Pancake sorting
Given an unsorted array, sort the given array. You are allowed to do only following operation on array.
flip(arr, i): Reverse array from 0 to i
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.
Following are the detailed steps. 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..curr_szie-1]. Let the index be ‘mi’
- Call flip(arr, mi)
- Call flip(arr, curr_size-1)
See following video for visualization of the above algorithm.
http://www.youtube.com/embed/kk-_DDgoXfk
C
// C program to// sort array using// pancake sort#include <stdio.h>#include <stdlib.h>/* Reverses arr[0..i] */void flip(int arr[], int i){ int temp, start = 0; while (start < i) { temp = arr[start]; arr[start] = arr[i]; arr[i] = temp; start++; i--; }}// Returns index of the// maximum element in// arr[0..n-1]int findMax(int arr[], int n){ int mi, i; for (mi = 0, i = 0; i < n; ++i) if (arr[i] > arr[mi]) mi = i; return mi;}// The main function that// sorts given array using// flip operationsvoid pancakeSort(int* arr, int n){ // Start from the complete // array and one by one // reduce current size // by one for (int curr_size = n; curr_size > 1; --curr_size) { // Find index of the // maximum element in // arr[0..curr_size-1] int 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); } }}// A utility function to print// n array of size nvoid printArray(int arr[], int n){ for (int i = 0; i < n; ++i) printf("%d ", arr[i]);}// Driver program to test above functionint main(){ int arr[] = { 23, 10, 20, 11, 12, 6, 7 }; int n = sizeof(arr) / sizeof(arr[0]); pancakeSort(arr, n); puts("Sorted Array "); printArray(arr, n); return 0;} |
CPP
// C++ program to// sort array using// pancake sort#include<bits/stdc++.h>using namespace std;/* Reverses arr[0..i] */void flip(int arr[], int i){ int temp, start = 0; while (start < i) { temp = arr[start]; arr[start] = arr[i]; arr[i] = temp; start++; i--; }}// Returns index of the// maximum element in// arr[0..n-1]int findMax(int arr[], int n){int mi, i;for (mi = 0, i = 0; i < n; ++i) if (arr[i] > arr[mi]) mi = i;return mi;}// The main function that// sorts given array using// flip operationsvoid pancakeSort(int *arr, int n){ // Start from the complete // array and one by one // reduce current size // by one for (int curr_size = n; curr_size > 1; --curr_size) { // Find index of the // maximum element in // arr[0..curr_size-1] int 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); } }}// A utility function to print// n array of size nvoid printArray(int arr[], int n){ for (int i = 0; i < n; ++i) cout<< arr[i]<<" ";}// Driver program to test above functionint main(){ int arr[] = {23, 10, 20, 11, 12, 6, 7}; int n = sizeof(arr)/sizeof(arr[0]); pancakeSort(arr, n); cout<<"Sorted Array "<<endl; printArray(arr, n); return 0;}//This code is contributed by rathbhupendra |
Java
// Java program to// sort array using// pancake sortimport java.io.*;class PancakeSort { /* Reverses arr[0..i] */ static void flip(int arr[], int i) { int temp, start = 0; while (start < i) { temp = arr[start]; arr[start] = arr[i]; arr[i] = temp; start++; i--; } } // Returns index of the // maximum element in // arr[0..n-1] static int findMax(int arr[], int n) { int mi, i; for (mi = 0, i = 0; i < n; ++i) if (arr[i] > arr[mi]) mi = i; return mi; } // The main function that // sorts given array using // flip operations static int pancakeSort(int arr[], int n) { // Start from the complete // array and one by one // reduce current size by one for (int curr_size = n; curr_size > 1; --curr_size) { // Find index of the // maximum element in // arr[0..curr_size-1] int 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); } } return 0; } /* Utility function to print array arr[] */ static void printArray(int arr[], int arr_size) { for (int i = 0; i < arr_size; i++) System.out.print(arr[i] + " "); System.out.println(""); } /* Driver function to check for above functions*/ public static void main (String[] args) { int arr[] = {23, 10, 20, 11, 12, 6, 7}; int n = arr.length; pancakeSort(arr, n); System.out.println("Sorted Array: "); printArray(arr, n); }}/* This code is contributed by Devesh Agrawal*/ |
