并查集

ATC(ABC287C Path Graph?)

#include <bits/stdc++.h>

using namespace std;

struct DSU {
    vector<int> f, siz;
    DSU(int n) : f(n), siz(n, 1) { iota(f.begin(), f.end(), 0); }
    int leader(int x) {
        while (x != f[x]) x = f[x] = f[f[x]];
        return x;
    }
    bool same(int x, int y) { return leader(x) == leader(y); }
    bool merge(int x, int y) {
        x = leader(x);
        y = leader(y);
        if (x == y) return false;
        siz[x] += siz[y];
        f[y] = x;
        return true;
    }
    int size(int x) { return siz[leader(x)]; }
};


int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    
    int N, M;
    cin >> N >> M;
    
    if (M != N - 1) {
        cout << "No\n";
        return 0;
    }
    
    vector<int> deg(N);
    DSU dsu(N);
    for (int i = 0; i < M; i++) {
        int u, v;
        cin >> u >> v;
        // u--, v--;
        deg[u]++, deg[v]++;
        dsu.merge(u, v);
    }
    for (int i = 0; i < N; i++) {
        if (deg[i] > 2) {
            cout << "No\n";
            return 0;
        }
        if (!dsu.same(i, 0)) { // 如果不连通
            cout << "No\n";
            return 0;
        }
    }
    cout << "Yes\n";
    
    return 0;
}

ATC(ABC288C Don't be cycle)

#include <bits/stdc++.h>

using namespace std;

struct DSU {
    std::vector<int> f, siz;
    DSU(int n) : f(n), siz(n, 1) { std::iota(f.begin(), f.end(), 0); }
    int leader(int x) {
        while (x != f[x]) x = f[x] = f[f[x]];
        return x;
    }
    bool same(int x, int y) { return leader(x) == leader(y); }
    bool merge(int x, int y) {
        x = leader(x);
        y = leader(y);
        if (x == y) return false;
        siz[x] += siz[y];
        f[y] = x;
        return true;
    }
    int size(int x) { return siz[leader(x)]; }
};

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    
    int n, m;
    std::cin >> n >> m;
    int comp = n;
    DSU dsu(n);
    for (int i = 0; i < m; i++) {
        int u, v;
        std::cin >> u >> v;
        u--, v--;
        comp -= dsu.merge(u, v); // comp：连通块数
    }
    std::cout << m - (n - comp) << "\n";
    
    return 0;
}