MaxPath.java

package practise.leetCode;

public class MaxPath {

    public static void main(String[] args) {

        int[][] matrix = {
                {5, 1, 2, 3},
                {4, 8, 1, 2},
                {3, 2, 9, 4},
                {1, 7, 6, 5}
        };

        System.out.println("Maximum Path Sum: " + maxPath(matrix));
    }

    public static int maxPath(int[][] matrix) {

        int rows = matrix.length;
        int cols = matrix[0].length;

        // Start from bottom-left
        int[][] dp = new int[rows][cols];

        dp[rows - 1][0] = matrix[rows - 1][0];

        // First column - can only move UP
        for (int i = rows - 2; i >= 0; i--) {
            dp[i][0] = matrix[i][0] + dp[i + 1][0];
        }



        // Remaining cells
        // From each cell, we can come from:
        // 1. Bottom -> moving UP
        // 2. Left  -> moving RIGHT
        for (int i = rows - 2; i >= 0; i--) {
            for (int j = 1; j < cols; j++) {

                dp[i][j] = matrix[i][j]
                        + Math.max(dp[i + 1][j], dp[i][j - 1]);
            }
        }

        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                System.out.print(dp[i][j] + " ");
            }
            System.out.println();
        }

        // Top-right is the destination
        return dp[0][cols - 1];
    }
}