> For the complete documentation index, see [llms.txt](https://jaywin.gitbook.io/leetcode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jaywin.gitbook.io/leetcode/solutions/0120-triangle.md).

# 0120. Triangle

<https://leetcode.com/problems/triangle>

## Description

Given a `triangle` array, return *the minimum path sum from top to bottom*.

For each step, you may move to an adjacent number of the row below. More formally, if you are on index `i` on the current row, you may move to either index `i` or index `i + 1` on the next row.

**Example 1:**

```
**Input:** triangle = [[2],[3,4],[6,5,7],[4,1,8,3]]
**Output:** 11
**Explanation:** The triangle looks like:
   2
  3 4
 6 5 7
4 1 8 3
The minimum path sum from top to bottom is 2 + 3 + 5 + 1 = 11 (underlined above).
```

**Example 2:**

```
**Input:** triangle = [[-10]]
**Output:** -10
```

**Constraints:**

* `1 <= triangle.length <= 200`
* `triangle[0].length == 1`
* `triangle[i].length == triangle[i - 1].length + 1`
* `-104 <= triangle[i][j] <= 104`

**Follow up:** Could you do this using only `O(n)` extra space, where `n` is the total number of rows in the triangle?

## ac

```java
```