NYOJ 42 一笔画问题

http://acm.nyist.net/JudgeOnline/problem.php?pid=42

 

判断一个无向图是否存在欧拉通路。

首先用并查集排除图不联通的情况

 

如果存在欧拉回路的话，那么所有顶点的度数应该都是偶数。

如果存在欧拉通路的话，那么有且仅有两个顶点的度数是奇数，其他的都是偶数。

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <algorithm>
#define IOS ios::sync_with_stdio(false)
using namespace std;
#define inf (0x3f3f3f3f)
typedef long long int LL;

#include <iostream>
#include <sstream>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <string>
const int maxn = 1000 + 20;
int Degree[maxn];
int fa[maxn];
int find(int u) {
    if (fa[u] == u) return fa[u];
    else return fa[u] = find(fa[u]);
}
void merge(int x, int y) {
    x = find(x);
    y = find(y);
    if (x != y) fa[y] = x;
}
void work() {
    memset(Degree, 0, sizeof Degree);
    for (int i = 0; i <= maxn - 20; ++i) fa[i] = i;
    int n, m;
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= m; ++i) {
        int a, b;
        scanf("%d%d", &a, &b);
        Degree[a]++;
        Degree[b]++;
        merge(a, b);
    }
    int flag = 0;
    for (int i = 1; i <= n; ++i) {
        flag += find(i) == i;
    }
    if (flag != 1) {
        printf("No\n");
        return;
    }
    int odd = 0;
    for (int i = 1; i <= n; ++i) {
        odd += Degree[i] & 1;
    }
    if (odd == 0 || odd == 2) {
        cout << "Yes" << endl;
    } else cout << "No" << endl;
}

int main() {
#ifdef local
    freopen("data.txt","r",stdin);
#endif
    int t;
    scanf("%d", &t);
    while (t--) work();
    return 0;
}