并查集(1)-判断无向图是否存在环

0
|  |    1-----2

0 1 2
-1 -1 -1

0   1   2    <----- 1 成为 0 的 父集合 (1 现在代表集合 {0, 1})
1  -1  -1

0   1   2    <----- 2 作为 1的父集合 (2 现在代表集合 {0, 1, 2})
1   2  -1

// 用并查集判断是否存在环
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

// 图中的边
struct Edge
{
    int src, dest;
};

// 图结构体
struct Graph
{
    // V-> 顶点个数, E-> 边的个数
    int V, E;

    // 每个图就是 边的集合
    struct Edge* edge;
};

// 创建一个图
struct Graph* createGraph(int V, int E)
{
    struct Graph* graph = (struct Graph*) malloc( sizeof(struct Graph) );
    graph->V = V;
    graph->E = E;

    graph->edge = (struct Edge*) malloc( graph->E * sizeof( struct Edge ) );

    return graph;
}

// 查找元素i 所在的集合( 根 )
int find(int parent[], int i)
{
    if (parent[i] == -1)
        return i;
    return find(parent, parent[i]);
}

// 合并两个集合
void Union(int parent[], int x, int y)
{
    int xset = find(parent, x);
    int yset = find(parent, y);
    parent[xset] = yset;
}

// 检测环
int isCycle( struct Graph* graph )
{
    int *parent = (int*) malloc( graph->V * sizeof(int) );

    // 初始化所有集合
    memset(parent, -1, sizeof(int) * graph->V);

    // 遍历所有边
    for(int i = 0; i < graph->E; ++i)
    {
        int x = find(parent, graph->edge[i].src);
        int y = find(parent, graph->edge[i].dest);

        if (x == y) //如果在一个集合，就找到了环
            return 1;

        Union(parent, x, y);
    }
    return 0;
}

// 测试
int main()
{
    /* 创建一些的图
         0
        |          |            1-----2 */
    struct Graph* graph = createGraph(3, 3);

    // 添加边 0-1
    graph->edge[0].src = 0;
    graph->edge[0].dest = 1;

    // 添加边 1-2
    graph->edge[1].src = 1;
    graph->edge[1].dest = 2;

    // 添加边 0-2
    graph->edge[2].src = 0;
    graph->edge[2].dest = 2;

    if (isCycle(graph))
        printf( "Graph contains cycle" );
    else
        printf( "Graph doesn‘t contain cycle" );

    return 0;
}