无向图连通分量正好是一个环

连通分量可以用并查集处理。

连通分量是环的条件可以是：边数等于点数，每个点的度都为2。

例题：AcWing 4493. 环形连通分量

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;

int p[200010];
int sz[200010];
int ec[200010];
bool flag[200010];
int find(int a)
{
    if (p[a] != a)
    {
        p[a] = find(p[a]);
    }
    return p[a];
}
void merge(int a, int b)
{
    int pa = find(a);
    int pb = find(b);
    if (pa!=pb)
    {
        p[pa] = pb;
        sz[pb] += sz[pa];
    }
}

void YD()
{
    int n, m;
    cin >> n >> m;
    for (int i = 1; i <= n; i++)
    {
        p[i] = i;
        sz[i] = 1;
    }
    for (int i = 1; i <= m; i++)
    {
        int a, b;
        cin >> a >> b;
        merge(a, b);
        ec[a]++;
        ec[b]++;
    }
    for (int i = 1; i <= n; i++)
    {
        int pi = find(i);
        if (pi != i)
        {
            ec[pi] += ec[i];
            if (ec[i] != 2)
                flag[pi] = true;
        }
    }
    LL res = 0;
    for (int i = 1; i <= n; i++)
    {
        int pi = find(i);
        if (pi == i)
        {
            if (sz[i] * 2 == ec[i]&&!flag[i])
                res++;
        }
    }
    cout << res << endl;

}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    int T = 1;
    //cin >> T;
    while (T--)
    {
        YD();
    }
    return 0;
}