hdu 2833 WuKong(最短路径+记忆化搜索) - c++编程基础

http://acm.hdu.edu.cn/showproblem.php pid=2833

大致题意：给定一个无向图，以及悟空和师傅起点与终点，求它们分别从起点到终点的最短路径中经过相同的点的最大个数。

思路：首先dijkstra求出最短路，那么如果有dis[a] + map[a][b] = dis[b]，则边（a,b）一定在最短路径上。根据这一定理可以求出所有最短路径。然后类似于求最长公共子序列求经过的相同点的最大个数。

即若a==b ,dp[a][b] = max(dp[i][j]+1)

否则 dp[a][b] = max(dp[a][j],dp[i][b])，其中i,j分别是a,b的直接前驱节点。

#include 
  
   
#include 
   
     #include 
    
      #include 
     
       #include 
       #include 
       
         #include 
        
          #include 
         
           #include 
          
            #include 
           
             #define LL long long #define _LL __int64 using namespace std; const int INF = 1<<28; const int maxn = 310; int Map[maxn][maxn]; int n,m; int s1,t1,s2,t2; int dis1[maxn],dis2[maxn]; int dp[maxn][maxn]; void init() { for(int i = 1; i <= n; i++) { for(int j = 1; j <= n; j++) Map[i][j] = INF; } } void dijkstra(int s, int f) { int dis[maxn],vis[maxn]; memset(vis,0,sizeof(vis)); for(int i = 1; i <= n; i++) dis[i] = Map[s][i]; vis[s] = 1; dis[s] = 0; for(int i = 1; i <= n; i++) { int Min = INF,pos = -1; for(int j = 1; j <= n; j++) { if(!vis[j] && dis[j] < Min) { Min = dis[j]; pos = j; } } if(pos == -1) break; vis[pos] = 1; for(int j = 1; j <= n; j++) { if(!vis[j] && dis[j] > dis[pos] + Map[pos][j]) dis[j] = dis[pos] + Map[pos][j]; } } if(f == 1) memcpy(dis1,dis,sizeof(dis)); else memcpy(dis2,dis,sizeof(dis)); } int dfs (int a, int b) { if(a == s1 && b == s2) return dp[s1][s2]; if(dp[a][b] > -1) return dp[a][b]; //记忆化 int v = 0; if(a == b) // dp[a][b] = max(dp[i][j]+1) { v++; for(int i = 1; i <= n; i++) { if(dis1[i] + Map[i][a] != dis1[a]) continue; for(int j = 1; j <= n; j++) if(dis2[j] + Map[j][b] == dis2[b]) v = max(v,dfs(i,j)+1); } return dp[a][b] = v; } //dp[a][b] = max(dp[i][b],dp[a][j]). v = 0; for(int i = 1; i <= n; i++) { if(dis1[i] + Map[i][a] == dis1[a]) v = max(v,dfs(i,b)); } for(int i = 1; i <= n; i++) { if(dis2[i] + Map[i][b] == dis2[b]) v = max(v,dfs(a,i)); } return dp[a][b] = v; } int main() { while(~scanf("%d %d",&n,&m)) { init(); if(n == 0 && m == 0) break; int u,v,w; for(int i = 1; i <= m; i++) { scanf("%d %d %d",&u,&v,&w); if(w < Map[u][v]) Map[u][v] = Map[v][u] = w; } scanf("%d %d %d %d",&s1,&t1,&s2,&t2); memset(dp,-1,sizeof(dp)); dp[s1][s2] = 0; if(s1 == s2) // 注意起点相同的情况 dp[s1][s2] = 1; dijkstra(s1,1); dijkstra(s2,2); int ans = dfs(t1,t2); printf("%d\n",ans); } return 0; }