# problem931

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Published: Mar 23, 2021 License: MIT

### 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:

```Input: matrix = [[2,1,3],[6,5,4],[7,8,9]]
Output: 13
Explanation: There are two falling paths with a minimum sum underlined below:
[[2,1,3],      [[2,1,3],
[6,5,4],       [6,5,4],
[7,8,9]]       [7,8,9]]
```

Example 2:

```Input: matrix = [[-19,57],[-40,-5]]
Output: -59
Explanation: The falling path with a minimum sum is underlined below:
[[-19,57],
[-40,-5]]
```

Example 3:

```Input: matrix = [[-48]]
Output: -48
```

Constraints:

• `n == matrix.length`
• `n == matrix[i].length`
• `1 <= n <= 100`
• `-100 <= matrix[i][j] <= 100`

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