Matrix Chain Multiplication

class Solution {
    static int matrixMultiplication(int arr[]) {
        int n = arr.length;
        int[][] dp = new int[n + 1][n + 1];

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++)
                dp[i][j] = -1;
        }

        return mcm(arr, 1, n - 1, dp);
    }

    public static int mcm(int[] arr, int i, int j, int[][] dp) {
        // base case
        if (i >= j)
            return 0;

        if (dp[i][j] != -1)
            return dp[i][j];

        int mn = Integer.MAX_VALUE;
        for (int k = i; k <= j - 1; k++) { // ((A)(BCD) -> ((AB(CD))) -> ((ABC)(D))
            int temp = mcm(arr, i, k, dp) + mcm(arr, k + 1, j, dp) + arr[i - 1] * arr[k] * arr[j];
            mn = Math.min(mn, temp);
        }

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