POJ 1236 Network of Schools

题目链接

题意：题意本质上就是，给定一个有向图，问两个问题

1、从哪几个顶点出发，能走全全部点

2、最少连几条边，使得图强连通

思路：

#include <cstdio>

#include <cstring>

#include <vector>

#include <stack>

using namespace std;

const int N = 105;

int n;

vector<int> g[N];

int pre[N], sccno[N], dfn[N], dfs_clock, sccn;

stack<int> S;

void dfs_scc(int u) {

	pre[u] = dfn[u] = ++dfs_clock;

	S.push(u);

	for (int i = 0; i < g[u].size(); i++) {

		int v = g[u][i];

		if (!pre[v]) {

			dfs_scc(v);

			dfn[u] = min(dfn[u], dfn[v]);

		} else if (!sccno[v]) dfn[u] = min(dfn[u], pre[v]);

	}

	if (dfn[u] == pre[u]) {

		sccn++;

		while (1) {

			int x = S.top(); S.pop();

			sccno[x] = sccn;

			if (x == u) break;

		}

	}

}

void find_scc() {

	sccn = dfs_clock = 0;

	memset(pre, 0, sizeof(pre));

	memset(sccno, 0, sizeof(sccno));

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

		if (!pre[i]) dfs_scc(i);

}

int in[N], out[N];

int main() {

	while (~scanf("%d", &n)) {

		int v;

		for (int i = 1; i <= n; i++) g[i].clear();

		int cnt = n;

		for (int u = 1; u <= n; u++) {

			while (~scanf("%d", &v) && v)

				g[u].push_back(v);

		}

		find_scc();

		memset(in, 0, sizeof(in));

		memset(out, 0, sizeof(out));

		for (int u = 1; u <= n; u++) {

			for (int j = 0; j < g[u].size(); j++) {

				int v = g[u][j];

				if (sccno[u] != sccno[v]) {

					in[sccno[v]]++;

					out[sccno[u]]++;

				}

			}

		}

		int ins = 0, outs = 0;

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

			if (!in[i]) ins++;

			if (!out[i]) outs++;

		}

		int ans1 = ins, ans2 = max(ins, outs);

		if (sccn == 1) ans2 = 0;

		printf("%d\n%d\n", ans1, ans2);

	}

	return 0;

}