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

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2019-11-15 12:59:38 +01:00
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;
}