pta 编程题21 公路村村通

其它pta数据结构编程题请参见：pta

题目

这道题考察最小生成树问题，用的是Prim算法。

和Dijkstra算法相比，没有了collect数组，因为dist[v] == 0就代表v被已收录。

 #include <iostream>
 using namespace std;

 int N, M;
 int** G;
 void buildGraph();
 void deleteGraph();
 int prim();
 int findMinDist(int dist[]);

 int main()
 {
     cin >> N >> M;
     buildGraph();
     cout << prim();
     deleteGraph();
     return ;
 }

 void buildGraph()
 {
     int i, j;
     G = new int*[N];
     for (i = ; i < N; i++)
     {
         G[i] = new int[N];
         for (j = ; j < N; j++)
             G[i][j] = INT_MAX;
     }    

     int v, w, d;
     for (i = ; i < M; i++)
     {
         cin >> v >> w >> d;
         v--; w--;//输入从1计数
         G[v][w] = d;
         G[w][v] = d;
     }
 }

 void deleteGraph()
 {
     for (int i = ; i < N; i++)
         delete[] G[i];
     delete[] G;
 }

 int findMinDist(int dist[])
 { /*返回未收录进MST的顶点中dist最小的顶点*/
     int minV, v;
     int minDist = INT_MAX;
     for (v = ; v < N; v++)
     {
         if (dist[v] !=  && dist[v] < minDist)
         {
             minDist = dist[v];
             minV = v;
         }
     }
     if (minDist < INT_MAX)
         return minV;
     return -;
 }

 int prim()
 { /*返回最小生成树的权重*/
     int v, w, vCount = ;
     int totalWeight = ;
     int* dist = new int[N];

     /*初始化，初始点下标为0*/
     for (v = ; v < N; v++)
         dist[v] = G[][v];

     /*将0收进最小生成树MST*/
     dist[] = ;
     vCount++;

     while (true)
     {
         v = findMinDist(dist);
         if (v == -)
             break;

         totalWeight += dist[v];
         dist[v] = ; //收录v
         vCount++;

         for (w = ; w < N; w++)
         {
             /*如果w没有被收录*/
             if (dist[w] !=  && G[v][w] < dist[w])
             {
                 dist[w] = G[v][w];
             }
         }
     }

     delete[] dist;

     if (vCount < N)
         return -;
     return totalWeight;
 }