Python3
# 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 operationsdef 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 ndef printArray(arr, n): for i in range(0,n): print ("%d"%( arr[i]),end=" ")# Driver programarr = [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. |
C#
// C# program to sort array using// pancake sortusing System;class GFG { // Reverses arr[0..i] static void flip(int []arr, int i) { int temp, start = 0; while (start < i) { temp = arr[start]; arr[start] = arr[i]; arr[i] = temp; start++; i--; } } // Returns index of the // maximum element in // arr[0..n-1] static int findMax(int []arr, int n) { int mi, i; for (mi = 0, i = 0; i < n; ++i) if (arr[i] > arr[mi]) mi = i; return mi; } // The main function that // sorts given array using // flip operations static int pancakeSort(int []arr, int n) { // Start from the complete // array and one by one // reduce current size by one for (int curr_size = n; curr_size > 1; --curr_size) { // Find index of the // maximum element in // arr[0..curr_size-1] int 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); } } return 0; } // Utility function to print // array arr[] static void printArray(int []arr, int arr_size) { for (int i = 0; i < arr_size; i++) Console.Write(arr[i] + " "); Console.Write(""); } // Driver function to check for // above functions public static void Main () { int []arr = {23, 10, 20, 11, 12, 6, 7}; int n = arr.Length; pancakeSort(arr, n); Console.Write("Sorted Array: "); printArray(arr, n); }}// This code is contributed by nitin mittal. |
PHP
<?php// PHP program to// sort array using// pancake sort/* Reverses arr[0..i] */function flip(&$arr, $i){ $start = 0; while ($start < $i) { $temp = $arr[$start]; $arr[$start] = $arr[$i]; $arr[$i] = $temp; $start++; $i--; }}// Returns index of the// maximum element in// arr[0..n-1]function findMax($arr, $n){ $mi = 0; for ($i = 0; $i < $n; ++$i) if ($arr[$i] > $arr[$mi]) $mi = $i; return $mi;}// The main function that// sorts given array using// flip operationsfunction pancakeSort(&$arr, $n){ // Start from the complete // array and one by one // reduce current size // by one for ($curr_size = $n; $curr_size > 1; --$curr_size) { // 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, $curr_size-1); } }}// A utility function to print// n array of size nfunction printArray($arr, $n){ for ($i = 0; $i < $n; ++$i) print($arr[$i]." ");}// Driver code$arr = array(23, 10, 20, 11, 12, 6, 7);$n = count($arr);pancakeSort($arr, $n);echo("Sorted Array \n");printArray($arr, $n);return 0; // This code is contributed by chandan_jnu?> |
Javascript
<script> // JavaScript program to sort array using pancake sort // Reverses arr[0..i] function flip(arr, i) { let temp, start = 0; while (start < i) { temp = arr[start]; arr[start] = arr[i]; arr[i] = temp; start++; i--; } } // Returns index of the // maximum element in // arr[0..n-1] function findMax(arr, n) { let mi, i; for (mi = 0, i = 0; i < n; ++i) if (arr[i] > arr[mi]) mi = i; return mi; } // The main function that // sorts given array using // flip operations function pancakeSort(arr, n) { // Start from the complete // array and one by one // reduce current size by one for (let curr_size = n; curr_size > 1; --curr_size) { // Find index of the // maximum element in // arr[0..curr_size-1] let 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); } } return 0; } // Utility function to print // array arr[] function printArray(arr, arr_size) { for (let i = 0; i < arr_size; i++) document.write(arr[i] + " "); document.write(""); } let arr = [23, 10, 20, 11, 12, 6, 7]; let n = arr.length; pancakeSort(arr, n); document.write("Sorted Array: " + "</br>"); printArray(arr, n); </script> |
Output:
Sorted Array 6 7 10 11 12 20 23
Total O(n) flip operations are performed in above code. The overall time complexity is O(n^2).
References:
http://en.wikipedia.org/wiki/Pancake_sorting
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