POJ 2186.Popular Cows (强连通)

强连通缩点,统计入度为1的缩点后的点的个数

个数1的话输出这个强连通分量的点的数量

否则输出0;

code

/*
Kosaraju算法,无向图的强连通分量,时间复杂度O(n+m)
思路:
按照图G的深度遍历序列,在G的反图上进行深搜
能够搜到的点集就是一个强联通分量
*/ #include <iostream>
#include <cstring>
using namespace std;
const int INF = 10009;
//链接表,偶数边为原图,奇数边为反图
struct node {
int v, ne;
} edge[100009];
/*
scc是强连通子图的个数
dfn为深度遍历序列(逆序即反图的拓扑排序)
vis为访问标记,sum记录每个强连通分量的节点数
*/
int head[INF], dfn[INF], vis[INF], sum[INF], n, m, scc, cnt = 1, tol;
void adde (int u, int v) {
edge[++cnt].v = v;
edge[cnt].ne = head[u];
head[u] = cnt;
}
void dfs (int k) {
vis[k] = 1;
for (int i = head[k]; i != 0; i = edge[i].ne)
if ( (i & 1) == 0 && !vis[edge[i].v])
dfs (edge[i].v);
dfn[++tol] = k;
}
void ndfs (int k) {
vis[k] = scc, sum[scc]++;
for (int i = head[k]; i != 0; i = edge[i].ne)
if ( (i & 1) && !vis[edge[i].v])
ndfs (edge[i].v);
}
void Kosaraju() {
for (int i = 1; i <= n; i++)
if (!vis[i]) dfs (i);
memset (vis, 0, sizeof vis);
for (int i = n; i > 0; i--)
if (!vis[dfn[i]]) scc++, ndfs (dfn[i]);
}
int make() {
int deg[INF] = {0};
//由反图统计每个强联通点的有无出度
for (int i = 3; i <= cnt; i += 2) {
if (vis[edge[i].v] == vis[edge[i ^ 1].v]) continue;
deg[vis[edge[i].v]]++;
}
int j, t = 0;
for (int i = 1; i <= scc; i++)
if (deg[i] == 0) j = i, t++;
if (t == 1) return sum[j];
return 0;
}
int main() {
int x, y;
cin >> n >> m;
for (int i = 1; i <= m; i++) {
cin >> x >> y;
adde (x, y), adde (y, x);
}
Kosaraju();
cout << make();
return 0;
}

  

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