969 - Pancake Sorting.

Medium

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 <code>arr = <ins>1</ins>,<ins>2</ins>,<ins>3</ins>,4</code> 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 = <ins>1</ins>, <ins>4</ins>, <ins>2</ins>, <ins>3</ins>

After 2nd flip (k = 2): arr = <ins>4</ins>, <ins>1</ins>, 2, 3

After 3rd flip (k = 4): arr = <ins>3</ins>, <ins>2</ins>, <ins>1</ins>, <ins>4</ins>

After 4th flip (k = 3): arr = <ins>1</ins>, <ins>2</ins>, <ins>3</ins>, 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).