Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

Example:

Input:
[
  [1,3,1],
  [1,5,1],
  [4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.

Solution

class Solution {
    public int minPathSum(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        int[][] map = new int[m][n];
        if (m == 0 || n == 0) {return 0;}
        map[0][0] = grid[0][0];
        for (int i = 0; i < m; i++){
            for (int j = 0; j < n; j++){
                if (i == 0) {
                    if (j > 0){
                        map[i][j] = grid[i][j] + map[i][j-1];
                    }
                }
                else if (j == 0) {
                    if (i > 0){
                         map[i][j] = grid[i][j] + map[i-1][j];
                    }
                }
                else {
                    map[i][j] = Math.min(map[i-1][j], map[i][j-1]) + grid[i][j];
                }
                
            }
        }
        return map[m-1][n-1];
    }
}