Bipartite Graph km algorithm HDU 2255

I learned the KM Algorithm in Baidu encyclopedia ..

The KM algorithm is the maximum weight for a complete match.

KM algorithm flow:

1. initialize two vertices of a bipartite graph.

2. Search for complete matching using the Hungary algorithm using the KM Algorithm

3. Modify the vertex value if not found.

4. Repeat (2) (3) until a complete matching of an equal subgraph is found;

HDU 2255 is a bare question ..

Unoptimized version:

View code

#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( );
  }
}

Optimized version, more time to run, optimized

 

View code

#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;
}