Sort array after converting elements to their squares

Given a array of both positive and negative integers ‘arr[]’ which are sorted. Task is to sort 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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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

Below is the implementation of 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. 

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 given array is already sorted. We do following two steps.

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

Below is the implementation of 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 dived array into part negative and positive 
    int K = 0; 
    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 
    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 dived array into part negative and positive 
        int 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 
        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 dived array into part negative and positive 
    K = 0
    for K in range(n): 
        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 
    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 dived array into part negative and positive 
        int 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 
        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 

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 on 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

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 =" " )  

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)

This article is contributed by Nishant singh. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

C++

Java

Python3

C#

Python3

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