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74 lines
2.6 KiB
C++
74 lines
2.6 KiB
C++
Fig10_53.cpp - All-pairs algorithm, with a test program
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#include <iostream.h>
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#include "matrix.h"
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/* START: Fig10_53.txt */
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const int NOT_A_VERTEX = -1;
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/**
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* Compute all-shortest paths.
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* a[ ][ ]contains the adjacency matrix with
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* a[ i ][ i ] presumed to be zero.
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* d[ ] contains the values of the shortest path.
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* Vertices are numbered starting at 0; all arrays
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* have equal dimension. A negative cycle exists if
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* d[ i ][ i ] is set to a negative value.
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* Actual path can be computed using path[ ][ ].
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* NOT_A_VERTEX is -1
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*/
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void allPairs( const matrix<int> & a,
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matrix<int> & d, matrix<int> & path )
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{
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int n = a.numrows( );
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// Initialize d and path
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/* 1*/ for( int i = 0; i < n; i++ )
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/* 2*/ for( int j = 0; j < n; j++ )
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{
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/* 3*/ d[ i ][ j ] = a[ i ][ j ];
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/* 4*/ path[ i ][ j ] = NOT_A_VERTEX;
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}
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/* 5*/ for( int k = 0; k < n; k++ )
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// Consider each vertex as an intermediate
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/* 6*/ for( int i = 0; i < n; i++ )
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/* 7*/ for( int j = 0; j < n; j++ )
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/* 8*/ if( d[ i ][ k ] + d[ k ][ j ] < d[ i ][ j ] )
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{
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// Update shortest path
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/* 9*/ d[ i ][ j ] = d[ i ][ k ] + d[ k ][ j ];
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/*10*/ path[ i ][ j ] = k;
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}
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}
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/* END */
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int main( )
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{
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matrix<int> a( 4, 4 );
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a[ 0 ][0 ] = 0; a[ 0 ][ 1 ] = 2; a[ 0 ][ 2 ] = -2; a[ 0 ][ 3 ] = 2;
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a[ 1 ][ 0 ] = 1000; a[ 1 ][ 1 ] = 0; a[ 1 ][ 2 ] = -3; a[ 1 ][ 3 ] = 1000;
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a[ 2 ][ 0 ] = 4; a[ 2 ][ 1 ] = 1000; a[ 2 ][ 2 ] = 0; a[ 2 ][ 3 ] = 1000;
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a[ 3 ][ 0 ] = 1000; a[ 3 ][ 1 ] = -2; a[ 3 ][ 2 ] = 3; a[ 3 ][ 3 ] = 0;
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matrix<int> d( 4, 4 );
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matrix<int> path( 4, 4 );
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allPairs( a, d, path );
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int i;
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for( i = 0; i < d.numrows( ); i++ )
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{
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for( int j = 0; j < d.numcols( ); j++ )
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cout << d[ i ][ j ] << " " ;
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cout << endl;
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}
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for( i = 0; i < path.numrows( ); i++ )
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{
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for( int j = 0; j < path.numcols( ); j++ )
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cout << path[ i ][ j ] << " " ;
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cout << endl;
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}
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return 0;
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}
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