Sort the given Array in Spiral manner starting from the center

Given an array arr[] of size N, the task is to sort the array in descending order starting from the mid of the array having the next largest element at the right of the middle element and the next largest at the left of the middle element and so on.

Examples:

Input: arr[] = {4, 9, 3, 5, 7}
Output: 3 5 9 7 4
Explanation:
The largest element in the array is 9 is kept in the middle of the array at index = 2.
The next largest element is 7 is placed to the right of the middle element at index = 3.
The 3rd largest element is 5 is placed to the left of the middle element at index = 1.
The 4th largest element is 4 is placed to the right of the element is 7 at index = 4.
The smallest element is 3 is placed to left of the element is 5 at index = 0.

Input: arr[] = {4, 5, 3, 7, 6, 9, 7}
Output: 3 5 7 9 7 6 4
Explanation:
The largest element in the array is 9 is kept in the middle of the array at index = 3.
The next largest element is 7 is placed to the right of the middle element at index = 3.
The 3rd largest element is 7 is placed to the left of the middle element at index = 2.
The 4th largest element is 6 is placed to the right of the element 7 at index = 5.
The 5th largest element is 5 is placed to the left of the element 7 at index = 1.
The 6th largest element is 4 is placed at the right of the element 6 at index = 6.
The smallest element is 3 is placed to the left of the element 5 at index = 0.

Approach: The idea is to use bubble sort and to start sorting the array from the smallest element. First, place the smallest element in the left-most index and then, place the next smallest element in the rightmost index. Below are the steps:

• Initialize variables, say left = 0, right = N – 1 and i = 1.
• Start at the left position i.e. from left = 0 then perform bubble sort in the remaining part of the array finding the smallest element and placing it at the left-most position until i == right.
• Increase the value of left by 1 since its element is already placed, and doesn’t need to be changed.
• Start at the right position and perform bubble sort traversing in reverse direction again finding the smallest element and placing it in the position right until i == left.
• Decrement the value of right by 1 since its element is already placed, and doesn’t need to be changed.
• If N is even, the smallest element should come at the right extreme of the array but in our approach, the smallest element is placed at the left-most extreme. So, for achieving the required pattern, reverse the first half of the array.
• Print the modified sorted array.

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to sort the array
// according to the given pattern
void centerSpiralSort(int arr[], int N)
{
    // Initializing the variables
    int left = 0;
    int right = N - 1;
    int i = 1;

    while (left < right) {

        // Performing bubble sort
        for (i = left + 1; i <= right;
             i++) {
            if (arr[left] > arr[i]) {

                // Swapping if
                // arr[left] > arr[i]
                swap(arr[left], arr[i]);
            }
        }

        // Increment left by 1
        left++;

        // Performing bubble sort
        for (i = right - 1; i >= left;
             i--) {
            if (arr[right] > arr[i]) {

                // Swapping if
                // arr[right] > arr[i]
                swap(arr[right], arr[i]);
            }
        }

        // Decrement right by 1
        right--;
    }

    // If N is an even number
    // Reversing the array from 0 to N/2-1
    if (N % 2 == 0) {

        // Reversing the half array
        for (int i = 0; i < N / 2; i++) {
            swap(arr[i], arr[N - 1 - i]);
        }
    }

    // Print the elements of the array
    for (int i = 0; i < N; i++) {
        cout << arr[i] << " ";
    }
}

// Driver Code
int main()
{
    // Given array
    int arr[] = { 4, 9, 3, 5, 7 };

    // Size of the array
    int N = sizeof arr / sizeof arr[0];

    // Function Call
    centerSpiralSort(arr, N);

    return 0;
}

Java

// Java program for the above approach
import java.io.*;
class GFG
{

    // Function to sort the array
    // according to the given pattern
    static void centerSpiralSort(int arr[], int N)
    {

        // Initializing the variables
        int left = 0;
        int right = N - 1;
        int i = 1;
        int temp;

        while (left < right) {

            // Performing bubble sort
            for (i = left + 1; i <= right; i++) {
                if (arr[left] > arr[i]) {

                    // Swapping if
                    // arr[left] > arr[i]
                    temp = arr[left];
                    arr[left] = arr[i];
                    arr[i] = temp;
                }
            }

            // Increment left by 1
            left++;

            // Performing bubble sort
            for (i = right - 1; i >= left; i--) {
                if (arr[right] > arr[i]) {

                    // Swapping if
                    // arr[right] > arr[i]
                    temp = arr[right];
                    arr[right] = arr[i];
                    arr[i] = temp;
                }
            }

            // Decrement right by 1
            right--;
        }

        // If N is an even number
        // Reversing the array from 0 to N/2-1
        if (N % 2 == 0) {

            // Reversing the half array
            for (i = 0; i < N / 2; i++) {
                temp = arr[i];
                arr[i] = arr[N - 1 - i];
                arr[N - 1 - i] = temp;
            }
        }

        // Print the elements of the array
        for (i = 0; i < N; i++) {
            System.out.print(arr[i] + " ");
        }
    }

