并查集

并查集

1）概念：处理不相交集合合并及查询问题的树型数据结构
2）基本功能：查找（find），合并（union）
3）代码实现：

#include<iostream>
using namespace std;


//并查集优化：扁平化（路径压缩），小挂大
const int MAXN = 1000005;
int father[MAXN];
int sizeOfu[MAXN];
int st[MAXN];

int find(int i){
    int k = 0;
    while(i!=father[i]){
        st[k++] = i;
        i = father[i];
    }
    while(k > 0){
        father[st[--k]] = i;
    }

    return i;
}


bool isSameUnion(int a,int b){
    return find(a) == find(b);
}

void Union(int a,int b){
    int fa = find(a);
    int fb = find(b);

    if(fa != fb){
        if(sizeOfu[fa] >= sizeOfu[fb]){
            sizeOfu[fa] += sizeOfu[fb];
            father[fb] = fa;
        }
        else {
            sizeOfu[fb] += sizeOfu[fa];
            father[fa] = fb; 
        }
    }
}

int main(){

    int n,m;
    cin >> n >> m;
    
    for(int i = 1;i<=n;i++){
        father[i] = i;
        sizeOfu[i] = 1;
    }

    while(m--){
        int opt;
        cin >> opt;
        int n1,n2;
        cin >> n1 >> n2;
        if(opt == 1){
            if(isSameUnion(n1,n2)){
                cout << "Yes" << endl;
            }
            else{
                cout << "No" << endl;
            }
        }
        if(opt == 2){
            Union(n1,n2);
        }
    }

    return 0;
}

更简洁的写法如下：

#include<iostream>
using namespace std;

const int MAXN = 200005;

int father[MAXN];


int find(int i){
    if(father[i] != i){
        //扁平化
        father[i] = find(father[i]);
    }
    return father[i];
}

bool isSame(int a,int b){
    return find(a) == find(b);
}

void Union(int a,int b){
    father[find(a)] = find(b);
}

int main(){

    int n,m;
    cin >> n >> m;
    for(int i = 0;i<=n;i++){
        father[i] = i;
    }
    while(m--){
        int opt;
        int n1,n2;
        cin >> opt >> n1 >> n2;
        if(opt == 1){
            Union(n1,n2);
        }
        else if(opt == 2){
            if(isSame(n1,n2)){
                cout << "Y" << endl;
            }
            else {
                cout << "N" << endl;
            }
        }
    }

    return 0;
}