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 0;
}

void buildGraph()
{
    int i, j;
    G = new int*[N];
    for (i = 0; i < N; i++)
    {
        G[i] = new int[N];
        for (j = 0; j < N; j++)
            G[i][j] = INT_MAX;
    }    

    int v, w, d;
    for (i = 0; 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 = 0; 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 = 0; v < N; v++)
    {
        if (dist[v] != 0 && dist[v] < minDist)
        {
            minDist = dist[v];
            minV = v;
        }
    }
    if (minDist < INT_MAX)
        return minV;
    return -1;
}

int prim()
{ /*返回最小生成树的权重*/
    int v, w, vCount = 0;
    int totalWeight = 0;
    int* dist = new int[N];

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

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

    while (true)
    {
        v = findMinDist(dist);
        if (v == -1)
            break;

        totalWeight += dist[v];
        dist[v] = 0; //收录v
        vCount++;

        for (w = 0; w < N; w++)
        {
            /*如果w没有被收录*/
            if (dist[w] != 0 && G[v][w] < dist[w])
            {
                dist[w] = G[v][w];
            }
        }
    }

    delete[] dist;

    if (vCount < N)
        return -1;
    return totalWeight;
}