# 0969. Pancake Sorting

<https://leetcode.com/problems/pancake-sorting>

## Description

Given an array of integers `arr`, sort the array by performing a series of **pancake flips**.

In one pancake flip we do the following steps:

* Choose an integer `k` where `1 <= k <= arr.length`.
* Reverse the sub-array `arr[0...k-1]` (**0-indexed**).

For example, if `arr = [3,2,1,4]` and we performed a pancake flip choosing `k = 3`, we reverse the sub-array `[3,2,1]`, so `arr = [1,2,3,4]` after the pancake flip at `k = 3`.

Return *an array of the* `k`*-values corresponding to a sequence of pancake flips that sort* `arr`. Any valid answer that sorts the array within `10 * arr.length` flips will be judged as correct.

**Example 1:**

```
**Input:** arr = [3,2,4,1]
**Output:** [4,2,4,3]
**Explanation:** 
We perform 4 pancake flips, with k values 4, 2, 4, and 3.
Starting state: arr = [3, 2, 4, 1]
After 1st flip (k = 4): arr = [1, 4, 2, 3]
After 2nd flip (k = 2): arr = [4, 1, 2, 3]
After 3rd flip (k = 4): arr = [3, 2, 1, 4]
After 4th flip (k = 3): arr = [1, 2, 3, 4], which is sorted.
```

**Example 2:**

```
**Input:** arr = [1,2,3]
**Output:** []
**Explanation:** The input is already sorted, so there is no need to flip anything.
Note that other answers, such as [3, 3], would also be accepted.
```

**Constraints:**

* `1 <= arr.length <= 100`
* `1 <= arr[i] <= arr.length`
* All integers in `arr` are unique (i.e. `arr` is a permutation of the integers from `1` to `arr.length`).

## ac

```java
```