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73 lines
2.6 KiB
C++
73 lines
2.6 KiB
C++
Fig10_46.cpp - Dynamic programming algorithm for optimal chain matrix multiplication,
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with a test program
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#include <iostream.h>
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#include <limits.h>
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#include "matrix.h"
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/* START: Fig10_46.txt */
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const long INFINITY = LONG_MAX;
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/**
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* Compute optimal ordering of matrix multiplication.
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* c contains the number of columns for each of the n matrices.
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* c[ 0 ] is the number of rows in matrix 1.
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* The minimum number of multiplications is left in m[ 1 ][ n ].
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* Actual ordering is computed via another procedure using lastChange.
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* m and lastChange are indexed starting at 1, instead of 0.
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* Note: Entries below main diagonals of m and lastChange
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* are meaningless and uninitialized.
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*/
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void optMatrix( const vector<int> & c,
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matrix<long> & m, matrix<int> & lastChange )
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{
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int n = c.size( ) - 1;
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for( int left = 1; left <= n; left++ )
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m[ left ][ left ] = 0;
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for( int k = 1; k < n; k++ ) // k is right - left
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for( int left = 1; left <= n - k; left++ )
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{
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// For each position
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int right = left + k;
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m[ left ][ right ] = INFINITY;
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for( int i = left; i < right; i++ )
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{
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long thisCost = m[ left ][ i ] + m[ i + 1 ][ right ]
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+ c[ left - 1 ] * c[ i ] * c[ right ];
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if( thisCost < m[ left ][ right ] ) // Update min
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{
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m[ left ][ right ] = thisCost;
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lastChange[ left ][ right ] = i;
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}
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}
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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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vector<int> c( 5 );
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c[ 0 ] = 50; c[ 1 ] = 10; c[ 2 ] = 40; c[ 3 ] = 30; c[ 4 ] = 5;
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matrix<long> m( 5, 5 );
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matrix<int>lastChange( 5, 5 );
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optMatrix( c, m, lastChange );
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int i;
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for( i = 1; i < m.numrows( ); i++ )
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{
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for( int j = 1; j < m.numcols( ); j++ )
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cout << m[ i ][ j ] << " ";
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cout << endl;
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}
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for( i = 1; i < lastChange.numrows( ); i++ )
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{
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for( int j = 1; j < lastChange.numcols( ); j++ )
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cout << lastChange[ 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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