******** fig10.46 **********

	/* Compute optimal ordering of matrix multiplication */
	/* c contains number of columns for each of the n matrices */
	/* c[0] is the number of rows in matrix 1 */
	/* Minimum number of multiplications is left in M[1][n] */
	/* Actual ordering can be computed via another procedure using last_change */
	/* M and last_change are indexed starting at 1, instead of zero */

	void
	opt_matrix( int c[], unsigned int n, two_d_array M, two_d_array last_change )
	{
		int i, k, Left, Right, this_M;

		for( Left=1; Left <= n; Left++ )
			M[Left][Left] = 0;
		for(k=1; k<n; k++ )			/* k is Right-Left */
			for( Left=1; Left <= n-k; Left++ )	/* for each position */
			{
				Right = Left + k;
				M[Left][Right] = INT_MAX;
				for( i=Left; i<Right; i++ )
				{
					this_M=M[Left][i]+M[i+1][Right]+c[Left-1]*c[i]*c[Right];
					if( this_M < M[Left][Right] )	/* Update min */
					{
						M[Left][Right] = this_M;
						last_change[Left][Right] = i;
					}
				}
			}
	}