Given amxngrid filled with non-negative numbers, find a path from top left to bottom right whichminimizesthe sum of all numbers along its path.

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

Example 1:

[[1,3,1],
 [1,5,1],
 [4,2,1]]

Given the above grid map, return

7

. Because the path 1→3→1→1→1 minimizes the sum.

tag: DP

class Solution {
    public int minPathSum(int[][] grid) {
        if (grid == null || grid.length == 0) return 0;
        int n = grid.length, m = grid[0].length;
        int[][] dp = new int[n][m];

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

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

        for (int i = 1; i < n; i++){
            for (int j = 1; j < m; j++){
                dp[i][j] = grid[i][j] + Math.min(dp[i - 1][j], dp[i][j - 1]);
            }
        }

        return dp[n - 1][m - 1];
    }
}