[POJ3463] Sightseeing（次短路 Heap + Dijkstra）

传送门

用dijkstra比较好，spfa可能有的重复

dis[x][2]:dis[x][0]表示起点到x的最短路、dis[x][1]表示起点到x的次短路；

tot[x][2]:tot[x][0]表示起点到x的最短路条数、tot[x][1]表示起点到x的次短路的条数；

vis[x][2]对应于x和0、1功能为记录该点是否被访问！

那么如何更新最小和次小路呢？显然我们容易想到下面的方法：

1.if(x<最小)更新最小，次小；
2.else if(x==最小)更新方法数；
3.else if(x<次小)更新次小；
4.else if(x==次小)更新方法数；

——代码

 #include <queue>
 #include <cstdio>
 #include <cstring>
 #include <iostream>
 #include <algorithm>

 using namespace std;

 struct heap
 {
     int x, y, z;
     heap(int x = , int y = , int z = ) : x(x), y(y), z(z) {}
     bool operator < (const heap &rhs) const
     {
         return y > rhs.y;
     }
 };

 const int MAXM = , MAXN = ;
 int T, n, m, cnt;
 int dis[MAXN][], head[MAXN], to[MAXM << ], next[MAXM << ], val[MAXM << ], tot[MAXN][];
 priority_queue <heap> q;
 bool vis[MAXN][];

 inline int read()
 {
     int x = , f = ;
     char ch = getchar();
     for(; !isdigit(ch); ch = getchar()) if(ch == '-') f = -;
     for(; isdigit(ch); ch = getchar()) x = (x << ) + (x << ) + ch - '';
     return x * f;
 }

 inline void add(int x, int y, int z)
 {
     to[cnt] = y;
     val[cnt] = z;
     next[cnt] = head[x];
     head[x] = cnt++;
 }

 inline void dijkstra(int s)
 {
     int i, u, v, d, p;
     heap now;
     memset(vis, , sizeof(vis));
     memset(tot, , sizeof(tot));
     memset(dis,  / , sizeof(dis));
     dis[s][] = ;
     tot[s][] = ;
     q.push(heap(s, , ));
     while(!q.empty())
     {
         now = q.top();
         q.pop();
         u = now.x;
         p = now.z;
         if(vis[u][p]) continue;
         vis[u][p] = ;
         for(i = head[u]; i ^ -; i = next[i])
         {
             v = to[i];
             if(dis[v][] > dis[u][p] + val[i])
             {
                 dis[v][] = dis[v][];
                 tot[v][] = tot[v][];
                 dis[v][] = dis[u][p] + val[i];
                 tot[v][] = tot[u][p];
                 q.push(heap(v, dis[v][], ));
                 q.push(heap(v, dis[v][], ));
             }
             else if(dis[v][] == dis[u][p] + val[i]) tot[v][] += tot[u][p];
             else if(dis[v][] > dis[u][p] + val[i])
             {
                 dis[v][] = dis[u][p] + val[i];
                 tot[v][] = tot[u][p];
                 q.push(heap(v, dis[v][], ));
             }
             else if(dis[v][] == dis[u][p] + val[i]) tot[v][] += tot[u][p];
         }
     }
 }

 int main()
 {
     int i, j, x, y, z, s, t;
     T = read();
     while(T--)
     {
         n = read();
         m = read();
         cnt = ;
         memset(head, -, sizeof(head));
         for(i = ; i <= m; i++)
         {
             x = read();
             y = read();
             z = read();
             add(x, y, z);
         }
         s = read();
         t = read();
         dijkstra(s);
         if(dis[t][] == dis[t][] + ) tot[t][] += tot[t][];
         printf("%d\n", tot[t][]);
     }
 }