/*
 * MatMult.java
 *
 * Created on November 8, 2001, 11:12 PM
 */

/**
 *
 * @author  lziegler
 * @version 
 */
public class MatMult {

    /** Creates new MatMult */
    public MatMult() {
    }

    static void FindMatMult(int [] r)
    {
        int N=r.length;
        int [] [] M=new int[N][N];
        int n=N-1;
        int i,j,k,l,kmin,MinSoFar;
        for(i=1;i<=n;i++) 
        {
            M[i][i]=0;
            System.out.print("M["+i+"]["+i+"]=0 and r["+i+"]="+r[i]+"    ");
        }
        System.out.println("");
        for(l=1;l<n;l++)
        {
            for(i=1;i<=n-l;i++)
            {
                j=i+l;
                kmin=i;
                MinSoFar=M[i][kmin]+M[kmin+1][j]+r[i-1]*r[kmin]*r[j];
                for(k=i+1;k<j;k++)
                    if(MinSoFar>M[i][k]+M[k+1][j]+r[i-1]*r[k]*r[j])
                    {
                        kmin=k;
                        MinSoFar=M[i][k]+M[k+1][j]+r[i-1]*r[k]*r[j];
                    }
                M[i][j]=MinSoFar;
                System.out.print("M["+i+"]["+j+"]="+M[i][j]+" and k="+kmin+
                    " and r"+(i-1)+"*r"+kmin+"*r"+j+"="+(r[i-1]*r[kmin]*r[j])+" | ");
            }
            System.out.println("");
        }        
        System.out.println("");       
    }
    /**
    * @param args the command line arguments
    */
    public static void main (String args[]) {
        int [] r={10,20,50,1,100};
        FindMatMult(r);
    }

}