# C++ Programming Code Examples

## C++ > Data Structures and Algorithm Analysis in C++ Code Examples

### Dynamic programming algorithm for optimal chain matrix multiplication,

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