Pancake Sorting in Python
Pancake Sorting is a sorting algorithm that involves a scenario where you have a stack of pancakes of varying sizes and you want to sort them by size, with the smallest pancake on top and the largest on the bottom. The only operation allowed to sort the pancakes is to insert a spatula at some point in the stack and flip all the pancakes above the spatula. This operation is known as a “prefix reversal” or simply a “flip.”
What is Pancake Sort?
Pancake Sorting works by repeatedly finding the largest unsorted element in the list and flipping it to the top, and then flipping it again to its correct position. The process is repeated for the remaining unsorted portion of the list.
Approach: To solve the problem, follow the below idea:
Unlike a traditional sorting algorithm, which attempts to sort with the fewest comparisons possible, the goal is to sort the sequence in as few reversals as possible. The idea is to do something similar to Selection Sort. We one by one place maximum element at the end and reduce the size of current array by one.
Step-by-step algorithm:
- Let given array be arr[] and size of array be n.
- Start from current size equal to n and reduce current size by one while it’s greater than 1. Let the current size be curr_size.
- Do following for every curr_size
- Find index of the maximum element in arr[0 to curr_szie-1]. Let the index be ‘mi’
- Call flip(arr, mi)
- Call flip(arr, curr_size – 1)
Below is the implementation of the algorithm:
# Python3 program to
# sort array using
# pancake sort
# Reverses arr[0..i] */
def flip(arr, i):
start = 0
while start < i:
temp = arr[start]
arr[start] = arr[i]
arr[i] = temp
start += 1
i -= 1
# Returns index of the maximum
# element in arr[0..n-1] */
def findMax(arr, n):
mi = 0
for i in range(0,n):
if arr[i] > arr[mi]:
mi = i
return mi
# The main function that
# sorts given array
# using flip operations
def pancakeSort(arr, n):
# Start from the complete
# array and one by one
# reduce current size
# by one
curr_size = n
while curr_size > 1:
# Find index of the maximum
# element in
# arr[0..curr_size-1]
mi = findMax(arr, curr_size)
# Move the maximum element
# to end of current array
# if it's not already at
# the end
if mi != curr_size-1:
# To move at the end,
# first move maximum
# number to beginning
flip(arr, mi)
# Now move the maximum
# number to end by
# reversing current array
flip(arr, curr_size-1)
curr_size -= 1
# A utility function to
# print an array of size n
def printArray(arr, n):
for i in range(0,n):
print ("%d"%( arr[i]),end=" ")
# Driver program
arr = [23, 10, 20, 11, 12, 6, 7]
n = len(arr)
pancakeSort(arr, n);
print ("Sorted Array ")
printArray(arr,n)
# This code is contributed by shreyanshi_arun.
Output
Sorted Array 6 7 10 11 12 20 23
Time Complexity: O(n2), total O(n) flip operations are performed.
Auxiliary Space: O(1)