To prove two sets A and B are equivalent, we can first prove A is a subset of B, and then prove B is a subset of A, so finally we got that these two sets are equivalent. You are to prove N sets are equivalent, using the method above: in each step you can prove a set X is a subset of another set Y, and there are also some sets that are already proven to be subsets of some other sets. Now you want to know the minimum steps needed to get the problem proved.
Input
The input file contains multiple test cases, in each case, the first line contains two integers N <= 20000 and M <= 50000. Next M lines, each line contains two integers X, Y, means set X in a subset of set Y.
Output
For each case, output a single integer: the minimum steps needed.
Sample Input
4 0 3 2 1 2 1 3
Sample Output
4 3
題目大意：給你一張有向圖要求最少加多少條邊時該圖變成強連通圖。 Tarjan縮點。。
#include<bits/stdc++.h>
using namespace std;
const int N = 20100;
struct Tarjan_scc {stack<int> s;bool instack[N];struct edge { int to, next; }G[N * 3];int idx, scc, tot, in[N], out[N], dfn[N], low[N], head[N], sccnum[N];inline void init(int n) {idx = scc = tot = 0;while (!s.empty()) s.pop();for (int i = 0; i < n + 2; i++) {head[i] = -1;instack[i] = false;in[i] = out[i] = dfn[i] = low[i] = sccnum[i] = 0;}}inline void add_edge(int u, int v) {G[tot].to = v, G[tot].next = head[u], head[u] = tot++;}inline void built(int m) {int u, v;while (m--) {scanf("%d %d", &u, &v);add_edge(u, v);}}inline void tarjan(int u) {dfn[u] = low[u] = ++idx;instack[u] = true;s.push(u);for (int i = head[u]; ~i; i = G[i].next) {int &v = G[i].to;if (!dfn[v]) {tarjan(v);low[u] = min(low[u], low[v]);} else if (instack[v] && dfn[v] < low[u]) {low[u] = dfn[v];}}if (dfn[u] == low[u]) {int v = 0;scc++;do {v = s.top(); s.pop();instack[v] = false;sccnum[v] = scc;} while (u != v);}}inline void solve(int n, int m) {init(n);built(m);for (int i = 1; i <= n; i++) {if (!dfn[i]) tarjan(i);}int x1 = 0, x2 = 0;for (int u = 1; u <= n; u++) {for (int i = head[u]; ~i; i = G[i].next) {int v = G[i].to;if (sccnum[u] != sccnum[v]) {in[sccnum[v]]++;out[sccnum[u]]++;}}}for (int i = 1; i <= scc; i++) {if (!in[i]) x1++;if (!out[i]) x2++;}printf("%d\n", 1 == scc ? 0 : max(x1, x2));}
}go;
int main() {
#ifdef LOCALfreopen("in.txt", "r", stdin);freopen("out.txt", "w+", stdout);
#endifint n, m;while (~scanf("%d %d", &n, &m)) {go.solve(n, m);}return 0;
}
