【luogu P2194 HXY烧情侣】 题解

题目链接：https://www.luogu.org/problemnew/show/P2194

第一问：缩点并且统计其强连通分量里的最小耗费。把所有强连通分量的最小耗费加起来。

第二问：统计在每个强连通分量里与最小耗费相同的点数。乘法原理统计所有强连通分量答案。

#include <stack>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
const int maxn = 300000 + 10;
const int inf = 0x7fffffff;
const int mod = 1e9 + 7;
struct edge{
	int from, to, next;
}e[maxn<<2];
int head[maxn], cnt;
int n, m, ans1, ans2 = 1, dfn[maxn], low[maxn], tim, color[maxn], num, val[maxn], minpay[maxn], tot[maxn];
bool vis[maxn];
stack<int> s;
void add(int u, int v)
{
	e[++cnt].from = u;
	e[cnt].next = head[u];
	e[cnt].to = v;
	head[u] = cnt;
}
void tarjan(int x)
{
	dfn[x] = low[x] = ++tim;
	vis[x] = 1; s.push(x);
	for(int i = head[x]; i != -1; i = e[i].next)
	{
		int v = e[i].to;
		if(!dfn[v])
		{
			tarjan(v);
			low[x] = min(low[x], low[v]);
		}
		else if(vis[v])
		{
			low[x] = min(low[x], low[v]);
		}
	}
	if(dfn[x] == low[x])
	{
		color[x] = ++num;
		vis[x] = 0;
		minpay[num] = min(minpay[num], val[x]);
		while(s.top() != x)
		{
			color[s.top()] = num;
			vis[s.top()] = 0;
			minpay[num] = min(minpay[num], val[s.top()]);
			s.pop();
		}
		s.pop();
	}
}
int main()
{
	memset(head, -1, sizeof(head));
	scanf("%d",&n);
	for(int i = 1; i <= n; i++) minpay[i] = inf;
	for(int i = 1; i <= n; i++) scanf("%d",&val[i]);
	scanf("%d",&m);
	for(int i = 1; i <= m; i++)
	{
		int u, v;
		scanf("%d%d",&u,&v);
		add(u,v);
	}
	for(int i = 1; i <= n; i++)
		if(!dfn[i]) tarjan(i);
	//for(int i = 1; i <= n; i++) cout<<minpay[i];
	for(int i = 1; i <= num; i++) ans1 += minpay[i];
	cout<<ans1<<" ";
	for(int i = 1; i <= n; i++)
	{
		if(val[i] == minpay[color[i]])
		tot[color[i]]++;
	}
	for(int i = 1; i <= num; i++) ans2 = (ans2*tot[i])%mod;
	cout<<ans2<<endl;
	return 0;
}