\/h4>\n<\/p>\n
BFS\u662f\u4e00\u79cd\u5229\u7528\u961f\u5217\u7ed3\u6784\u7684\u56fe\u904d\u5386\u7b97\u6cd5\uff0c\u4ece\u4e00\u4e2a\u8d77\u59cb\u8282\u70b9\u5f00\u59cb\uff0c\u9996\u5148\u8bbf\u95ee\u6240\u6709\u76f8\u90bb\u8282\u70b9\uff0c\u7136\u540e\u518d\u8bbf\u95ee\u8fd9\u4e9b\u76f8\u90bb\u8282\u70b9\u7684\u76f8\u90bb\u8282\u70b9\uff0c\u4ee5\u6b64\u7c7b\u63a8\u3002BFS\u9002\u5408\u7528\u4e8e\u5bfb\u627e\u6700\u77ed\u8def\u5f84\u3002<\/p>\n<\/p>\n
3\u3001DFS\u5b9e\u73b0\u6b65\u9aa4<\/h4>\n<\/p>\n
\u4ee5\u4e0b\u662f\u4f7f\u7528Python\u5b9e\u73b0DFS\u6765\u8ba1\u7b97\u53ef\u8fbe\u77e9\u9635\u7684\u5177\u4f53\u6b65\u9aa4\uff1a<\/p>\n<\/p>\n
import numpy as np<\/p>\n
def dfs(graph, start, visited):<\/p>\n
    stack = [start]<\/p>\n
    while stack:<\/p>\n
        node = stack.pop()<\/p>\n
        for neighbor, connected in enumerate(graph[node]):<\/p>\n
            if connected and not visited[neighbor]:<\/p>\n
                visited[neighbor] = 1<\/p>\n
                stack.append(neighbor)<\/p>\n
def dfs_reachability(adj_matrix):<\/p>\n
    n = len(adj_matrix)<\/p>\n
    reach_matrix = np.zeros((n, n), dtype=int)<\/p>\n
    for i in range(n):<\/p>\n
        visited = np.zeros(n, dtype=int)<\/p>\n
        dfs(adj_matrix, i, visited)<\/p>\n
        reach_matrix[i] = visited<\/p>\n
    return reach_matrix<\/p>\n
\u793a\u4f8b\u90bb\u63a5\u77e9\u9635\uff080\u8868\u793a\u65e0\u8fde\u63a5\uff0c1\u8868\u793a\u6709\u8fde\u63a5\uff09<\/strong><\/h2>\n
adj_matrix = np.array([<\/p>\n
    [0, 1, 0, 0],<\/p>\n
    [0, 0, 1, 0],<\/p>\n
    [0, 0, 0, 1],<\/p>\n
    [1, 0, 0, 0]<\/p>\n
])<\/p>\n
reach_matrix = dfs_reachability(adj_matrix)<\/p>\n
print("\u53ef\u8fbe\u77e9\u9635:")<\/p>\n
print(reach_matrix)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u901a\u8fc7DFS\u904d\u5386\u6bcf\u4e2a\u8282\u70b9\u7684\u53ef\u8fbe\u6027\uff0c\u5e76\u5c06\u7ed3\u679c\u5b58\u50a8\u5728\u53ef\u8fbe\u77e9\u9635 reach_matrix<\/code> \u4e2d\u3002<\/p>\n<\/p>\n
4\u3001BFS\u5b9e\u73b0\u6b65\u9aa4<\/h4>\n<\/p>\n
\u4ee5\u4e0b\u662f\u4f7f\u7528Python\u5b9e\u73b0BFS\u6765\u8ba1\u7b97\u53ef\u8fbe\u77e9\u9635\u7684\u5177\u4f53\u6b65\u9aa4\uff1a<\/p>\n<\/p>\n
import numpy as np<\/p>\n
from collections import deque<\/p>\n
def bfs(graph, start, visited):<\/p>\n
    queue = deque([start])<\/p>\n
    visited[start] = 1<\/p>\n
    while queue:<\/p>\n
        node = queue.popleft()<\/p>\n
        for neighbor, connected in enumerate(graph[node]):<\/p>\n
            if connected and not visited[neighbor]:<\/p>\n
                visited[neighbor] = 1<\/p>\n
                queue.append(neighbor)<\/p>\n
def bfs_reachability(adj_matrix):<\/p>\n
    n = len(adj_matrix)<\/p>\n
    reach_matrix = np.zeros((n, n), dtype=int)<\/p>\n
    for i in range(n):<\/p>\n
        visited = np.zeros(n, dtype=int)<\/p>\n
        bfs(adj_matrix, i, visited)<\/p>\n
        reach_matrix[i] = visited<\/p>\n
    return reach_matrix<\/p>\n
\u793a\u4f8b\u90bb\u63a5\u77e9\u9635\uff080\u8868\u793a\u65e0\u8fde\u63a5\uff0c1\u8868\u793a\u6709\u8fde\u63a5\uff09<\/strong><\/h2>\n
adj_matrix = np.array([<\/p>\n
    [0, 1, 0, 0],<\/p>\n
    [0, 0, 1, 0],<\/p>\n
    [0, 0, 0, 1],<\/p>\n
    [1, 0, 0, 0]<\/p>\n
])<\/p>\n
reach_matrix = bfs_reachability(adj_matrix)<\/p>\n
print("\u53ef\u8fbe\u77e9\u9635:")<\/p>\n
print(reach_matrix)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u4e0a\u8ff0\u4ee3\u7801\u4e2d\uff0c\u6211\u4eec\u901a\u8fc7BFS\u904d\u5386\u6bcf\u4e2a\u8282\u70b9\u7684\u53ef\u8fbe\u6027\uff0c\u5e76\u5c06\u7ed3\u679c\u5b58\u50a8\u5728\u53ef\u8fbe\u77e9\u9635 reach_matrix<\/code> \u4e2d\u3002<\/p>\n<\/p>\n
\u56db\u3001\u603b\u7ed3<\/h3>\n<\/p>\n
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