pta 编程题21 公路村村通

Posted 2020-11-02 bloglxc

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。

  1 #include <iostream>
  2 using namespace std;
  3 
  4 int N, M;
  5 int** G;
  6 void buildGraph();
  7 void deleteGraph();
  8 int prim();
  9 int findMinDist(int dist[]);
 10 
 11 int main()
 12 {
 13     cin >> N >> M;
 14     buildGraph();
 15     cout << prim();
 16     deleteGraph();
 17     return 0;
 18 }
 19 
 20 void buildGraph()
 21 {
 22     int i, j;
 23     G = new int*[N];
 24     for (i = 0; i < N; i++)
 25     {
 26         G[i] = new int[N];
 27         for (j = 0; j < N; j++)
 28             G[i][j] = INT_MAX;
 29     }    
 30 
 31     int v, w, d;
 32     for (i = 0; i < M; i++)
 33     {
 34         cin >> v >> w >> d;
 35         v--; w--;//输入从1计数
 36         G[v][w] = d;
 37         G[w][v] = d;
 38     }
 39 }
 40 
 41 void deleteGraph()
 42 {
 43     for (int i = 0; i < N; i++)
 44         delete[] G[i];
 45     delete[] G;
 46 }
 47 
 48 int findMinDist(int dist[])
 49 { /*返回未收录进MST的顶点中dist最小的顶点*/
 50     int minV, v;
 51     int minDist = INT_MAX;
 52     for (v = 0; v < N; v++)
 53     {
 54         if (dist[v] != 0 && dist[v] < minDist)
 55         {
 56             minDist = dist[v];
 57             minV = v;
 58         }
 59     }
 60     if (minDist < INT_MAX)
 61         return minV;
 62     return -1;
 63 }
 64 
 65 int prim()
 66 { /*返回最小生成树的权重*/
 67     int v, w, vCount = 0;
 68     int totalWeight = 0;
 69     int* dist = new int[N];
 70 
 71     /*初始化，初始点下标为0*/
 72     for (v = 0; v < N; v++)
 73         dist[v] = G[0][v];
 74 
 75     /*将0收进最小生成树MST*/
 76     dist[0] = 0;
 77     vCount++;
 78 
 79     while (true)
 80     {
 81         v = findMinDist(dist);
 82         if (v == -1)
 83             break;
 84 
 85         totalWeight += dist[v];
 86         dist[v] = 0; //收录v
 87         vCount++;
 88 
 89         for (w = 0; w < N; w++)
 90         {
 91             /*如果w没有被收录*/
 92             if (dist[w] != 0 && G[v][w] < dist[w])
 93             {
 94                 dist[w] = G[v][w];
 95             }
 96         }
 97     }
 98 
 99     delete[] dist;
100 
101     if (vCount < N)
102         return -1;
103     return totalWeight;
104 }