趣味算法-城市之间最短路径

城市之间最短路径：

算法描述：

(1) 图中所有顶点集合为V，最小生成树顶点集合为U，初始时V包含所有顶点，U中只有起始顶点。

(2) 计算下一个顶点到其实顶点V0的最短路径，并加入U。

(3) 更新未加入U中的各个顶点到起始顶点的距离值为发现的最小的权值。

(4) 重复该计算方法。

#include <stdio.h>

#define MAX_DIST 65535
#define MAX_POINT 5

void calc_dist(int arr[MAX_POINT][MAX_POINT], int nSize, int nStart)
{
    int arrWeight[MAX_POINT];
    int arrPoints[MAX_POINT];
    int i = 0, j = 0;
    int min = 0;
    int nPoint = 0;
    
    // Get the distance of reference points
    for (i = 0; i < MAX_POINT; i++)
    {
        arrWeight[i] = arr[nStart][i];
        arrPoints[i] = 0;
    }

    arrPoints[nStart] = 1;
    arrWeight[nStart] = 0;

    for (i = 0; i < MAX_POINT; i++)
    {
        // Get the min distance of reference point
        min = MAX_DIST;
        nPoint = 0;

        for (j = 0; j < MAX_POINT; j++)
        {
            if (arrPoints[j] == 0 
                && arrWeight[j] != MAX_DIST 
                && arrWeight[j] < min)
            {
                min = arrWeight[j];
                nPoint = j;
            }
        }

        arrPoints[nPoint] = 1;
        printf("point:%d  dist:%d \n", nPoint, min);

        // Update the distance of the point from the start point
        for (j = 0; j < MAX_POINT; j++)
        {
            if ((arrPoints[j] == 0) 
             && (arrWeight[nPoint]+arr[nPoint][j] < arrWeight[j]))
            {
                arrWeight[j] = arrWeight[nPoint]+arr[nPoint][j];
            }
        }
    }

}

int main()
{
    int arrTest[MAX_POINT][MAX_POINT]=
    {
        MAX_DIST,       10, MAX_DIST,       30,      100,
        MAX_DIST, MAX_DIST,       50, MAX_DIST, MAX_DIST,
        MAX_DIST, MAX_DIST, MAX_DIST, MAX_DIST,       10,
        MAX_DIST, MAX_DIST,       20, MAX_DIST,       60,
        MAX_DIST, MAX_DIST, MAX_DIST, MAX_DIST, MAX_DIST,
    };
    int i = 0;

    calc_dist(arrTest, MAX_POINT, 0);

    scanf("%d", &i);
    return 0;
}

算法复杂度：

n*(2*n)