[BZOJ 1741] Asteroids

[题目链接]

         https://www.lydsy.com/JudgeOnline/problem.php?id=1741

[算法]

        将每颗小行星的行，列相连，问题就转化为了求这张图的最小覆盖

        由konig定理可知，最小覆盖  = 最大匹配，因此，用匈牙利算法求二分图最大匹配即可

[代码]

         

#include<bits/stdc++.h>
using namespace std;
#define MAXN 510
#define MAXK 10010

struct edge
{
        int to,nxt;
} e[MAXK];

int n,k,i,r,c,ans,tot;
int head[MAXN],match[MAXN << 1];
bool visited[MAXN << 1];

inline void addedge(int u,int v)
{
        tot++;
        e[tot] = (edge){v,head[u]};
        head[u] = tot;
}
inline bool hungary(int u)
{
        int i,v;
        visited[u] = true;
        for (i = head[u]; i; i = e[i].nxt)    
        {
                v = e[i].to;
                if (!visited[v])
                {
                        visited[v] = true;
                        if (!match[v] || hungary(match[v]))    
                        {
                                match[v] = u;
                                return true;        
                        }    
                }    
        }    
        return false;
}

int main() 
{
        
        scanf("%d%d",&n,&k);
        for (i = 1; i <= k; i++)
        {
                scanf("%d%d",&r,&c);
                addedge(r,c + n);
        }
        for (i = 1; i <= n; i++)
        {
                memset(visited,false,sizeof(visited));
                if (hungary(i)) ans++;
        }
        printf("%d
",ans);
        
        return 0;
    
}