【luogu P4017 最大食物链计数】 题解

题目链接：https://www.luogu.org/problemnew/show/P4017

DAG + DP

#include <queue>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
const int maxn = 500010;
const int mod = 80112002;
struct edge{
	long long from, to, next;
}e[maxn<<2];
long long head[maxn], cnt;
long long n, m, indrg[maxn], outdrg[maxn], f[maxn], str[maxn], strnum, end[maxn], endnum, ans;
long long H, T, Q[maxn];
void add(long long u, long long v)
{
	e[++cnt].from = u;
	e[cnt].next = head[u];
	e[cnt].to = v;
	head[u] = cnt;
}
int main()
{
	memset(head, -1, sizeof(head));
	scanf("%lld%lld",&n,&m);
	for(long long i = 1; i <= m; i++)
	{
		long long u, v;
		scanf("%lld%lld",&u,&v);
		add(u, v);
		indrg[v]++; outdrg[u]++;
	}
	T = 0, H = 1;
	for(long long i = 1; i <= n; i++)
	{
		if(indrg[i] == 0)
		Q[++T] = i, str[++strnum] = i;
		if(outdrg[i] == 0)
		end[++endnum] = i;
	}
		
	while(H <= T)
	{
		long long u = Q[H++];
		for(long long i = head[u]; i != -1; i = e[i].next)
		{
			long long v = e[i].to;
			indrg[v]--;
			if(indrg[v] == 0)
			Q[++T] = v;
		}
	}
	
	for(int i = 1; i <= strnum; i++)
	f[str[i]] = 1;
	
	for(long long i = 1; i <= n; i++)
	{
		long long u = Q[i];
		for(long long j = head[u]; j != -1; j = e[j].next)
		{
			long long v = e[j].to;
			f[v] += f[u] % mod;
		}
	}
	
	for(int i = 1; i <= endnum; i++)
	ans += f[end[i]] % mod;
	
	printf("%lld",ans % mod);
	return 0;
}