Sort array after converting elements to their squares

Given an array of both positive and negative integers ‘arr[]’ which are sorted. The task is to sort the square of the numbers of the Array. 

Examples:

Input  : arr[] =  {-6, -3, -1, 2, 4, 5}
Output : 1, 4, 9, 16, 25, 36 

Input  : arr[] = {-5, -4, -2, 0, 1}
Output : 0, 1, 4, 16, 25

Simple solution is to first convert each array element into its square and then apply any “O(nlogn)” sorting algorithm to sort the array elements.

Below is the implementation of the above idea  

C++

// C++ program to Sort square of the numbers
// of the array
#include <bits/stdc++.h>
using namespace std;

// Function to sort an square array
void sortSquares(int arr[], int n)
{
    // First convert each array elements
    // into its square
    for (int i = 0; i < n; i++)
        arr[i] = arr[i] * arr[i];

    // Sort an array using "sort STL function "
    sort(arr, arr + n);
}

// Driver program to test above function
int main()
{
    int arr[] = { -6, -3, -1, 2, 4, 5 };
    int n = sizeof(arr) / sizeof(arr[0]);

    cout << "Before sort " << endl;
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
    sortSquares(arr, n);

    cout << "\nAfter Sort " << endl;
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";

    return 0;
}

Java

// Java program to Sort square of the numbers
// of the array
import java.util.*;
import java.io.*;

class GFG {
    // Function to sort an square array
    public static void sortSquares(int arr[])
    {
        int n = arr.length;

        // First convert each array elements
        // into its square
        for (int i = 0; i < n; i++)
            arr[i] = arr[i] * arr[i];

        // Sort an array using "inbuild sort function"
        // in Arrays class.
        Arrays.sort(arr);
    }

    // Driver program to test above function
    public static void main(String[] args)
    {
        int arr[] = { -6, -3, -1, 2, 4, 5 };
        int n = arr.length;

        System.out.println("Before sort ");
        for (int i = 0; i < n; i++)
            System.out.print(arr[i] + " ");

        sortSquares(arr);
        System.out.println("");
        System.out.println("After Sort ");
        for (int i = 0; i < n; i++)
            System.out.print(arr[i] + " ");
    }
}

Python3

# Python program to Sort square
# of the numbers of the array

# Function to sort an square array
def sortSquare(arr, n):

    # First convert each array
    # elements into its square
    for i in range(n):
        arr[i]= arr[i] * arr[i]
    arr.sort()

# Driver code
arr = [-6, -3, -1, 2, 4, 5]
n = len(arr)

print("Before sort")
for i in range(n):
    print(arr[i], end = " ")

print("\n")

sortSquare(arr, n)

print("After sort")
for i in range(n):
    print(arr[i], end = " ")

# This code is contributed by
# Shrikant13

C#

// C# program to Sort square
// of the numbers of the array
using System;

class GFG {

    // Function to sort
    // an square array
    public static void sortSquares(int[] arr)
    {
        int n = arr.Length;

        // First convert each array
        // elements into its square
        for (int i = 0; i < n; i++)
            arr[i] = arr[i] * arr[i];

        // Sort an array using
        // "inbuild sort function"
        // in Arrays class.
        Array.Sort(arr);
    }

    // Driver Code
    public static void Main()
    {
        int[] arr = { -6, -3, -1,
                      2, 4, 5 };
        int n = arr.Length;

        Console.WriteLine("Before sort ");
        for (int i = 0; i < n; i++)
            Console.Write(arr[i] + " ");

        sortSquares(arr);
        Console.WriteLine("");
        Console.WriteLine("After Sort ");

        for (int i = 0; i < n; i++)
            Console.Write(arr[i] + " ");
    }
}

// This code is contributed by anuj_67.

