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.*;
import java.io.*;
import static java.lang.System.*;
import static java.lang.Math.*;

public class Main {
	static int[][] dp;
	static int[] p;

	public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = Integer.parseInt(sc.nextLine());

    dp = new int[n+1][n+1];
    p = new int[n+1];

    for (int i = 0; i < n; i++) {
      int[] input = Arrays.stream(sc.nextLine().split(" ")).mapToInt(Integer::parseInt).toArray();
      p[i] = input[0];
      p[i+1] = input[1];
    }

    out.println(count(1,n));
	}

	static int count(int i,int j) {
		if (dp[i][j] != 0 || i==j) return dp[i][j];
    if (i-j == 1) return dp[i][j] = p[i-1] * p[i] * p[j];

		int min = Integer.MAX_VALUE;
		for (int k=i; k<j; k++){
			min = min(min, count(i,k) + count(k+1,j) + p[i-1] * p[k] * p[j]);
    }

		return dp[i][j] = min;
	}
}