Problem:
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Matrix-chain Multiplication

The goal of the matrix-chain multiplication problem is to find the most efficient way to multiply given $n$ matrices $M_1, M_2, M_3,...,M_n$.

Write a program which reads dimensions of $M_i$, and finds the minimum number of scalar multiplications to compute the maxrix-chain multiplication $M_1M_2...M_n$.

Input

In the first line, an integer $n$ is given. In the following $n$ lines, the dimension of matrix $M_i$ ($i = 1...n$) is given by two integers $r$ and $c$ which respectively represents the number of rows and columns of $M_i$.

Output

Print the minimum number of scalar multiplication in a line.

Constraints

$1 \leq n \leq 100$

$1 \leq r, c \leq 100$

Sample Input 1

6
30 35
35 15
15 5
5 10
10 20
20 25

Sample Output 1

15125

Solution in JAVA (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

    private static final int r     = 0,
    		                 c     = 1,
    		                 EMPTY = -1;

    private static int[]   p;
    private static int[][] m;

    public static void main(String[] args) {

        //input
         Scanner sc = new Scanner(System.in).useDelimiter(System.getProperty("line.separator"));
         int N = sc.nextInt();
         p = new int[N+1];
         m = new int[N][N];
         String[] s = null;
       	 for(int i=0;i<N;i++){
       		 s = sc.next().split("\\s");
       		 p[i] = Integer.parseInt(s[r]);
       	 }
       	 p[N] = Integer.parseInt(s[c]);

         //calculation
       	 int i,j,k,l,q;
       	 for(l=1;l<N;l++){
       		 for(i=0;i<N-l;i++){
       			 j = i + l;
       			 m[i][j] = EMPTY;
       			 for(k=i;k<j;k++){
//       				 System.out.println("i:"+i+", k:"+k+", j:"+j);
       				 q = m[i][k] + m[k+1][j] + p[i]*p[k+1]*p[j+1];
//       				 System.out.println("m["+i+"]["+k+"]:"+m[i][k]+" + m["+(k+1)+"]["+j+"]:"+m[k+1][j]+" + p["+i+"]*p["+(k+1)+"]*p["+(j+1)+"]:"+p[i]*p[k+1]*p[j+1]);
       				 if(q < m[i][j] || m[i][j] == EMPTY){
       					 m[i][j] = q;
       				 }
       			 }
       		 }
       	 }

       	 for(i=0;i<N;i++){
       		 for(j=0;j<N;j++){
//       			 System.out.println("m["+i+"]["+j+"]:"+m[i][j]);
       		 }
       	 }

         //output
       	 System.out.println(m[0][N-1]);
    }
}