Javascript

<script>

// JavaScript program for the above approach

    // Function to sort an square array
    function sortSquares(arr)
    {
        let n = arr.length;

        // First convert each array elements
        // into its square
        for (let i = 0; i < n; i++)
            arr[i] = arr[i] * arr[i];

        // Sort an array using "inbuild sort function"
        // in Arrays class.
        arr.sort();
    }

// Driver Code
    let arr = [ -6, -3, -1, 2, 4, 5 ];
    let n = arr.length;

    document.write("Before sort " + "<br/>");
    for (let i = 0; i < n; i++)
        document.write(arr[i] + " ");

    sortSquares(arr);
    document.write("" + "<br/>");
    document.write("After Sort " + "<br/>");
    for (let i = 0; i < n; i++)
        document.write(arr[i] + " ");

// This code is contributed by chinmoy1997pal.
</script>

Output

Before sort 
-6 -3 -1 2 4 5 
After Sort 
1 4 9 16 25 36 

Time complexity: O(n log n)

Efficient solution is based on the fact that the given array is already sorted. We do the following two steps. 

1. Divide the array into two-part “Negative and positive “.
2. Use merge function to merge two sorted arrays into a single sorted array.

Below is the implementation of the above idea.

C++

// C++ program to Sort square of the numbers of the array
#include <bits/stdc++.h>
using namespace std;

// function to sort array after doing squares of elements
void sortSquares(int arr[], int n)
{
    // first divide array into negative and positive part
    int K = 0;
    for (K = 0; K < n; K++)
        if (arr[K] >= 0)
            break;

    // Now do the same process that we learnt
    // in merge sort to merge two sorted array
    // here both two half are sorted and we traverse
    // first half in reverse manner because
    // first half contains negative elements
    int i = K - 1; // Initial index of first half
    int j = K; // Initial index of second half
    int ind = 0; // Initial index of temp array

    // store sorted array
    int temp[n];
    while (i >= 0 && j < n) {
        if (arr[i] * arr[i] < arr[j] * arr[j]) {
            temp[ind] = arr[i] * arr[i];
            i--;
        }
        else {
            temp[ind] = arr[j] * arr[j];
            j++;
        }
        ind++;
    }

    /* Copy the remaining elements of first half */
    while (i >= 0) {
        temp[ind] = arr[i] * arr[i];
        i--;
        ind++;
    }

    /* Copy the remaining elements of second half */
    while (j < n) {
        temp[ind] = arr[j] * arr[j];
        j++;
        ind++;
    }

    // copy 'temp' array into original array
    for (int i = 0; i < n; i++)
        arr[i] = temp[i];
}

// Driver program to test above function
int main()
{
    int arr[] = { -6, -3, -1, 2, 4, 5 };
    int n = sizeof(arr) / sizeof(arr[0]);

    cout << "Before sort " << endl;
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
    sortSquares(arr, n);

    cout << "\nAfter Sort " << endl;
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";

    return 0;
}

Java

// Java program to Sort square of the numbers
// of the array
import java.util.*;
import java.io.*;

class GFG {
    // Function to sort an square array
    public static void sortSquares(int arr[])
    {
        int n = arr.length;
        // first divide the array into negative and positive part
        int k;
        for (k = 0; k < n; k++) {
            if (arr[k] >= 0)
                break;
        }

        // Now do the same process that we learnt
        // in merge sort to merge two sorted arrays
        // here both two halves are sorted and we traverse
        // first half in reverse manner because
        // first half contains negative elements
        int i = k - 1; // Initial index of first half
        int j = k; // Initial index of second half
        int ind = 0; // Initial index of temp array

        int[] temp = new int[n];
        while (i >= 0 && j < n) {
            if (arr[i] * arr[i] < arr[j] * arr[j]) {
                temp[ind] = arr[i] * arr[i];
                i--;
            }
            else {

                temp[ind] = arr[j] * arr[j];
                j++;
            }
            ind++;
        }

        while (i >= 0) {
            temp[ind++] = arr[i] * arr[i];
            i--;
        }
        while (j < n) {
            temp[ind++] = arr[j] * arr[j];
            j++;
        }

