题目截图

题目分析

• 找割边

割边

割点

强连通子图

• 我觉得就是割边左右的两个子图？
• 应该是去掉n条割边后，剩下n + 1个强连通子图的意思吧。。。

ac code

class Solution:
    def criticalConnections(self, n: int, connections: List[List[int]]) -> List[List[int]]:

        def check_graph(edge, n):
            # edge为边连接关系，n为节点数

            # 访问序号与根节点序号
            visit = [0] * n
            root = [0] * n
            # 割点
            cut_node = []
            # 割边
            cut_edge = []
            # 强连通分量子树
            sub_group = []

            # 中间变量
            stack = []
            index = 1

            def tarjan(i, father):
                nonlocal index
                visit[i] = root[i] = index
                index += 1
                stack.append(i)
                for j in edge[i]:
                    if j != father:
                        if not visit[j]:
                            tarjan(j, i)
                            root[i] = min(root[i], root[j])
                            if visit[i] < root[j]:
                                cut_edge.append([i, j])
                            if visit[i] < root[j]:
                                cut_node.append(i)
                        elif j in stack:
                            root[i] = min(root[i], visit[j])

                if root[i] == visit[i]:
                    lst = []
                    while stack[-1] != i:
                        lst.append(stack.pop())
                    lst.append(stack.pop())
                    r = min(root[ls] for ls in lst)
                    for ls in lst:
                        root[ls] = r
                    sub_group.append(lst)
                return

            for k in range(n):
                if not visit[k]:
                    tarjan(k, -1)
            return cut_edge, cut_node, sub_group

        edges = defaultdict(list)
        for a, b in connections:
            edges[a].append(b)
            edges[b].append(a)
        cut_edge, cut_node, sub_group = check_graph(edges, n)
        print(cut_node)
        return cut_edge

tarjan模版

        def check_graph(edge, n):
            # edge为边连接关系，n为节点数

            # 访问序号与根节点序号
            visit = [0] * n
            root = [0] * n
            # 割点
            cut_node = []
            # 割边
            cut_edge = []
            # 强连通分量子树
            sub_group = []

            # 中间变量
            stack = []
            index = 1

            def tarjan(i, father):
                nonlocal index
                visit[i] = root[i] = index
                index += 1
                stack.append(i)
                for j in edge[i]:
                    if j != father:
                        if not visit[j]:
                            tarjan(j, i)
                            root[i] = min(root[i], root[j])
                            if visit[i] < root[j]:
                                cut_edge.append([i, j])
                            if visit[i] < root[j]:
                                cut_node.append(i)
                        elif j in stack:
                            root[i] = min(root[i], visit[j])

                if root[i] == visit[i]:
                    lst = []
                    while stack[-1] != i:
                        lst.append(stack.pop())
                    lst.append(stack.pop())
                    r = min(root[ls] for ls in lst)
                    for ls in lst:
                        root[ls] = r
                    sub_group.append(lst)
                return

            for k in range(n):
                if not visit[k]:
                    tarjan(k, -1)
            return cut_edge, cut_node, sub_group

• 输入：图g(defaultdict)，总点数n
• 输出：割边，割点，极大连通子图

总结

• tarjan裸题