Python算法教程：强连通分量

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#Python算法教程 #强连通分量

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本文深入探讨了有向图中的强连通分量(SCCs)概念，详细介绍了Kosaraju算法如何高效地找出图中所有强连通分量。通过示例代码展示了算法的具体实现过程。

强连通分量(strongly connected components, SCCs)是一个能让有向路径上所有节点彼此到达的最大子图。

Kosaraju的查找强连通分量算法

def strongly_connected_components(graph):
    transpose_graph = get_transpose_graph(graph)
    scc, seen = [], set()
    for u in dfs_top_sort(graph):
        if u in seen:
            continue
        component = walk(transpose_graph, u, seen)
        seen.update(component)
        scc.append(component)
    return scc


def get_transpose_graph(graph):
    transposed = {}
    for u in graph:
        transposed[u] = set()
    for u in graph:
        for v in graph[u]:
            transposed[v].add(u)
    return transposed


def dfs_top_sort(graph):
    visited, res = set(), []

    def recurse(u):
        if u in visited:
            return
        visited.add(u)
        for v in graph[u]:
            recurse(v)
        res.append(u)

    for u in graph:
        recurse(u)

    res.reverse()
    return res


def walk(graph, start, s=None):
    nodes, current = set(), dict()
    current[start] = None
    nodes.add(start)
    while nodes:
        u = nodes.pop()
        for v in graph[u].difference(current, s):
            nodes.add(v)
            current[v] = u
    return current


graph = {
    'a': set('bc'),
    'b': set('dei'),
    'c': set('d'),
    'd': set('ah'),
    'e': set('f'),
    'f': set('g'),
    'g': set('eh'),
    'h': set('i'),
    'i': set('h'),
}
print(strongly_connected_components(graph))
# [{'a': None, 'd': 'a', 'b': 'd', 'c': 'd'}, {'e': None, 'g': 'e', 'f': 'g'}, {'h': None, 'i': 'h'}]