Pancake Sorting

Problem Source: Leetcode

Problem 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:

1. Choose an integer k where 1 <= k <= arr.length.
2. 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.

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)

tests

def test(fn):
    value = [3,2,4,1]
    expected = [1,2,3,4]
    ans, actual = fn(value)
    assert actual == expected 

    value = [1,2,3]
    expected = [1,2,3]
    ans, actual = fn(value)
    assert actual == expected 

Solution

• Time Complexity: O(n^2)
• Space Complexity: O(n)

from typing import List

def reverse(l, n):
    for i in range(n//2): 
        # inplace swaps means go through 1/2 the list portion we want to swap
        l[i], l[n-i-1] = l[n-i-1], l[i]

    
def pancakeSort(arr: List[int]) -> List[int]:
    swap_points = []
    for value_to_sort in range(len(arr),1,-1): # if n-1 elements are correct, then n elements are correct, so don't check the smallest value (1)
        current_location = arr.index(value_to_sort)+1
        if value_to_sort == current_location: 
            # If value already in correct position continue
            continue
        if current_location != 1: # If value is in front, this step isn't needed
            # If not, flip to get desired value in front
            reverse(arr, current_location)
            swap_points.append(current_location)
        # flip to get value in final position
        reverse(arr,value_to_sort)
        swap_points.append(value_to_sort)
    return swap_points, arr

test(pancakeSort)