Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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{
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int[]p = new int[n + 1];
		int[][]m = new int[n + 1][n + 1];
		for(int i = 0; i < n; i++) {
			int r = scan.nextInt();
			int c = scan.nextInt();
			p[i] = r;
			p[i + 1] = c;
		}
		scan.close();
		for(int l = 2; l <= n; l++) {
			for(int i = 1; i <= n - l + 1; i++) {
				int j = i + l - 1;
				m[i][j] = (1 << 21);
				for(int k = i; k <= j - 1; k++) {
					m[i][j] = Math.min(m[i][j],
							+ m[i][k] + m[j][k] + m[k + 1][j] + p[i - 1] * p[k] * p[j]);
				}
			}
		}
		System.out.println(m[1][n]);
	}
}