poj 2289 二分+多重匹配

最大值最小的一个常用方法是二分。二分“the size of the largest group”然后每次判断最大匹配数是否为人数即可。

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

const int X = 1000;
const int Y = 500;
int head[X];
int cnt[Y];
int mark[Y][X];
bool visit[Y];
int n, m, e, sz;

void init()
{
    e = 0;
    memset( head, -1, sizeof(head) );
}

struct Edge 
{
    int v, next;
} edge[X * Y];

void addEdge( int u, int v )
{
    edge[e].v = v;
    edge[e].next = head[u];
    head[u] = e++;
}

int dfs( int u )
{
    for ( int i = head[u]; i != -1; i = edge[i].next )
    {
        int v = edge[i].v;
        if ( !visit[v] )
        {
            visit[v] = 1;
            if ( cnt[v] < sz )
            {
                mark[v][cnt[v]++] = u;
                return 1;
            }
            else
            {
                for ( int j = 0; j < cnt[v]; j++ )
                {
                    if ( dfs( mark[v][j] ) )
                    {
                        mark[v][j] = u;
                        return 1;
                    }
                }
            }
        }
    }
    return 0;
}

bool hungary()
{
    memset( cnt, 0, sizeof(cnt) );
    for ( int i = 0; i < n; i++ )
    {
        memset( visit, 0, sizeof(visit) );
        if ( !dfs(i) ) return false;
    }
    return true;
}

const int L = 501;
char list[L];

int main ()
{
    while ( scanf("%d%d", &n, &m) != EOF )
    {
        if ( n == 0 && m == 0 ) break;
        init();
        getchar();
        for ( int i = 0; i < n; i++ )
        {
            gets(list);
            int len = strlen(list);
            int j = 0, ret;
            while ( 1 )
            {
                while ( !isdigit(list[j]) ) j++;
                ret = 0;
                while ( isdigit(list[j]) )
                {
                    ret = ret * 10 + list[j] - '0';
                    j++;
                }
                addEdge( i, ret );
                if ( j == len ) break;
            }
        }
        int lb = 1, ub = n;
        while ( lb < ub )
        {
            sz = ( lb + ub ) >> 1;
            if ( hungary() )
            {
                ub = sz;
            }
            else
            {
                lb = sz + 1;
            }
        }
        printf("%d
", lb);
    }
    return 0;
}