图论--边双连通V-DCC缩点

// tarjan算法求无向图的割点、点双连通分量并缩点

#include<iostream>

#include<cstdio>

#include<cstring>

#include<algorithm>

#include<vector>

using namespace std;

const int SIZE = 100010;

int head[SIZE], ver[SIZE * 2], Next[SIZE * 2];

int dfn[SIZE], low[SIZE], stack[SIZE], new_id[SIZE], c[SIZE];

int n, m, tot, num, root, top, cnt, tc;

bool cut[SIZE];

vector<int> dcc[SIZE];

int hc[SIZE], vc[SIZE * 2], nc[SIZE * 2];

void add(int x, int y) {

	ver[++tot] = y, Next[tot] = head[x], head[x] = tot;

}

void add_c(int x, int y) {

	vc[++tc] = y, nc[tc] = hc[x], hc[x] = tc;

}

void tarjan(int x) {

	dfn[x] = low[x] = ++num;

	stack[++top] = x;

	if (x == root && head[x] == 0) { // 孤立点

		dcc[++cnt].push_back(x);

		return;

	}

	int flag = 0;

	for (int i = head[x]; i; i = Next[i]) {

		int y = ver[i];

		if (!dfn[y]) {

			tarjan(y);

			low[x] = min(low[x], low[y]);

			if (low[y] >= dfn[x]) {

				flag++;

				if (x != root || flag > 1) cut[x] = true;

				cnt++;

				int z;

				do {

					z = stack[top--];

					dcc[cnt].push_back(z);

				} while (z != y);

				dcc[cnt].push_back(x);

			}

		}

		else low[x] = min(low[x], dfn[y]);

	}

}

int main() {

	cin >> n >> m;

	tot = 1;

	for (int i = 1; i <= m; i++) {

		int x, y;

		scanf("%d%d", &x, &y);

		if (x == y) continue;

		add(x, y), add(y, x);

	}

	for (int i = 1; i <= n; i++)

		if (!dfn[i]) root = i, tarjan(i);

	for (int i = 1; i <= n; i++)

		if (cut[i]) printf("%d ", i);

	puts("are cut-vertexes");

	for (int i = 1; i <= cnt; i++) {

		printf("v-DCC #%d:", i);

		for (int j = 0; j < dcc[i].size(); j++)

			printf(" %d", dcc[i][j]);

		puts("");

	}

	// 给每个割点一个新的编号(编号从cnt+1开始)

	num = cnt;

	for (int i = 1; i <= n; i++)

		if (cut[i]) new_id[i] = ++num;

	// 建新图，从每个v-DCC到它包含的所有割点连边

	tc = 1;

	for (int i = 1; i <= cnt; i++)

		for (int j = 0; j < dcc[i].size(); j++) {

			int x = dcc[i][j];

			if (cut[x]) {

				add_c(i, new_id[x]);

				add_c(new_id[x], i);

			}

			else c[x] = i; // 除割点外，其它点仅属于1个v-DCC

		}

	printf("缩点之后的森林，点数 %d，边数 %d\n", num, tc / 2);

	printf("编号 1~%d 的为原图的v-DCC，编号 >%d 的为原图割点\n", cnt, cnt);

	for (int i = 2; i < tc; i += 2)

		printf("%d %d\n", vc[i ^ 1], vc[i]);

}
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图论--边双连通V-DCC缩点

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