一步一步學數據結構之n--n（kruskal算法）

代碼：

#include <stdio.h>


//鬧了好長時間才鬧好，若是有不懂的地方能夠留言
//裏面判斷環的地方用到並查集

//並查集資料：<a target="_blank" href="http://dongxicheng.org/structure/union-find-set/">http://dongxicheng.org/structure/union-find-set/</a>
#define ENUM 15//邊的數量 
#define VNUM 9//頂點的數量 
#define MV 0

typedef struct _tag_Edge //存儲邊的信息
{
    int begin;
    int end;
    int weight;//權值 
}Edge;

int father[VNUM]; //存儲 
int son[VNUM];
int Matvix[VNUM][VNUM]=
{//圖 
    {0, 10, MV, MV, MV, 11, MV, MV, MV},
    {10, 0, 18, MV, MV, MV, 16, MV, 12},
    {MV, 18, 0, 22, MV, MV, MV, MV, 8},
    {MV, MV, 22, 0, 20, MV, 24, 16, 21},
    {MV, MV, MV, 20, 0, 26, MV, 7, MV},
    {11, MV, MV, MV, 26, 0, 17, MV, MV},
    {MV, 16, MV, 24, MV, 17, 0, 19, MV},
    {MV, MV, MV, 16, 7, MV, 19, 0, MV},
    {MV, 12, 8, 21, MV, MV, MV, MV, 0},
};

void swap(Edge array[], int i, int j)
{
    Edge temp = array[i];    
    array[i] = array[j];   
    array[j] = temp;
}

void SelectionSort(Edge array[], int len) // O(n*n)
{
    int i = 0;
    int j = 0;
    int k = -1;
    
    for(i=0; i<len; i++)
    {
        k = i;       
        for(j=i; j<len; j++)
        {
            if( array[j].weight < array[k].weight )
            {
                k = j;
            }
        }        
        swap(array, i, k);
    }
}

int unionsearch(int x) //查找根結點+路徑壓縮
{
    if(x != father[x])
    {//經過遞歸找到根結點，注意邊最終的end爲根結點 
        father[x] =    unionsearch(father[x]);
    }
    //father[x]爲x的父結點 
    return father[x];
}

int join(int x, int y) //合併
{
    int root1, root2;
    root1 = unionsearch(x);
    root2 = unionsearch(y);
    if(root1 == root2) //爲環
        return 0;
    else 
    {   //root2爲root1的父結點 
        father[root1] = root2;
        son[root2] += son[root1];
    }

    return 1;
}

int main()
{
        int i, j;//要使用的循環變量 
        int total = 0;//最後選出邊的數量 
        int sum = 0;//最後總權值 
        int flag = 0;
        int eNUM = ENUM-1;
        
        Edge array[ENUM];//總共的邊
         
        for(i=0; i<VNUM; ++i) //初始化
        {
            father[i] = i;
            son[i] = 1;
        }
              
        for(i=0; i<VNUM; i++)
        {
            for(j=0; j<VNUM; j++)
            {
                if((i<j) && (0 < Matvix[i][j]))
                {//給邊的結構體初始化 
                    array[eNUM].begin = i;
                    array[eNUM].end   = j;
                    array[eNUM--].weight= Matvix[i][j];
                }
            }
        } 
        
        //排序 ，對邊按照權值排序，從小到大 
        SelectionSort(array, ENUM);
        
        for(i=0; i<ENUM; i++)
        {    
            if(join(array[i].begin, array[i].end))
            {//判斷是否成環
                total++; //邊數加1
                sum += array[i].weight; //記錄權值之和
                printf("%d -> %d  weight:%d\n", array[i].begin, array[i].end, array[i].weight);
            }
            if(total == VNUM-1) //最小生成樹條件：邊數=頂點數-1
            {
                flag = 1;
                break;
            }
        }
        if(flag)
            printf("%d\n", sum);
        else
            printf("error.\n");

        return 0;
}