64\. Minimum Path Sum

Medium

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 1:**

![](https://assets.leetcode.com/uploads/2020/11/05/minpath.jpg)

**Input:** grid = [[1,3,1],[1,5,1],[4,2,1]]

**Output:** 7

**Explanation:** Because the path 1 → 3 → 1 → 1 → 1 minimizes the sum. 

**Example 2:**

**Input:** grid = [[1,2,3],[4,5,6]]

**Output:** 12 

**Constraints:**

*   `m == grid.length`
*   `n == grid[i].length`
*   `1 <= m, n <= 200`
*   `0 <= grid[i][j] <= 100`