二分图

二分图判定：二着色

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

int T;
int N, M;
int c[10001];
bool visit[10001];
vector<vector<int> > m;

bool bfs(int idx, int flag) {
    visit[idx] = true;
    c[idx] = flag;
    for (int i = 0; i < m[idx].size(); ++i) {
        if (c[m[idx][i]] == c[idx]) return false;
        else c[m[idx][i]] = -flag;
    }
    for (int i = 0; i < m[idx].size(); ++i) {
        if (!visit[m[idx][i]] && !bfs(m[idx][i], -flag))
            return false;
    }
    return true;
}

void solve() {
    memset(c, 0, sizeof(c));
    memset(visit, false, sizeof(visit));
    for (int i = 0; i < N; ++i) {
        if (!visit[i] && !bfs(i, 1)) {
            cout << "Wrong" << endl;
            return;
        }
    }
    cout << "Correct" << endl;
}

int main() {
    cin >> T;
    for (int t = 0; t < T; ++t) {
        m.clear();
        cin >> N >> M;
        m.resize(N + 1);
        int u, v;
        for (int i = 0; i < M; ++i) {
            cin >> u >> v;
            m[u].push_back(v);
            m[v].push_back(u);
        }
        solve();
    }
    return 0;
}

二分图最大匹配：Hungary算法

#include <bits/stdc++.h>
using namespace std;

int N, M;
vector<vector<int>> graph;
vector<int> link;
vector<bool> visited;
int a, b;

int dfs(int u) {
    for (auto v : graph[u]) if (!visited[v]) {
        visited[v] = true;
        if (link[v] == -1 || dfs(link[v])) {
            link[v] = u;
            return 1;
        }
    }
    return 0;
}

int hungary() {
    int res = 0;
    for (int i = 0; i <= N; ++i) {
        visited.assign(N + 1, false);
        res += dfs(i);
    }
    return res / 2;
}

int main() {
    while (cin >> N >> M) {
        graph.assign(N + 1, vector<int>());
        link.assign(N + 1, -1);
        for (int i = 0; i < M; ++i) {
            cin >> a >> b;
            graph[a].push_back(b);
            graph[b].push_back(a);
        }
        int res = hungary();
        cout << res << endl;
    }
    return 0;
}