[BZOJ1576][Usaco2009 Jan]安全路径Travel（堆优化dijkstra+并查集）

题目描述

传送门

题解

思路和BZOJ3694相同，但是最短路径树需要自己求出。
学习了一下dijsktra的堆优化～

代码

#include<algorithm>
#include<iostream>
#include<cstring>
#include<queue>
#include<cstdio>
using namespace std;

const int max_n=1e5+5;
const int max_m=2e5+5;
const int max_e=max_m*2;

int n,m,x,y,z,cnt;
int tot,point[max_n],next[max_e],v[max_e],c[max_e];
int dis[max_n],father[max_n],son[max_n],h[max_n],belong[max_n],f[max_n],re[max_n];
bool vis[max_e];
struct hp{int x,y,l,len;}edge[max_m],e[max_e];

struct p{
    int pt,v;
    bool operator < (const p &x)const{
        return v>x.v;
    }
};
priority_queue<p>q;
inline void add(int x,int y,int z){++tot;next[tot]=point[x];point[x]=tot;v[tot]=y;c[tot]=z;}
inline int cmp(hp a,hp b){return a.len<b.len;}
inline int find(int x){if (x==f[x]) return x;else return f[x]=find(f[x]);}
inline void dijkstra(){
    memset(dis,0x7f,sizeof(dis));
    dis[1]=0;
    q.push((p){1,0});
    while (!q.empty()){
        p now=q.top(); q.pop();
        int x=now.pt;
        for (int i=point[x];i;i=next[i])
          if (dis[v[i]]>dis[x]+c[i]){
            dis[v[i]]=dis[x]+c[i];
            h[v[i]]=h[x]+1; re[v[i]]=i;father[v[i]]=x;
            q.push((p){v[i],dis[v[i]]});
          }
    }
}
int main(){
    scanf("%d%d",&n,&m);
    for (int i=1;i<=m;++i) scanf("%d%d%d",&x,&y,&z),add(x,y,z),add(y,x,z),e[i].x=x,e[i].y=y,e[i].l=z;
    dijkstra();

    for (int i=2;i<=n;++i) vis[re[i]]=1;
    for (int i=1;i<=m;++i) if (!vis[i*2-1]&&!vis[i*2]) edge[++cnt].x=e[i].x,edge[cnt].y=e[i].y,edge[cnt].l=e[i].l;

    for (int i=1;i<=cnt;++i) edge[i].len=edge[i].l+dis[edge[i].x]+dis[edge[i].y];
    sort(edge+1,edge+cnt+1,cmp);
    for (int i=1;i<=n;++i) f[i]=i;
    for (int i=1;i<=cnt;++i){
        int u=edge[i].x,t=edge[i].y,f1=find(u),f2=find(t),lastu=0,lastt=0;
        while (f1!=f2){
            if (h[f1]<h[f2]) swap(u,t),swap(f1,f2),swap(lastu,lastt);
            if (!belong[u]){
                belong[u]=i;
                if (lastu) f[lastu]=u;
            }
            else if (lastu) f[lastu]=f1;
            lastu=f1;u=father[lastu];f1=find(u);
        }
    }
    for (int i=2;i<=n;++i)
      if (belong[i]) printf("%d\n",edge[belong[i]].len-dis[i]); 
      else printf("-1\n");
}