Minimum Path Sum
Difficulty: Medium
Category: DSA
Topics: Array, Dynamic Programming, Matrix
Asked at: Google, Amazon, Goldman Sachs, Facebook, Apple, Snapchat, Tesla
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:**
**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.
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**Example 2:**
**Input:** grid = [[1,2,3],[4,5,6]]
**Output:** 12
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**Constraints:**
- `m == grid.length`
- `n == grid[i].length`
- `1 <= m, n <= 200`
- `0 <= grid[i][j] <= 200`