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);
}