    // Driver Code
    public static void main(String[] args)
    {

        // Given array
        int arr[] = { 4, 9, 3, 5, 7 };

        // Size of the array
        int N = arr.length;

        // Function Call
        centerSpiralSort(arr, N);
    }
}

// This code is contributed by Potta Lokesh

Python3

# Python3 program for the above approach

# Function to sort the array
# according to the given pattern
def centerSpiralSort(arr, N):

    # Initializing the variables
    left = 0
    right = N - 1
    i = 1

    while (left < right):

        # Performing bubble sort
        for i in range(left + 1, right + 1, 1):
            if (arr[left] > arr[i]):

                # Swapping if
                # arr[left] > arr[i]
                temp = arr[left]
                arr[left] = arr[i]
                arr[i] = temp

        # Increment left by 1
        left += 1

        # Performing bubble sort
        i = right - 1

        while(i >= left):
            if (arr[right] > arr[i]):

                # Swapping if
                # arr[right] > arr[i]
                temp = arr[right]
                arr[right] = arr[i]
                arr[i] = temp

            i -= 1

        # Decrement right by 1
        right -= 1

    # If N is an even number
    # Reversing the array from 0 to N/2-1
    if (N % 2 == 0):

        # Reversing the half array
        for i in range(N / 2):
            temp = arr[i]
            arr[i] = arr[N - 1 - i]
            arr[N - 1 - i] = temp

    # Print the elements of the array
    for i in range(N):
        print(arr[i], end = " ")

# Driver Code
if __name__ == '__main__':

    # Given array
    arr = [ 4, 9, 3, 5, 7 ]

    # Size of the array
    N = len(arr)

    # Function Call
    centerSpiralSort(arr, N)

# This code is contributed by ipg2016107

C#

// C# program for the above approach
using System;

class GFG{

// Function to sort the array
// according to the given pattern
static void centerSpiralSort(int []arr, int N)
{

    // Initializing the variables
    int left = 0;
    int right = N - 1;
    int i = 1;
    int temp;

    while (left < right)
    {

        // Performing bubble sort
        for(i = left + 1; i <= right; i++)
        {
            if (arr[left] > arr[i])
            {

                // Swapping if
                // arr[left] > arr[i]
                temp = arr[left];
                arr[left] = arr[i];
                arr[i] = temp;
            }
        }

        // Increment left by 1
        left++;

        // Performing bubble sort
        for(i = right - 1; i >= left; i--)
        {
            if (arr[right] > arr[i])
            {

                // Swapping if
                // arr[right] > arr[i]
                temp = arr[right];
                arr[right] = arr[i];
                arr[i] = temp;
            }
        }

        // Decrement right by 1
        right--;
    }

    // If N is an even number
    // Reversing the array from 0 to N/2-1
    if (N % 2 == 0)
    {

        // Reversing the half array
        for(i = 0; i < N / 2; i++)
        {
            temp = arr[i];
            arr[i] = arr[N - 1 - i];
            arr[N - 1 - i] = temp;
        }
    }

    // Print the elements of the array
    for(i = 0; i < N; i++)
    {
        Console.Write(arr[i] + " ");
    }
}

// Driver Code
public static void Main(String[] args)
{

    // Given array
    int []arr = { 4, 9, 3, 5, 7 };

    // Size of the array
    int N = arr.Length;

    // Function Call
    centerSpiralSort(arr, N);
}
}

// This code is contributed by shivanisinghss2110

Javascript

<script>

// JavaScript program for the above approach

// Function to sort the array
// according to the given pattern
function centerSpiralSort(arr, N) {
  // Initializing the variables
  let left = 0;
  let right = N - 1;
  let i = 1;

  while (left < right) {
    // Performing bubble sort
    for (i = left + 1; i <= right; i++) {
      if (arr[left] > arr[i]) {
        // Swapping if
        // arr[left] > arr[i]
        let temp = arr[left];
        arr[left] = arr[i];
        arr[i] = temp;
      }
    }

    // Increment left by 1
    left++;

    // Performing bubble sort
    for (i = right - 1; i >= left; i--) {
      if (arr[right] > arr[i]) {
        // Swapping if
        // arr[right] > arr[i]
        let temp = arr[right];
        arr[right] = arr[i];
        arr[i] = temp;
      }
    }

    // Decrement right by 1
    right--;
  }

  // If N is an even number
  // Reversing the array from 0 to N/2-1
  if (N % 2 == 0) {
    // Reversing the half array
    for (let i = 0; i < N / 2; i++) {
      let temp = arr[N - 1 - i];
      arr[N - 1 - i] = arr[i];
      arr[i] = temp;
    }
  }

  // Print the elements of the array
  for (let i = 0; i < N; i++) {
    document.write(arr[i] + " ");
  }
}

// Driver Code

// Given array
let arr = [4, 9, 3, 5, 7];

// Size of the array
let N = arr.length;

// Function Call
centerSpiralSort(arr, N);

</script>

Output

3 5 9 7 4 

Time Complexity: O(N²)
Auxiliary Space: O(1)