hdoj 1878 欧拉回路(无向图欧拉回路+并查集)

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=1878

思路分析：该问题给定一个无向图，要求判断该无向图是否存在欧拉回路；无向图判断存在欧拉回路的两个必要条件：该无向图为连通图且所有的结点的度数为偶数；

代码如下：

#include <cstdio>
#include <cstring>
#include <iostream>
using namespace std;

const int MAX_N = 1000 + 10;
int fa[MAX_N];
int link[MAX_N];

void Init()
{
    for (int i = 0; i < MAX_N; ++i)
    {
        fa[i] = i;
        link[i] = 0;
    }
}

int Find(int a)
{
    if (fa[a] == a)
        return a;
    else
        return fa[a] = Find(fa[a]);
}

int Union(int a, int b)
{
    int fa_a = Find(a);
    int fa_b = Find(b);

    if (fa_a == fa_b)
        return -1;
    if (fa_a > fa_b)
        fa[fa_b] = fa_a;
    else
        fa[fa_a] = fa_b;
    return 1;
}

int main()
{
    int ver_num, road_num;
    int ver_1, ver_2;

    while (scanf("%d", &ver_num) != EOF && ver_num)
    {
        scanf("%d", &road_num);
        Init();
        for (int i = 0; i < road_num; ++i)
        {
            scanf("%d %d", &ver_1, &ver_2);
            link[ver_1]++;
            link[ver_2]++;
            Union(ver_1, ver_2);
        }
        int set_count = 0;
        bool ok = true;
        for (int i = 1; i <= ver_num; ++i)
        {
            if (fa[i] == i)
                set_count++;
            if ((link[i] & 1) != 0 || set_count > 1)
                ok = false;
            if (!ok)
                break;
        }
        if (ok)
            printf("1\n");
        else
            printf("0\n");
    }
    return 0;
}