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Java-based LeetCode algorithm problem solutions, regularly updated
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931\. Minimum Falling Path Sum
Medium
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:**
![](https://assets.leetcode.com/uploads/2021/11/03/failing1-grid.jpg)
**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:**
![](https://assets.leetcode.com/uploads/2021/11/03/failing2-grid.jpg)
**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`
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