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.

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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.
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class Solution {

    public int minPathSum(int[][] grid) {
        if (grid.length == 0) {
            return 0;
        }
        int[][] dp = new int[grid.length][grid[0].length];
        for (int i = 0; i < dp.length; i++) {
            for (int j = 0; j < dp[i].length; j++) {
                dp[i][j] = grid[i][j];
                // We omit first row and first column
                if (i > 0 && j > 0) {
                    dp[i][j] += Math.min(dp[i - 1][j], dp[i][j - 1]);
                } else if (i > 0) {
                    dp[i][j] += dp[i - 1][j];
                } else if (j > 0)  {
                    dp[i][j] += dp[i][j - 1];
                }
            }
        }
        return dp[dp.length - 1][dp[0].length - 1];
    }
}