染色法

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;

const int N = 10010;
int h[N], ne[N], e[N], idx;
int color[N];
int n, m;

//用邻接表存储图
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;

    //遍历当前这点的所有邻点
    for(int i = h[u]; i != -1; i = ne[i])
    {
        int j = e[i];
        if(!color[j])
        {
            if(!dfs(j, 3 - c))  return false;
        }
        else if(color[j] == c)  return false;   //一条边相连的两点怎么能是相同的颜色呢
    }
    return true;
}

int main()
{
    cin >> n >> m;
    memset(h, -1, sizeof h);
    while (m -- )
    {
        int a, b;
        cin >> a >> b;
        add(a, b), add(b, a);
    }

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

匈牙利算法：给定一个二分图，求最大匹配

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;

const int N = 510, M = 10010;
int match[N];
bool st[N];
int h[N], e[M], ne[M], idx;
int n1, n2, m;

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

bool find(int x)
{
   for(int i = h[x]; i != -1; i = ne[i])
   {
       int j = e[i];
       if(!st[j])
       {
           st[j] = true;
           if(match[j] == 0 || find(match[j]))  return true;
       }
   }
   return false;
}

int main()
{
    cin >> n1 >> n2 >> m;
    while (m -- )
    {
        int a, b;
        cin >> a >> b;
        add(a, b);
    }


    int res = 0;
    for(int i = 1; i <= n1; i ++ )
    {
        memset(st, false, sizeof st);
        if(find(i)) res ++ ;
    }

    cout << res << endl;
    return 0;
}