二分图KM算法 HDU 2255

在百度百科学了KM算法。。

km算法是求完备匹配下的最大权

KM算法流程:

1.对二分图的两部分顶点初始化

2.KM算法用匈牙利算法寻找完备匹配

3.如果未找到就修改相应顶点值

4重复（2）(3)直到找到相等子图的完备匹配为止；

HDU 2255是裸题。。

未优化版:

#include<stdio.h>
#include<string.h>
#include<stdlib.h>
int match[1000];
int mp[400][400];
bool visitx[400], visity[400];
int xx[400], yy[400];
const int inf = 0x7f7f7f7f;
int minx, N;

void init( )
{
  memset(match, -1, sizeof(match));
  memset(mp, 0, sizeof(mp));
  memset(xx, 0, sizeof(xx));
  memset(yy, 0, sizeof(yy));
}

bool Hungary( int x)
{
   visitx[x] = true;
   for( int i = 1; i <= N; i++)
   {   
       if( visity[i] ) continue;
       int temp = xx[x] +  yy[i] - mp[x][i]; 
       if( temp == 0 )
       {
            visity[i] = true;
            if( match[i] ==  -1 || Hungary(match[i]))
             {
                  match[i] = x;
                  return true;
             }
       }
       else
       {
           if( temp < minx )
               minx = temp;
       }
   } 
   return false;
}

void KM( )
{
   for( int i = 1; i <= N; i++)
   {
      for( int j = 1; j <= N; j++)
        {
           if( mp[i][j] > xx[i] )
            xx[i] = mp[i][j];
            yy[j] = 0;
        }
    }
    for( int i = 1; i <= N; i++)
    {
        while( 1 )
        {
          memset(visitx, 0, sizeof(visitx));
          memset(visity, 0, sizeof(visity));
          minx = inf;
          if( Hungary( i ) )
            break;
          else
          {
             for(int j = 1; j <= N; j++)
             {
                if( visitx[j] )
                     xx[j] -= minx;
                if( visity[j] )
                     yy[j] += minx;   
             
             }
          }
        }
    }
    int sum = 0;
    for( int i = 1; i <= N; i++)
        sum += mp[match[i]][i];
    printf("%d\n", sum);

}

int main( )
{

  while( scanf("%d",&N) != EOF )
  { 
     init( );
     for( int i = 1; i <= N; i++)
        for( int j = 1; j <= N; j++)
        scanf("%d",&mp[i][j]);
     KM( );
  }
}

优化版，跑出来时间到多一些，囧

 

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <algorithm>
using namespace std;

int match[310];
int xx[310], yy[310];
int visitx[310], visity[310];
int mp[310][310];
int slack[310];
const int inf = 0x7f7f7f7f;
int N;

void init( )
{
  memset(match, -1, sizeof(match));
  memset(xx, 0, sizeof(xx));
  memset(yy, 0, sizeof(yy));
  memset(mp, 0, sizeof(mp));
}

bool Hungary( int x)
{
   visitx[x] = true;
   for( int i = 1; i <= N; i++)
   {
      if( visity[i] )
        continue;
      int temp = xx[x] + yy[i] - mp[x][i];
      if( temp == 0)
      { 
        visity[i] = 1;
        if( match[i] == -1 || Hungary(match[i]))
        {
          match[i] = x;
          return true;
        }
      }
      else
         slack[i] = min(slack[i], temp); 
   }
   return false;
}

void KM( )
{
  for( int i = 1; i <= N; i++)
   for( int j = 1; j <= N; j++)
    {
      if( mp[i][j] > xx[i] )
          xx[i] = mp[i][j];
         yy[j] = 0;
    }
 for( int i = 1; i <= N; i++)
 {  
    for( int j = 1; j <= N; j++)
        slack[j] = inf;
    while( 1 )
    {
      memset(visitx, 0, sizeof(visitx));
      memset(visity, 0, sizeof(visity));
      if( Hungary(i) )
        break;
      else
      {
        int temp = inf;
        for( int j = 1; j <= N; j++)
        {
           if( !visity[j] && slack[j] < temp )
                temp = slack[j];
        }
        for( int k = 1; k <= N; k++)
        {
           if(visitx[k])
            xx[k] -= temp;
           if(visity[k])
            yy[k] += temp;
           else
            slack[k] -= temp;
        }
      }
    }
 }
 int sum = 0;
    for( int i = 1; i <= N; i++)
        sum += mp[match[i]][i];
    printf("%d\n", sum);
 
}
int main( )
{
  while( scanf("%d",&N) != EOF )
  { 
    init( );
    for( int i = 1; i <= N; i++)
        for( int j = 1; j <= N; j++)
            scanf("%d",&mp[i][j]);
    KM( );
  }
  return 0;
}