边双连通分量(e-DCC)的求法+e-DCC缩点
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2024-01-04 15:54:40
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#include <bits/stdc++.h>
using namespace std;
const int SIZE = 1e5 + 10;
int head[SIZE], ver[SIZE * 2], Next[SIZE * 2];
int dfn[SIZE], low[SIZE], n, m, tot, num;
bool bridge[SIZE * 2];
int c[SIZE], dcc;
int hc[SIZE], vc[SIZE * 2], nc[SIZE * 2], tc;
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, int in_edge) {
dfn[x] = low[x] = ++num;
for (int i = head[x]; i; i = Next[i]) {
int y = ver[i];
if (!dfn[y]) {
tarjan(y, i);
low[x] = min(low[x], low[y]);
if (low[y] > dfn[x])
bridge[i] = bridge[i ^ 1] = true;
} else if (i != (in_edge ^ 1))
low[x] = min(low[x], dfn[y]);
}
}
void dfs(int x) {
c[x] = dcc;
for (int i = head[x]; i; i = Next[i]) {
int y = ver[i];
if (c[y] || bridge[i])
continue;
dfs(y);
}
}
int main() {
cin >> n >> m;
tot = 1;
for (int i = 1; i <= m; i++) {
int x, y;
scanf("%d%d", &x, &y);
add(x, y);
add(y, x);
}
for (int i = 1; i <= n; i++)
if (!dfn[i])
tarjan(i, 0);
for (int i = 1; i <= n; i++)
if (!c[i]) {
++dcc;
dfs(i);
}
printf("There are %d e-DCCs.\n", dcc);
for (int i = 1; i <= n; i++)
printf("%d belongs to DCC %d\n", i, c[i]);
tc = 1;
for (int i = 2; i <= tot; i++) {
int x = ver[i ^ 1], y = ver[i];
if (c[x] == c[y])
continue;
add_c(c[x], c[y]);
}
printf("缩点之后的森林,点数%d,边数%d(可能有重边)\n", dcc, tc / 2);
for (int i = 2; i < tc; i += 2)
printf("%d %d\n", vc[i ^ 1], vc[i]);
return 0;
}
input:
9 11
1 2
2 3
3 4
4 5
5 1
5 2
1 6
6 9
6 8
9 8
6 7
output:
There are 3 e-DCCs.
1 belongs to DCC 1
2 belongs to DCC 1
3 belongs to DCC 1
4 belongs to DCC 1
5 belongs to DCC 1
6 belongs to DCC 2
7 belongs to DCC 3
8 belongs to DCC 2
9 belongs to DCC 2
缩点之后的森林,点数3,边数2(可能有重边)
1 2
2 3