并查集， 判断是否存在环

#include<iostream>
#include<vector>
using namespace std;
//n-节点数
//m-边的数
//给一幅图，判断是否存在环
int find_root(int x, vector<int>&parent) {
    if (parent[x] == -1) {
        return x;
    }
    int root = find_root(parent[x], parent);
    return root;
}

int main(){
    int n, m;
    cin >> n, m;
    vector<int>parent(n,-1);
    for (int i = 1; i < m; ++i) {
        int x, y;
        cin >> x >> y;
        //连通，且又存在一条相连的边
        if (find_root(x, parent) == find_root(y, parent)) {
            cout << "cycle found" << endl;
        }
        else {
            parent[find_root(x,parent)] = find_root(y, parent);
        }
    }
    cout << "no cycle" << endl;
    return 0;
}

 路径压缩

#include<iostream>
#include<vector>
using namespace std;

void ini(vector<int>parents,vector<int>&rank) {
    for (int i = 0; i < rank.size(); i++) {
        parents[i] = -1;
        rank[i] = 0;
    }
}

int findParent(vector<int>parents, int i) {
    int root = i;
    while (parents[root] != -1) {
        root = parents[root];
    }
    return root;
}

int unionPath(int i, int j, vector<int>parents, vector<int>rank) {
    int root1 = findParent(parents, i);
    int root2 = findParent(parents, j);
    if (root1 == root2) { return 0; }
    else {
        if (rank[root1] > rank[root2]) {
            parents[root2] = root1;
        }
        else if(rank[root1]<rank[root2]){
            parents[root1] = root2;
        }
        else {
            parents[root1] = root2;
            rank[root2]++;
        }
        return 1;
    }
}

int main() {
    int n = 0;
    cin >> n;

    vector<vector<int>>matrix(n, vector<int>(n, 0));
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; j++) {
            cin >> matrix[i][j];
        }
    }
    vector<int>rank(n, 0);
    vector<int>parents(n,0);
    ini(parents,rank);

    for (int i = 0; i < n; ++i) {
        for (int j = i + 1; j < n; ++j) {
            if (matrix[i][j]) {
                int b = unionPath(i, j,parents, rank);
                if (b == 0) {
                    cout << "Loop" << endl;
                    return 0;
                }
            }
        }
    }
    cout << "No Loop";
    return 0;
}