连通图 环

添加链接描述

题意

求连通图的数量，及多少个连通图有环，其中只存在一个结点的图不属于连通图

思路

用并查集维护连通图的数量，每个连通图含有的结点的数量及含有的边的数量

code

#include<bits/stdc++.h>
using namespace std;
const int N = 2e6+7;
int t, n, m, fa[N], son[N], edge[N], id;
void init(int n)
{
    for(int i = 1; i <= n; i++)
        fa[i] = i, son[i] = 1, edge[i] = 0;
}
int find(int x)
{
    return (x == fa[x] ? x : fa[x] = find(fa[x]));
}
void merge(int x, int y)
{
    int fx = find(x), fy = find(y);
    if(fx != fy)
    {
        fa[fx] = fy;
        son[fy] += son[fx];
        edge[fy] += edge[fx] + 1;
    }
    else
        edge[fy]++;
}
int main()
{
    scanf("%d", &t);
    while(t--)
    {
        cin >> n >> m;
        init(n);
        for(int i = 1; i <= m; i++)
        {
            int u, v;
            cin >> u >> v;
            merge(u, v);
        }
        int cnt1 = 0, cnt2 = 0;
        for(int i = 1; i <= n; i++)
        {
            if(fa[i] == i && son[i] > 1)
            {
                cnt1++;
                if(edge[i] > son[i] - 1)
                    cnt2++;
            }
        }
        printf("Night sky #%d: %d constellations, of which %d need to be fixed. \n\n", ++id, cnt1, cnt2);
    }
    return 0;
}