        // copy 'temp' array into original array
        for (int x = 0; x < n; x++)
            arr[x] = temp[x];
    }

    // Driver program to test above function
    public static void main(String[] args)
    {
        int arr[] = { -6, -3, -1, 2, 4, 5 };
        int n = arr.length;

        System.out.println("Before sort ");
        for (int i = 0; i < n; i++)
            System.out.print(arr[i] + " ");

        sortSquares(arr);
        System.out.println("");
        System.out.println("After Sort ");
        for (int i = 0; i < n; i++)
            System.out.print(arr[i] + " ");
    }
}

Python3

# Python3 program to Sort square of the numbers of the array

# function to sort array after doing squares of elements
def sortSquares(arr, n):

    # first divide array into  negative and positive part
    K = 0
    for K in range(n):
        if (arr[K] >= 0 ):
            break

    # Now do the same process that we learnt
    # in merge sort to merge to two sorted array
    # here both two halves are sorted and we traverse
    # first half in reverse manner because
    # first half contains negative elements
    i = K - 1 # Initial index of first half
    j = K # Initial index of second half
    ind = 0 # Initial index of temp array

    # store sorted array
    temp = [0]*n
    while (i >= 0 and j < n):

        if (arr[i] * arr[i] < arr[j] * arr[j]):
            temp[ind] = arr[i] * arr[i]
            i -= 1

        else:

            temp[ind] = arr[j] * arr[j]
            j += 1

        ind += 1

    ''' Copy the remaining elements of first half '''
    while (i >= 0):

        temp[ind] = arr[i] * arr[i]
        i -= 1
        ind += 1

    ''' Copy the remaining elements of second half '''
    while (j < n):
        temp[ind] = arr[j] * arr[j]
        j += 1
        ind += 1

    # copy 'temp' array into original array
    for i in range(n):
        arr[i] = temp[i]

# Driver code
arr = [-6, -3, -1, 2, 4, 5 ]
n = len(arr)

print("Before sort ")
for i in range(n):
    print(arr[i], end =" " )

sortSquares(arr, n)
print("\nAfter Sort ")
for i in range(n):
    print(arr[i], end =" " )

# This code is contributed by shubhamsingh10

C#

// C# program to Sort square of the numbers
// of the array
using System;

class GFG {

    // Function to sort an square array
    public static void sortSquares(int[] arr)
    {
        int n = arr.Length;

        // first divide array into negative and positive part
        int k;
        for (k = 0; k < n; k++) {
            if (arr[k] >= 0)
                break;
        }

        // Now do the same process that we learnt
        // in merge sort to merge to two sorted array
        // here both two halves are sorted and we traverse
        // first half in reverse manner because
        // first half contains negative elements
        int i = k - 1; // Initial index of first half
        int j = k; // Initial index of second half
        int ind = 0; // Initial index of temp array

        int[] temp = new int[n];
        while (i >= 0 && j < n) {
            if (arr[i] * arr[i] < arr[j] * arr[j]) {
                temp[ind] = arr[i] * arr[i];
                i--;
            }
            else {
                temp[ind] = arr[j] * arr[j];
                j++;
            }
            ind++;
        }

        while (i >= 0) {
            temp[ind++] = arr[i] * arr[i];
            i--;
        }
        while (j < n) {
            temp[ind++] = arr[j] * arr[j];
            j++;
        }

        // copy 'temp' array into original array
        for (int x = 0; x < n; x++)
            arr[x] = temp[x];
    }

    // Driver code
    public static void Main(String[] args)
    {
        int[] arr = { -6, -3, -1, 2, 4, 5 };
        int n = arr.Length;

        Console.WriteLine("Before sort ");
        for (int i = 0; i < n; i++)
            Console.Write(arr[i] + " ");

        sortSquares(arr);
        Console.WriteLine("");
        Console.WriteLine("After Sort ");
        for (int i = 0; i < n; i++)
            Console.Write(arr[i] + " ");
    }
}

