洛谷P2169 正则表达式

P2169 正则表达式

一句话题意：给你一张有向有环图，成环各点间距为0，求点1到点n的最短路。

前置技能：tarjan（缩点）+最短路算法

然后，这道题就没了。

此题只需要先用tarjan找到所有的环，进行缩点后跑一遍dijkstra即可。

---

Code：

#include <iostream>
#include <cstdio>
#include <queue>
#include <stack>
#include <cstring>
using namespace std;
//Mystery_Sky
//
#define maxn 1000010
#define maxm 5000050
#define INF 0x3f3f3f3f
stack <int> st;
struct Edge {
	int to, next, w;
}edge[maxn];
int head[maxn], cnt, n, m;
int low[maxn], dfn[maxn], col[maxn], vis[maxn];
int dis[maxn], vis1[maxn];
int scc, tot, ans;
inline void add_edge(int u, int v, int w)
{
	edge[++cnt].to = v;
	edge[cnt].w = w;
	edge[cnt].next = head[u];
	head[u] = cnt;
}

void Tarjan(int u)
{
	low[u] = dfn[u] = ++tot;
	st.push(u);
	vis[u] = 1; 
	for(int i = head[u]; i; i = edge[i].next) {
		int v = edge[i].to;
		if(!dfn[v]) {
			Tarjan(v);
			low[u] = min(low[u], low[v]);
		}
		else if(vis[v]) low[u] = min(low[u], dfn[v]);
	} 
	if(dfn[u] == low[u]) {
		scc++;
		int j;
		do {
			j = st.top();
			st.pop();
			col[j] = u;
			vis[j] = 0;
		} while(j != u);
	}
}

struct node{
	int dis;
	int pos;
	inline bool operator <(const node &x) const 
	{
		return x.dis < dis;
	}
};
priority_queue <node> q;

inline void dijkstra()
{
	dis[1] = 0;
	q.push((node) {0, 1});
	while(!q.empty()) {
		node top = q.top();
		q.pop();
		int x = top.pos;
		if(vis1[x]) continue;
		vis1[x] = 1;
		for(int i = head[x]; i; i = edge[i].next) {
			int y = edge[i].to;
			if(col[y] == col[x]) edge[i].w = 0;
			if(dis[y] > dis[x] + edge[i].w) {
				dis[y] = dis[x] + edge[i].w;
				if(!vis1[y]) q.push((node) {dis[y], y}); 
			}
		}
	}
}

int main() {
	memset(dis, INF, sizeof(dis));
	scanf("%d%d", &n, &m);
	int u, v, w;
	for(int i = 1; i <= m; i++) {
		scanf("%d%d%d", &u, &v, &w);
		add_edge(u, v, w);
	}
	for(int i = 1; i <= n; i++) 
		if(!dfn[i]) Tarjan(i);
	dijkstra();
	ans = dis[n];
	printf("%d\n", ans);
}