Minimum Falling Path Sum
Difficulty: Medium
Category: DSA
Topics: Array, Dynamic Programming, Matrix
Asked at: Amazon
Given an `n x n` array of integers `matrix`, return _the **minimum sum** of any **falling path** through_ `matrix`.
A **falling path** starts at any element in the first row and chooses the element in the next row that is either directly below or diagonally left/right. Specifically, the next element from position `(row, col)` will be `(row + 1, col - 1)`, `(row + 1, col)`, or `(row + 1, col + 1)`.
**Example 1:**
**Input:** matrix = [[2,1,3],[6,5,4],[7,8,9]]
**Output:** 13
**Explanation:** There are two falling paths with a minimum sum as shown.
```
**Example 2:**
**Input:** matrix = [[-19,57],[-40,-5]]
**Output:** -59
**Explanation:** The falling path with a minimum sum is shown.
```
**Constraints:**
- `n == matrix.length == matrix[i].length`
- `1 <= n <= 100`
- `-100 <= matrix[i][j] <= 100`