// This code is contributed by 29AjayKumar

Javascript

<script>

// Javascript program to Sort
// square of the numbers
// of the array

    // Function to sort an square array
    function sortSquares(arr)
    {
        let n = arr.length;
        // first dived array into part
        // negative and positive
        let k;
        for (k = 0; k < n; k++) {
            if (arr[k] >= 0)
                break;
        }

        // Now do the same process that we learn
        // in merge sort to merge to two sorted array
        // here both two half are sorted and we traverse
        // first half in reverse meaner because
        // first half contain negative element


        let i = k - 1; // Initial index of first half
        let j = k; // Initial index of second half
        let ind = 0; // Initial index of temp array

        let temp = new Array(n);
        while (i >= 0 && j < n) {
            if (arr[i] * arr[i] < arr[j] * arr[j]) {
                temp[ind] = arr[i] * arr[i];
                i--;
            }
            else {

                temp[ind] = arr[j] * arr[j];
                j++;
            }
            ind++;
        }

        while (i >= 0) {
            temp[ind++] = arr[i] * arr[i];
            i--;
        }
        while (j < n) {
            temp[ind++] = arr[j] * arr[j];
            j++;
        }

        // copy 'temp' array into original array
        for (let x = 0; x < n; x++)
            arr[x] = temp[x];
    }

    // Driver program to test above function
    let arr=[ -6, -3, -1, 2, 4, 5 ];
    let n = arr.length;
    document.write("Before sort <br>");
    for (let i = 0; i < n; i++)
        document.write(arr[i] + " ");

    sortSquares(arr);
    document.write("<br>");
    document.write("After Sort <br>");
    for (let i = 0; i < n; i++)
        document.write(arr[i] + " ");

    // This code is contributed by rag2127

</script>

Output

Before sort 
-6 -3 -1 2 4 5 
After Sort 
1 4 9 16 25 36 

Time complexity: O(n) 
space complexity: O(n) 

Method 3:
Another efficient solution is based on the two-pointer method as the array is already sorted we can compare the first and last element to check which is bigger and proceed with the result. 

Algorithm:

• Initialize left=0 and right=n-1
• if abs(left) >= abs(right) then store square(arr[left])
  at the end of result array and increment left pointer
• else store square(arr[right]) in the result array and decrement right pointer
• decrement index of result array

Implementation:

C++

// CPP code for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to sort an square array
void sortSquares(vector<int>& arr, int n)
{
    int left = 0, right = n - 1;
    int result[n];

    // Iterate from n - 1 to 0
    for (int index = n - 1; index >= 0; index--) {

        // Check if abs(arr[left]) is greater
        // than arr[right]
        if (abs(arr[left]) > arr[right]) {
            result[index] = arr[left] * arr[left];
            left++;
        }
        else {
            result[index] = arr[right] * arr[right];
            right--;
        }
    }
    for (int i = 0; i < n; i++)
        arr[i] = result[i];
}

// Driver Code
int main()
{
    vector<int> arr;
    arr.push_back(-6);
    arr.push_back(-3);
    arr.push_back(-1);
    arr.push_back(2);
    arr.push_back(4);
    arr.push_back(5);

    int n = 6;

    cout << "Before sort " << endl;
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";

    sortSquares(arr, n);
    cout << endl;
    cout << "After Sort " << endl;
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
    return 0;
}

// this code is contributed by Manu Pathria

Java

// Java program to Sort square of
// the numbers of the array
import java.util.*;
import java.io.*;

class GFG{

// Function to sort an square array
public static void sortSquares(int arr[])
{
    int n = arr.length, left = 0,
        right = n - 1;

    int result[] = new int[n];

    for(int index = n - 1; index >= 0; index--)
    {
        if (Math.abs(arr[left]) > arr[right])
        {
            result[index] = arr[left] * arr[left];
            left++;
        }
        else
        {
            result[index] = arr[right] * arr[right];
            right--;
        }
    }
    for(int i = 0; i < n; i++)
        arr[i] = result[i];
}

