Print squares of first n natural numbers without using *, / and –

Given a natural number ‘n’, print squares of first n natural numbers without using *, / and -. 
Examples :

Input:  n = 5
Output: 0 1 4 9 16

Input:  n = 6
Output: 0 1 4 9 16 25

We strongly recommend to minimize the browser and try this yourself first.
Method 1: The idea is to calculate next square using previous square value. Consider the following relation between square of x and (x-1). We know square of (x-1) is (x-1)² – 2*x + 1. We can write x² as 

x2 = (x-1)2 + 2*x - 1 
x2 = (x-1)2 + x + (x - 1)

When writing an iterative program, we can keep track of previous value of x and add the current and previous values of x to current value of square. This way we don’t even use the ‘-‘ operator.
Below is the implementation of above approach: 

C++

// C++ program to print squares of first 'n' natural numbers
// without using *, / and -
#include<iostream>
using namespace std;

void printSquares(int n)
{
    // Initialize 'square' and previous value of 'x'
    int square = 0, prev_x = 0;

    // Calculate and print squares
    for (int x = 0; x < n; x++)
    {
        // Update value of square using previous value
        square = (square + x + prev_x);

        // Print square and update prev for next iteration
        cout << square << " ";
        prev_x = x;
    }
}

// Driver program to test above function
int main()
{
   int n = 5;
   printSquares(n);
}

Java

// Java program to print squares
// of first 'n' natural numbers
// without using *, / and
import java.io.*;

class GFG
{
static void printSquares(int n)
{
    // Initialize 'square' and
    // previous value of 'x'
    int square = 0, prev_x = 0;

    // Calculate and
    // print squares
    for (int x = 0; x < n; x++)
    {
        // Update value of square
        // using previous value
        square = (square + x + prev_x);

        // Print square and update
        // prev for next iteration
        System.out.print( square + " ");
        prev_x = x;
    }
}

// Driver Code
public static void main (String[] args)
{
    int n = 5;
    printSquares(n);
}
}

// This code is contributed
// by akt_mit

Python 3

# Python 3 program to print squares of first
# 'n' natural numbers without using *, / and -
def printSquares(n):

    # Initialize 'square' and previous
    # value of 'x'
    square = 0; prev_x = 0;

    # Calculate and print squares
    for x in range(0, n):

        # Update value of square using
        # previous value
        square = (square + x + prev_x)

        # Print square and update prev
        # for next iteration
        print(square, end = " ")
        prev_x = x

# Driver Code
n = 5;
printSquares(n);

# This code is contributed
# by Akanksha Rai

C#

// C#  program to print squares
// of first 'n' natural numbers
// without using *, / and
using System;

public class GFG{

    static void printSquares(int n)
{
    // Initialize 'square' and
    // previous value of 'x'
    int square = 0, prev_x = 0;

    // Calculate and
    // print squares
    for (int x = 0; x < n; x++)
    {
        // Update value of square
        // using previous value
        square = (square + x + prev_x);

        // Print square and update
        // prev for next iteration
        Console.Write( square + " ");
        prev_x = x;
    }
}

// Driver Code

    static public void Main (){
        int n = 5;
        printSquares(n);
    }
}

// This code is contributed
// by ajit

PHP

<?php
// PHP program to print squares
// of first 'n' natural numbers
// without using *, / and -

function printSquares($n)
{

    // Initialize 'square' and
    // previous value of 'x'
    $square = 0; $prev_x = 0;

    // Calculate and
    // print squares
    for ($x = 0; $x < $n; $x++)
    {

        // Update value of square
        // using previous value
        $square = ($square + $x + $prev_x);

        // Print square and update
        // prev for next iteration
        echo $square, " ";
        $prev_x = $x;
    }
}

    // Driver Code
    $n = 5;
    printSquares($n);

// This code is contributed by ajit
?>

Javascript

<script>
// JavaScript program to print squares of first 'n' natural numbers
// without using *, / and -

    function printSquares(n)
    {
        // Initialize 'square' and previous value of 'x'
        let square = 0, prev_x = 0;

