C Program For Pancake Sorting Algorithm

Pancake sorting is a unique sorting algorithm where the only allowed operation is to reverse a prefix of the array. In this article, you will learn how the pancake sorting algorithm works and how to implement it in C.

Problem Statement

The goal of pancake sorting is to sort a given sequence of distinct numbers using only "flips". A flip operation involves choosing an arbitrary point in the array and reversing all elements up to that point. This problem is interesting in computer science, particularly in theoretical algorithm analysis, and is sometimes posed in programming challenges.

For example, given the array [3, 2, 4, 1], we want to transform it into [1, 2, 3, 4] using only prefix reversals.

Example

Consider an unsorted array: [3, 2, 4, 1]

The desired sorted output after applying pancake sort operations would be: [1, 2, 3, 4]

Background & Knowledge Prerequisites

To understand and implement pancake sorting in C, readers should have a basic understanding of:

• C Programming Fundamentals: Variables, data types, loops (for, while), conditional statements (if-else).
• Arrays: How to declare, initialize, and manipulate one-dimensional arrays.
• Functions: Defining and calling functions, passing arguments by value and by reference.
• Pointers: Basic understanding of pointers, especially for array manipulation in functions.

Use Cases or Case Studies

While not as common for general-purpose sorting as quicksort or mergesort, pancake sorting has a few interesting applications and theoretical implications:

• Robotics: In scenarios where physical manipulation involves reversing sequences, such as reordering items on a conveyer belt or aligning parts.
• Bioinformatics: Some theoretical models for DNA rearrangement or protein folding might involve operations similar to prefix reversals.
• Interview Questions: Its unique constraint makes it a common topic in algorithm design and problem-solving interviews to test understanding of greedy algorithms and array manipulation.
• Theoretical Computer Science: The "pancake problem" explores the minimum number of flips required to sort an array, contributing to the study of permutation groups and computational complexity.

Solution Approaches

The core idea behind pancake sorting is to repeatedly place the largest unsorted element in its correct sorted position. This is achieved by two flips: one to bring the largest element to the front, and another to move it to its final position.

Approach 1: Iterative Placement of Maximum Element

This approach sorts the array from largest to smallest element, placing them correctly at the end of the array one by one.

One-line summary: Find the largest unsorted element, bring it to the front using one flip, then move it to its correct final position using a second flip.

Code Example:

// Pancake Sort Algorithm
#include <stdio.h>
#include <stdlib.h> // For malloc (if dynamically allocating, not strictly needed for this example)

// Function to reverse a prefix of an array
void flip(int arr[], int k) {
    int start = 0;
    while (start < k) {
        int temp = arr[start];
        arr[start] = arr[k];
        arr[k] = temp;
        start++;
        k--;
    }
}

// Function to find the index of the maximum element in a given sub-array
int findMax(int arr[], int n) {
    int max_idx = 0;
    for (int i = 0; i < n; i++) {
        if (arr[i] > arr[max_idx]) {
            max_idx = i;
        }
    }
    return max_idx;
}

// The main pancake sort function
void pancakeSort(int arr[], int n) {
    // Start from the complete array and reduce the size of the current unsorted array
    for (int current_size = n; current_size > 1; current_size--) {
        // Step 1: Find the index of the maximum element in the current unsorted sub-array
        int max_idx = findMax(arr, current_size);

        // If the maximum element is not already at its correct position
        // (i.e., at the end of the current unsorted sub-array)
        if (max_idx != current_size - 1) {
            // Step 2: Move the maximum element to the beginning of the array
            // by flipping the sub-array from index 0 to max_idx
            flip(arr, max_idx);

            // Step 3: Move the maximum element from the beginning to its correct position
            // (current_size - 1) by flipping the entire current unsorted sub-array
            flip(arr, current_size - 1);
        }
    }
}

// Function to print an array
void printArray(int arr[], int n) {
    for (int i = 0; i < n; i++) {
        printf("%d ", arr[i]);
    }
    printf("\\n");
}

int main() {
    int arr[] = {3, 2, 4, 1};
    int n = sizeof(arr) / sizeof(arr[0]);

    printf("Original array: ");
    printArray(arr, n);

    pancakeSort(arr, n);

    printf("Sorted array (Pancake Sort): ");
    printArray(arr, n);

    int arr2[] = {10, 20, 30, 40, 50, 60, 70};
    int n2 = sizeof(arr2) / sizeof(arr2[0]);
    printf("Original array 2: ");
    printArray(arr2, n2);
    pancakeSort(arr2, n2);
    printf("Sorted array 2 (Pancake Sort): ");
    printArray(arr2, n2);

    int arr3[] = {5, 4, 3, 2, 1};
    int n3 = sizeof(arr3) / sizeof(arr3[0]);
    printf("Original array 3: ");
    printArray(arr3, n3);
    pancakeSort(arr3, n3);
    printf("Sorted array 3 (Pancake Sort): ");
    printArray(arr3, n3);

    return 0;
}

Run

Sample Output:

Original array: 3 2 4 1 
Sorted array (Pancake Sort): 1 2 3 4 
Original array 2: 10 20 30 40 50 60 70 
Sorted array 2 (Pancake Sort): 10 20 30 40 50 60 70 
Original array 3: 5 4 3 2 1 
Sorted array 3 (Pancake Sort): 1 2 3 4 5

Stepwise Explanation:

1. flip(int arr[], int k) Function:

• This helper function performs the actual pancake flip operation.
• It takes an array arr and an index k.
• It reverses the elements from arr[0] up to arr[k] (inclusive).
• It uses a while loop with start and k pointers to swap elements from both ends towards the center of the prefix.

1. findMax(int arr[], int n) Function:

• This helper function finds the index of the maximum element within the first n elements of the array.
• It iterates from index 0 to n-1, keeping track of the index of the largest element found so far.

1. pancakeSort(int arr[], int n) Function (Main Algorithm):

• The outer for loop iterates n down to 2 (since the last element will be sorted when the first n-1 are). current_size represents the unsorted portion of the array.
• Find Maximum: In each iteration, findMax(arr, current_size) is called to locate the index (max_idx) of the largest element within the current current_size elements.
• First Flip (Bring Max to Front): If max_idx is not already at current_size - 1 (its correct final position in the current unsorted segment), two flips are performed. The first flip(arr, max_idx) brings the largest element to arr[0].
• Second Flip (Place Max to End): The second flip(arr, current_size - 1) then moves this largest element from arr[0] to its correct final position at arr[current_size - 1].
• After these operations, the largest element is correctly placed, and current_size decrements, effectively "locking" that element into its sorted place.

1. main() Function:

• Initializes sample arrays.
• Prints the original array.
• Calls pancakeSort to sort the array.
• Prints the sorted array.

Conclusion

Pancake sorting provides a distinct approach to ordering elements, constrained by the "flip" operation. By repeatedly finding the largest unsorted element and using two flips to place it in its correct final position, the algorithm effectively sorts the entire array. While not competitive in performance with comparison sorts like quicksort for general-purpose use, it offers valuable insight into alternative sorting mechanisms and problem-solving strategies under specific constraints.

Summary

• Pancake sorting sorts an array using only prefix reversal operations (flips).
• The algorithm works by iteratively placing the largest unsorted element into its correct final position.
• This placement involves two key flips: one to bring the largest element to the array's front and another to move it to its target sorted position.
• Helper functions flip() and findMax() are crucial for implementing the algorithm.
• Its primary relevance is in theoretical computer science and specific constrained problem scenarios rather than general-purpose sorting.