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c++/Others/Fig10_53.cpp - All-pairs algorithm, with a test program.cpp

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+Fig10_53.cpp - All-pairs algorithm, with a test program
+	
+	#include <iostream.h>
+        #include "matrix.h"
+
+/* START: Fig10_53.txt */
+        const 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
+         */
+        void allPairs( const matrix<int> & a,
+                       matrix<int> & d, matrix<int> & path ) 
+        {
+            int n = a.numrows( );
+
+            // 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 */
+
+        int main( )
+        {
+            matrix<int> a( 4, 4 );
+            a[ 0 ][0 ] = 0; a[ 0 ][ 1 ] = 2; a[ 0 ][ 2 ] = -2; a[ 0 ][ 3 ] = 2;
+            a[ 1 ][ 0 ] = 1000; a[ 1 ][ 1 ] = 0; a[ 1 ][ 2 ] = -3; a[ 1 ][ 3 ] = 1000;
+            a[ 2 ][ 0 ] = 4; a[ 2 ][ 1 ] = 1000; a[ 2 ][ 2 ] = 0; a[ 2 ][ 3 ] = 1000;
+            a[ 3 ][ 0 ] = 1000; a[ 3 ][ 1 ] = -2; a[ 3 ][ 2 ] = 3; a[ 3 ][ 3 ] = 0;
+
+            matrix<int> d( 4, 4 );
+            matrix<int> path( 4, 4 );
+
+            allPairs( a, d, path );
+            int i;
+            for( i = 0; i < d.numrows( ); i++ )
+            {
+                for( int j = 0; j < d.numcols( ); j++ )
+                    cout << d[ i ][ j ] << "    " ;
+                cout << endl;
+            }
+            for( i = 0; i < path.numrows( ); i++ )
+            {
+                for( int j = 0; j < path.numcols( ); j++ )
+                    cout << path[ i ][ j ] << "    " ;
+                cout << endl;
+            }
+
+            return 0;
+        }