矩阵连乘

package martixchain;
import java.io.Reader;
import java.util.Scanner;

import javax.security.auth.kerberos.KerberosKey;

import org.omg.CORBA.PUBLIC_MEMBER;

/*--------------------------------------------------------------
 * Author:     DingWenchao
 * Writtern:   Dec 3,2014
 * 
 * martixchain
 *to produce the optimal array->the optimal computing orders
 *example:matrix[30,35,15,5,10,20,25]-> matrix 30 35 5 10 20 25
 *to produce: 15125 ((A1(A2A3))((A4A5)A6))
 *
 *Tests: matrix[30,35,15,5,10,20,25]
 *expected is : 15125 ((A1(A2A3))((A4A5)A6))
 * -------------------------------------------------------------*/

public class Martix_chain{
	public static void main(String args[]){
		System.out.println("Enter the number of martix");
	    Scanner reader = new Scanner(System.in);
		int n          = reader.nextInt();
		int []p        = new int[n+1];
		System.out.println("Enter ther a array of number "
				+ "for eample 30 35 15 5 10 20 25 stand for six martixs 30*35,35*15,15*5,5*10,10*20,20*25 ");
		for(int i = 0;i <= n;i++){
			p[i] = reader.nextInt();
		}
		reader.close();
		martix mx = new martix(n, p);
		int[][]s = mx.martixChain();
		for(int i = 1;i<=n;i++){
			  for(int j = 1;j<=n;j++){
				  System.out.println(s[i][j]);
			  }
			
		}
		mx.traceback(1, n);
	}
}
class martix{
	int n;      //the number of martix.
	int[]p;    //the array of martix.
	int[][]m; //to save each of 
	int[][]s;//to save k
	martix(int n,int[]p){//construct function
		this.n = n;
		this.p = p;
		this.m = new int[n+1][n+1];
		this.s = new int[n+1][n+1];
	}
	int[][] martixChain(){
		for(int i = 1;i <= n;i++)m[i][i] = 0;
		for(int r = 2;r <= n;r++)//diagonal cycle
			for(int i = 1;i <= n-r+1;i++){//
				int j = i + r - 1;
				m[i][j] = m[i][i] + m[i+1][j] + p[i-1]*p[i]*p[j];
				s[i][j] = i;
				for(int k = i+1;k < j;k++){
					int t = m[i][k] + m[k+1][j] + p[i-1]*p[k]*p[j];
					if(t < m[i][j]){
						m[i][j] = t;
						s[i][j] = k;
					}
				}
			}
		return s;
	}
	void traceback(int i,int j){
		if(i == j) return;
		traceback(i,s[i][j]);
		traceback(s[i][j]+1,j );
		System.out.println("Multiplay A" + i + "," + s[i][j] + "and A" + (s[i][j]+1)+"," + j);
	}
}