并查集判断几个环

2020-01-28 18:02:19 阅读：277 来源： 互联网

标签：判断几个查集 vertex vertices edge edges connected include

You are given an undirected graph consisting of nn vertices and mm edges. Your task is to find the number of connected components which are cycles.

Here are some definitions of graph theory.

An undirected graph consists of two sets: set of nodes (called vertices) and set of edges. Each edge connects a pair of vertices. All edges are bidirectional (i.e. if a vertex aa is connected with a vertex bb , a vertex bb is also connected with a vertex aa ). An edge can't connect vertex with itself, there is at most one edge between a pair of vertices.

Two vertices uu and vv belong to the same connected component if and only if there is at least one path along edges connecting uu and vv .

A connected component is a cycle if and only if its vertices can be reordered in such a way that:

the first vertex is connected with the second vertex by an edge,
the second vertex is connected with the third vertex by an edge,
...
the last vertex is connected with the first vertex by an edge,
all the described edges of a cycle are distinct.

A cycle doesn't contain any other edges except described above. By definition any cycle contains three or more vertices.

$\text{[math]}$ There are 66 connected components, 22 of them are cycles: [7,10,16][7,10,16] and [5,11,9,15][5,11,9,15] .

Input

The first line contains two integer numbers nn and mm (1≤n≤2⋅1051≤n≤2⋅105 , 0≤m≤2⋅1050≤m≤2⋅105 ) — number of vertices and edges.

The following mm lines contains edges: edge ii is given as a pair of vertices vivi , uiui (1≤vi,ui≤n1≤vi,ui≤n , ui≠viui≠vi ). There is no multiple edges in the given graph, i.e. for each pair (vi,uivi,ui ) there no other pairs (vi,uivi,ui ) and (ui,viui,vi ) in the list of edges.

Output

Print one integer — the number of connected components which are also cycles.

Examples

Input

Output

Input

Output

Note

In the first example only component [3,4,5][3,4,5] is also a cycle.

The illustration above corresponds to the second example.

大意：找出有多少个环

思路：算出每个顶点的度，只有度等于2的情况下才能成为环。如果两个顶点的度都为2，使用并查集，如果父节点相同，答案加一，否则联立。

AC代码：

#include<cstdio>
#include <map> 
#include<iostream>
#include<string>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
inline int read() {int x=0,f=1;char c=getchar();while(c!='-'&&(c<'0'||c>'9'))c=getchar();if(c=='-')f=-1,c=getchar();while(c>='0'&&c<='9')x=x*10+c-'0',c=getchar();return f*x;}
typedef long long ll;
const int maxn=5e5+10;
int f[maxn];
int sum[maxn];
int ans;
struct node{
    int u,v;
}a[maxn];
int find(int x){
    if(f[x]==x){
        return x;
    }
    else{
        return f[x]=find(f[x]);
    }
}
void unio(int x,int y){
    int f1=find(x);
    int f2=find(y);
    if(f1!=f2){
        f[f1]=f2;
    }
    else
        ans++;
}
int main(){
    int n,m;
    cin>>n>>m;
    for(int i=1;i<=n;i++){
        f[i]=i;
    }
    ans=0;
    for(int i=0;i<m;i++){
        cin>>a[i].u>>a[i].v;
        sum[a[i].u]++;
        sum[a[i].v]++;
    }
    for(int i=0;i<m;i++){
        if(sum[a[i].u]==2&&sum[a[i].v]==2){
            unio(a[i].u,a[i].v);
        }
    }
    printf("%d",ans);
}

标签：判断,几个,查集,vertex,vertices,edge,edges,connected,include
来源： https://www.cnblogs.com/lipu123/p/12238502.html

本站声明： 1. iCode9 技术分享网（下文简称本站）提供的所有内容，仅供技术学习、探讨和分享；
2. 关于本站的所有留言、评论、转载及引用，纯属内容发起人的个人观点，与本站观点和立场无关；
3. 关于本站的所有言论和文字，纯属内容发起人的个人观点，与本站观点和立场无关；
4. 本站文章均是网友提供，不完全保证技术分享内容的完整性、准确性、时效性、风险性和版权归属；如您发现该文章侵犯了您的权益，可联系我们第一时间进行删除；
5. 本站为非盈利性的个人网站，所有内容不会用来进行牟利，也不会利用任何形式的广告来间接获益，纯粹是为了广大技术爱好者提供技术内容和技术思想的分享性交流网站。

ICode9

并查集判断几个环