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)

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