Algorithms

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Hi...I wanna write a program in java that can count the number of balanced matrix of N*N...the only way that I know is to consider all the possible assginments for the matrix and then choose the answers...I searched the topic and found something about it in wikipedia...it solved the problem with dynamic programming but unfortunately I don't understand exactly the algorithm...can anyone help and explain completely with example for me what to do ?
this is the link that I found :
http://en.wikipedia.org/wiki/Dynamic_programming#A_type_of_balanced_0.E2.80.931_matrix[^]

public static System.Collections.Generic.IEnumerable<System.Collections.Generic.IList<int>>
nQueens
(
  int HowMany
)
{
  int[] board = new int [ HowMany ] ;
  int   row   = 0 ;
 
  board [ row ] = -1 ;
 
  while ( row >= 0 )
  {
    board [ row ]++ ;
 
    if ( board [ row ] == HowMany )
    {
      row-- ;
    }
    else
    {
      int i ;
 
      for ( i = 0 ; i < row ; i++ )
      {
        int diff = board [ row ] - board [ i ] ;
 
        if ( ( diff == 0 ) || ( System.Math.Abs ( diff ) == ( row - i ) ) )
        {
          break ;
        }
      }
 
      if ( i == row )
      {
        row++ ;
 
        if ( row == HowMany )
        {
          yield return ( System.Array.AsReadOnly ( board ) ) ;
 
          row-- ;
        }
        else
        {
          board [ row ] = -1 ;
        }
      }
    }
  }
 
  yield break ;
}

C:\Projects>nQueens 438330000
^C
C:\Projects>nQueens 438335000
System.OutOfMemoryException: Exception of type 'System.OutOfMemoryException' was thrown.
   at PIEBALD.Lib.LibMth.<nQueens>d__0.MoveNext()
   at PIEBALD.Utilities.nQueens.Main(String[] args)

Member 4194593 wrote:

Desert Rat from West Phoenix