Pancake sorting

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_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)

See following video for visualization of the above algorithm.
http://www.youtube.com/embed/kk-_DDgoXfk

Below is the implementation:

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 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)
        printf("%d ", 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);

    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 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

// Java program to
// sort array using
// pancake sort
import 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 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.

C#

// C# program to sort array using
// pancake sort
using 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 operations
function 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
?>

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 

Time Complexity: O(n²), Total O(n) flip operations are performed in above code
Auxiliary Space: O(1)

Recursive Approach 

Another approach to implement pancake sort in C++ is by using a recursive algorithm .

Approach :

Step 1: Define a function to flip a subarray of the given array. This function takes two arguments: the array to be flipped, and the index of the last element of the subarray to be flipped.

Step 2: Define a function to find the index of the maximum element in a given subarray of the array. This function takes two arguments: the array to be searched, and the index of the last element of the subarray to be searched.

Step 3: Iterate over the input array from the end towards the beginning, and for each element i, do the following:

• Find the index of the maximum element in the subarray arr[0:i].
• If the maximum element is not already at the end of the subarray, flip the subarray arr[0:max_index].
• Flip the entire subarray arr[0:i] to move the element i to its correct position.

Step 4: Repeat Step 3 for the subarray arr[0:n-1], arr[0:n-2], …, arr[0:1] until the entire array is sorted.

Implementation Of above approach:

C++

#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--;
    }
}

// Recursive function to sort the array using pancake sort
void pancakeSort(int arr[], int n)
{
    // Base case: If the array is already sorted or has only
    // one element, return
    if (n == 1)
        return;

    // Find the index of the maximum element in the unsorted
    // portion of the array
    int mi = 0;
    for (int i = 0; i < n; i++) {
        if (arr[i] > arr[mi]) {
            mi = i;
        }
    }

    // Move the maximum element to the front of the array if
    // it's not already there
    if (mi != 0) {
        flip(arr, mi);
    }

    // Flip the entire array to move the maximum element to
    // its correct position
    flip(arr, n - 1);

    // Recursively sort the remaining unsorted portion of
    // the array
    pancakeSort(arr, n - 1);
}

// 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: ";
    for (int i = 0; i < n; i++) {
        cout << arr[i] << " ";
    }
    cout << endl;

    return 0;
}

Java

import java.util.*;

public 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--;
        }
    }

    // Recursive function to sort the array using pancake
    // sort
    static void pancakeSort(int arr[], int n)
    {
        // Base case: If the array is already sorted or has
        // only one element, return
        if (n == 1)
            return;

        // Find the index of the maximum element in the
        // unsorted portion of the array
        int mi = 0;
        for (int i = 0; i < n; i++) {
            if (arr[i] > arr[mi]) {
                mi = i;
            }
        }

        // Move the maximum element to the front of the
        // array if it's not already there
        if (mi != 0) {
            flip(arr, mi);
        }

        // Flip the entire array to move the maximum element
        // to its correct position
        flip(arr, n - 1);

        // Recursively sort the remaining unsorted portion
        // of the array
        pancakeSort(arr, n - 1);
    }

    // Driver program to test above function
    public static void main(String args[])
    {
        int arr[] = { 23, 10, 20, 11, 12, 6, 7 };
        int n = arr.length;

        pancakeSort(arr, n);

        System.out.print("Sorted Array: ");
        for (int i = 0; i < n; i++) {
            System.out.print(arr[i] + " ");
        }
        System.out.println();
    }
}

// Contributed by sdeadityasharma

Python3

# Python code addition

# 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

# Recursive function to sort the array using pancake sort
def pancakeSort(arr, n):
    # Base case: If the array is already sorted or has only
    # one element, return
    if n == 1:
        return

    # Find the index of the maximum element in the unsorted
    # portion of the array
    mi = 0
    for i in range(n):
        if arr[i] > arr[mi]:
            mi = i

    # Move the maximum element to the front of the array if
    # it's not already there
    if mi != 0:
        flip(arr, mi)

    # Flip the entire array to move the maximum element to
    # its correct position
    flip(arr, n - 1)

    # Recursively sort the remaining unsorted portion of
    # the array
    pancakeSort(arr, n - 1)

# Driver program to test above function
arr = [23, 10, 20, 11, 12, 6, 7]
n = len(arr)

pancakeSort(arr, n)

print("Sorted Array:", end=" ")
for i in range(n):
    print(arr[i], end=" ")
print()

# The code is contributed by Nidhi goel.

C#

using System;

class Program {
    // 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--;
        }
    }

    // Recursive function to sort the array using pancake
    // sort
    static void PancakeSort(int[] arr, int n)
    {
        // Base case: If the array is already sorted or has
        // only one element, return
        if (n == 1)
            return;

        // Find the index of the maximum element in the
        // unsorted portion of the array
        int mi = 0;
        for (int i = 0; i < n; i++) {
            if (arr[i] > arr[mi]) {
                mi = i;
            }
        }

        // Move the maximum element to the front of the
        // array if it's not already there
        if (mi != 0) {
            Flip(arr, mi);
        }

        // Flip the entire array to move the maximum element
        // to its correct position
        Flip(arr, n - 1);

        // Recursively sort the remaining unsorted portion
        // of the array
        PancakeSort(arr, n - 1);
    }

    // Driver program to test above function
    static void Main()
    {
        int[] arr = { 23, 10, 20, 11, 12, 6, 7 };
        int n = arr.Length;

        PancakeSort(arr, n);

        Console.Write("Sorted Array: ");
        for (int i = 0; i < n; i++) {
            Console.Write(arr[i] + " ");
        }
        Console.WriteLine();
    }
}
// This code is contributed by sarojmcy2e

Javascript

// Reverses arr[0..i]
function flip(arr, i) {
    let start = 0;
    while (start < i) {
        let temp = arr[start];
        arr[start] = arr[i];
        arr[i] = temp;
        start++;
        i--;
    }
}
// Recursive function to sort the array using pancake sort
function pancakeSort(arr, n) {
    if (n === 1) {
        // Base case: If the array is already sorted or has only one element, return
        return;
    }

    // Find the index of the maximum element in the unsorted portion of the array
    let mi = 0;
    for (let i = 0; i < n; i++) {
        if (arr[i] > arr[mi]) {
            mi = i;
        }
    }

    // Move the maximum element to the front of the array if it's not already there
    if (mi !== 0) {
        flip(arr, mi);
    }
    // Flip the entire array to move the maximum element to its correct position
    flip(arr, n - 1);
    // Recursively sort the remaining unsorted portion of the array
    pancakeSort(arr, n - 1);
}

let arr = [23, 10, 20, 11, 12, 6, 7];
let n = arr.length;
pancakeSort(arr, n);
console.log("Sorted Array: " + arr.join(" "));

// This code is contributed by shiv1o43g

Output

Sorted Array: 6 7 10 11 12 20 23 

Complexity Analysis:

• The time complexity of pancake sort is O(n²), where n is the size of the input array. The worst case occurs when the input array is reverse sorted. 
• The space complexity is O(1) since the sorting is done in-place.
  

References:
http://en.wikipedia.org/wiki/Pancake_sorting
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