【luogu P2169 正则表达式】 题解

题目链接：https://www.luogu.org/problemnew/show/P2169

tarjan缩点 + SPFA

缩完点之后加边注意别写错。

也可以不用建两个图，可以在一张图上判断是否强连通再SPFA.

#include <queue>
#include <stack>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
const int maxn = 1000000 + 10;
const int inf = 0x7fffffff;
struct edge{
	int from, to, next, len;
}e1[maxn<<2], e2[maxn<<2];
int head1[maxn], head2[maxn], cnt1, cnt2;
int dfn[maxn], low[maxn], dis[maxn], tim;
bool vis1[maxn], vis2[maxn];
int n, m, color[maxn], num;
stack<int> s;
queue<int> q;
void add1(int u, int v, int w)
{
	e1[++cnt1].from = u;
	e1[cnt1].len = w;
	e1[cnt1].next = head1[u];
	e1[cnt1].to = v;
	head1[u] = cnt1;
}
void add2(int u, int v, int w)
{
	e2[++cnt2].from = u;
	e2[cnt2].len = w;
	e2[cnt2].next = head2[u];
	e2[cnt2].to = v;
	head2[u] = cnt2;
}
void tarjan(int x)
{
	dfn[x] = low[x] = ++tim;
	s.push(x); vis1[x] = 1;
	for(int i = head1[x]; i != -1; i = e1[i].next)
	{
		int v = e1[i].to;
		if(!dfn[v])
		{
			tarjan(v);
			low[x] = min(low[x], low[v]);
		}
		else if(vis1[v])
		{
			low[x] = min(low[x], low[v]);
		}
	}
	if(low[x] == dfn[x])
	{
		color[x] = ++num;
		vis1[x] = 0;
		while(s.top() != x)
		{
			color[s.top()] = num;
			vis1[s.top()] = 0;
			s.pop();
		}
		s.pop();
	}
}
void SPFA()
{
	while(!q.empty())
	{
		int now = q.front(); q.pop();
		vis2[now] = 0;
		for(int i = head2[now]; i != -1; i = e2[i].next)
		{
			int v = e2[i].to;
			if(dis[v] > dis[now] + e2[i].len)
			{
				dis[v] = dis[now] + e2[i].len;
				if(!vis2[v])
				{
					q.push(v);
					vis2[v] = 1;
				}
			}
		}
	}
}
int main()
{
	memset(head1, -1, sizeof(head1));
	memset(head2, -1, sizeof(head2));
	scanf("%d%d",&n,&m);
	for(int i = 1; i <= n; i++) dis[i] = inf;
	for(int i = 1; i <= m; i++)
	{
		int u, v, w;
		scanf("%d%d%d",&u,&v,&w);
		add1(u,v,w);
	}
	for(int i = 1; i <= n; i++)
	if(!dfn[i]) tarjan(i);
	for(int i = 1; i <= n; i++)
		for(int j = head1[i]; j != -1; j = e1[j].next)
		{
			int v = e1[j].to;
			if(color[v] != color[i])
			add2(color[i], color[v], e1[j].len);
		}
	q.push(color[1]);
	dis[color[1]] = 0;
	vis2[color[1]] = 1;
	SPFA();
	printf("%d",dis[color[n]]);
}