// Driver code
public static void main(String[] args)
{
    int arr[] = { -6, -3, -1, 2, 4, 5 };
    int n = arr.length;

    System.out.println("Before sort ");
    for(int i = 0; i < n; i++)
        System.out.print(arr[i] + " ");

    sortSquares(arr);
    System.out.println("");
    System.out.println("After Sort ");
    for(int i = 0; i < n; i++)
        System.out.print(arr[i] + " ");
}
}

// This code is contributed by jinalparmar2382

Python3

# Python3 program to Sort square of the numbers of the array

# function to sort array after doing squares of elements
def sortSquares(arr, n):
    left, right = 0, n - 1
    index = n - 1
    result = [0 for x in arr]

    while index >= 0:

        if abs(arr[left]) >= abs(arr[right]):
            result[index] = arr[left] * arr[left]
            left += 1
        else:
            result[index] = arr[right] * arr[right]
            right -= 1
        index -= 1

    for i in range(n):
        arr[i] = result[i]

# Driver code
arr = [-6, -3, -1, 2, 4, 5 ]
n = len(arr)

print("Before sort ")
for i in range(n):
    print(arr[i], end =" " )

sortSquares(arr, n)
print("\nAfter Sort ")
for i in range(n):
    print(arr[i], end =" " )

C#

// C# program to Sort square of
// the numbers of the array
using System;
class GFG{

// Function to sort an square array
public static void sortSquares(int [] arr)
{
  int n = arr.Length, left = 0,
  right = n - 1;
  int []result = new int[n];

  for(int index = n - 1;
          index >= 0; index--)
  {
    if (Math.Abs(arr[left]) >
        arr[right])
    {
      result[index] = arr[left] *
                      arr[left];
      left++;
    }
    else
    {
      result[index] = arr[right] *
                      arr[right];
      right--;
    }
  }
  for(int i = 0; i < n; i++)
    arr[i] = result[i];
}

// Driver code
public static void Main(string[] args)
{
  int []arr = {-6, -3, -1, 2, 4, 5};
  int n = arr.Length;
  Console.WriteLine("Before sort ");

  for(int i = 0; i < n; i++)
    Console.Write(arr[i] + " ");

  sortSquares(arr);
  Console.WriteLine("");
  Console.WriteLine("After Sort ");

  for(int i = 0; i < n; i++)
    Console.Write(arr[i] + " ");
}
}

// This code is contributed by Chitranayal

Javascript

<script>
    // This function squares each value in an array
    // and arranges the result in ascending order, using two pointers.
    // The first pointer points to the first element of the array, and the second
    // points to the last. On each iteration, each pointer is compared to the other
    // and the pointer which has the lowest value is shifted closer to the other.

    function sortSquares(arr) {
       let
            n = nums.length,
            left = 0,
            right = n -1,
               result = new Array(n)
       ;

        for (let i = n - 1; i >= 0; i--) {
            // Here, Math.abs() is used to convert any negative numbers to their
            // integer equivalent... i.e. -4 becomes 4.
            if (Math.abs(nums[left]) > Math.abs(nums[right])) {
                result[i] = nums[left] ** 2;
                left++;
            } else {
                result[i] = nums[right] **2;
                right--;
            }
        }

        return result;
    }

    let arr = [-6, -3, -1, 2, 4, 5];
    let n = arr.length;
    document.write("Before sort " + "</br>");

    for(let i = 0; i < n; i++)
      document.write(arr[i] + " ");

    sortSquares(arr);
    document.write("</br>");
    document.write("After Sort " + "</br>");

    for(let i = 0; i < n; i++)
      document.write(arr[i] + " ");

 // This code was contributed by rameshtravel07, then was edited by: Lewis Farnworth
</script>

Output

Before sort 
-6 -3 -1 2 4 5 
After Sort 
1 4 9 16 25 36 

Time complexity: O(n) 
Auxiliary Space: O(n) 

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