64 Minimum Path Sum ->DP

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.

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