Pancake sorting

Given an 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.

C

 `// C program to ` `// sort array using ` `// pancake sort ` `#include ` `#include ` ` `  `/* 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
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
// 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 "<

 `// 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. `

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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