Pancake sorting

14 Jun, 2022
Given an unsorted array, the task is to sort the given array. You are allowed to do only following operation on array. 
flip(arr, i): Reverse array from 0 to i 
Examples:
Input: arr[] = { 23, 10, 20, 11, 12, 6, 7 }Output: { 6, 7, 10, 11, 12, 20, 23}
Input: arr[] = { 0, 1, 1, 0, 0 }Output: { 0, 0, 0, 1, 1 }
Approach: 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_sizeFind 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)
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)
See following video for visualization of the above algorithm.http://www.youtube.com/embed/kk-_DDgoXfk
Below is the implementation:
C
CPP
Java
Python3
C#
PHP
Javascript
// 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;}
// 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 operations void 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 n void printArray(int arr[], int n) {     for (int i = 0; i < n; ++i)         cout<< arr[i]<<" "; }   // Driver program to test above function int 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 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 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 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.
// 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 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, $curr_size-1);        }    }}  // A utility function to print // n array of size n function printArray($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?>
<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>
Sorted Array 
6 7 10 11 12 20 23 
Time Complexity: O(n2), Total O(n) flip operations are performed in above codeAuxiliary Space: O(1)
References: http://en.wikipedia.org/wiki/Pancake_sortingPlease write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
nitin mittal
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