Maximum Path Sum in the matrix

//  this proble is preety tricky and solve like run a three thread in single node
// TC - O(3^N)   After take DP Solution otherwise it takes O(3^N * M)
// SC - O(N)

import java.util.* ;
import java.io.*; 

public class Solution {
	private static int[][] dp;
	public static int getMaxPathSum(int[][] matrix) {
		// Write your code here
		int n = matrix.length;
		int m = matrix[0].length;
		dp = new int[n][m];
		for (int[] x : dp) {
			Arrays.fill(x, -1);
		}

		int ans = Integer.MIN_VALUE;
		for (int i=0; i<m; i++)
			ans = Math.max(ans, helper(matrix, n-1, i));

		return ans;
	}
	private static int helper
	(
		int[][] mat,
		int i,
		int j
	) {
		if (j < 0 || j >= mat[0].length) {
			return -(int)1e8;
		}

		if (i == 0) {
			return mat[0][j];
		}

		if (dp[i][j] != -1) {
			return dp[i][j];
		}
		int s = mat[i][j] + helper(mat, i-1, j);
		int l = mat[i][j] + helper(mat, i-1, j-1);
		int r = mat[i][j] + helper(mat, i-1, j+1);


		return dp[i][j] = Math.max(s, Math.max(l, r));

	}
}