Pancake sorting - GeeksforGeeks

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.
1) 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
……a) Find index of the maximum element in arr[0..curr_szie-1]. Let the index be ‘mi’
……b) Call flip(arr, mi)
……c) 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 <stdlib.h> 
#include <stdio.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 
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); 
        } 
    } 
} 
  
// 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  
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);  
        }  
    }  
}  
  
// 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 
?> 

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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