二分图

二分图

mi0e

March 10, 2023

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836 words

C/C++ 算法

# 染色法

```cpp
#include <bits/stdc++.h>
using namespace std;
const int N = 1e2 + 10, M = 2 * N;

int h[N], e[M], ne[M], idx;
int color[N];
int n, m;

void add(int a, int b){
    e[idx] = b, ne[idx] = h[a], h[a] = idx++;
}

bool dfs(int u, int c){
    color[u] = c;
    for (int i = h[u]; ~i; i = ne[i]) {
        int j = e[i];
        if (!color[j]) {
            if (!dfs(j, 3 - c)) return false;
        } else if (color[j] == c) return false;
    }
    return true;
}

int main(){
    cin >> n >> m;
  
    int a, b;
    memset(h, -1, sizeof h);
    for (int i = 1; i <= m; i++) {
        cin >> a >> b;
        add(a, b), add(b, a);
    }

bool flag = true;
    for (int i = 1; i <= n; i++)
        if (!color[i])
            if (!dfs(i, 1)) flag = false;
  
    if (flag) cout << "YES" << endl;
    else cout << "NO" << endl;
  
    return 0;
}
```

# 匈牙利算法

```cpp
#include <bits/stdc++.h>
using namespace std;
const int N = 500, M = 1e5 + 10;

int h[N], e[M], ne[M], idx;
int n1, n2, m;
int match[N];
bool st[N];

void add(int a, int b){
    ne[idx] = h[a], e[idx] = b, h[a] = idx++;
}

int find(int u){
    for (int i = h[u]; ~i; i = ne[i]) {
        int j = e[i];
        if (!st[j]) {
            st[j] = true;
            if (!match[j] || find(match[j])) {
                match[j] = u;
                return true;
            }   
        }
    }
    return false;
}

int main(){
    cin >> n1 >> n2 >> m;
  
    int a, b;
    for (int i = 0; i < m; i++) {
        cin >> a >> b;
        add(a, b);
    }
  
    int res = 0;
    for (int i = 1; i <= n1; i++) {
        memset(st, 0, sizeof st);
        if (find(i)) res++;
    }
  
    cout << res;
  
    return 0;
}
```

Last modification：March 10, 2023