fig10_53.java

Data Structures and Algorithm Analysis in Java -- Source Code

    public class Fig10_53
    {
/* START: Fig10_53.txt */
        public static final int NOT_A_VERTEX = -1;

        /**
         * Compute all-shortest paths.
         * a[ ][ ] contains the adjacency matrix with
         * a[ i ][ i ] presumed to be zero.
         * d[ ] contains the values of the shortest path.
         * Vertices are numbered starting at 0; all arrays
         * have equal dimension. A negative cycle exists if
         * d[ i ][ i ] is set to a negative value.
         * Actual path can be computed using path[ ][ ].
         * NOT_A_VERTEX is -1
         */
        public static void allPairs( int [ ][ ] a,
                       int [ ][ ] d, int [ ][ ] path ) 
        {
            int n = a.length;

            // Initialize d and path
/* 1*/      for( int i = 0; i < n; i++ )
/* 2*/          for( int j = 0; j < n; j++ )
                {
/* 3*/              d[ i ][ j ] = a[ i ][ j ];
/* 4*/              path[ i ][ j ] = NOT_A_VERTEX;
                }

/* 5*/      for( int k = 0; k < n; k++ )
                // Consider each vertex as an intermediate
/* 6*/          for( int i = 0; i < n; i++ )
/* 7*/              for( int j = 0; j < n; j++ )
/* 8*/                  if( d[ i ][ k ] + d[ k ][ j ] < d[ i ][ j ] )
                        {
                            // Update shortest path
/* 9*/                      d[ i ][ j ] = d[ i ][ k ] + d[ k ][ j ];
/*10*/                      path[ i ][ j ] = k;
                        }
        }
/* END */

        public static void main( String [ ] args )
        {
            int [ ][ ] a = { { 0, 2, -2, 2 }, { 1000, 0, -3, 1000 },
                             { 4, 1000, 0, 1000 }, { 1000, -2, 3, 0 } };
            int d[ ][ ] = new int [ 4 ][ 4 ];
            int path[ ][ ] = new int [ 4 ][ 4 ];

            allPairs( a, d, path );
            for( int i = 0; i < 4; i++ )
            {
                for( int j = 0; j < 4; j++ )
                    System.out.print( d[ i ][ j ] + "    " );
                System.out.println( );
            }
            for( int i = 0; i < 4; i++ )
            {
                for( int j = 0; j < 4; j++ )
                    System.out.print( path[ i ][ j ] + "    " );
                System.out.println( );
            }
        }
    }