        // Calculate and print squares
        for (let x = 0; x < n; x++)
        {
            // Update value of square using previous value
            square = (square + x + prev_x);

            // Print square and update prev for next iteration
            document.write(square + " ");
            prev_x = x;
        }
    }

    // Driver program to test above function

   let n = 5;
   printSquares(n);

// This code is contributed by Surbhi Tyagi

</script>

Output:

0 1 4 9 16

Time Complexity: O(n)

Auxiliary Space: O(1)

Method 2: Sum of first n odd numbers are squares of natural numbers from 1 to n. For example 1, 1+3, 1+3+5, 1+3+5+7, 1+3+5+7+9, ….
Following is program based on above concept. Thanks to Aadithya Umashanker and raviteja for suggesting this method.

C++

// C++ program to print squares of first 'n' natural numbers
// without using *, / and -
#include<iostream>
using namespace std;

void printSquares(int n)
{
    // Initialize 'square' and first odd number
    int square = 0, odd = 1;

    // Calculate and print squares
    for (int x = 0; x < n; x++)
    {
        // Print square
        cout << square << " ";

        // Update 'square' and 'odd'
        square = square + odd;
        odd = odd + 2;
    }
}

// Driver program to test above function
int main()
{
   int n = 5;
   printSquares(n);
}

Java

// Java program to print
// squares of first 'n'
// natural numbers without
// using *, / and -
import java.io.*;

class GFG
{
static void printSquares(int n)
{
    // Initialize 'square'
    // and first odd number
    int square = 0, odd = 1;

    // Calculate and
    // print squares
    for (int x = 0; x < n; x++)
    {
        // Print square
        System.out.print(square +
                           " " );

        // Update 'square'
        // and 'odd'
        square = square + odd;
        odd = odd + 2;
    }
}

// Driver Code
public static void main (String[] args)
{
    int n = 5;
    printSquares(n);
}
}

// This code is contributed
// by ajit

Python3

# Python3 program to print squares
# of first 'n' natural numbers
# without using *, / and -

def printSquares(n):

    # Initialize 'square' and
    # first odd number
    square = 0
    odd = 1

    # Calculate and print squares
    for x in range(0 , n):

        # Print square
        print(square, end= " ")

        # Update 'square' and 'odd'
        square = square + odd
        odd = odd + 2

# Driver Code
n = 5;
printSquares(n)

# This code is contributed
# by Rajput-Ji

C#

// C# program to print squares of first 'n'
// natural numbers without using *, / and -
using System;

class GFG
{
static void printSquares(int n)
{
    // Initialize 'square'
    // and first odd number
    int square = 0, odd = 1;

    // Calculate and
    // print squares
    for (int x = 0; x < n; x++)
    {
        // Print square
        Console.Write(square + " " );

        // Update 'square'
        // and 'odd'
        square = square + odd;
        odd = odd + 2;
    }
}

// Driver Code
public static void Main ()
{
    int n = 5;
    printSquares(n);
}
}

// This code is contributed
// by inder_verma..

PHP

<?php
// PHP program to print squares
// of first 'n' natural numbers
// without using *, / and -
function printSquares($n)
{
    // Initialize 'square' and
    // first odd number
    $square = 0; $odd = 1;

    // Calculate and print squares
    for ($x = 0; $x < $n; $x++)
    {
        // Print square
        echo $square , " ";

        // Update 'square' and 'odd'
        $square = $square + $odd;
        $odd = $odd + 2;
    }
}

// Driver Code
$n = 5;
printSquares($n);

// This code is contributed by m_kit
?>

Javascript

<script>
// Javascript program to print squares of first 'n' natural numbers
// without using *, / and -

function printSquares(n)
{
    // Initialize 'square' and first odd number
    let square = 0, odd = 1;

    // Calculate and print squares
    for (let x = 0; x < n; x++)
    {
        // Print square
        document.write(square + " ");

        // Update 'square' and 'odd'
        square = square + odd;
        odd = odd + 2;
    }
}

// Driver program to test above function
let n = 5;
printSquares(n);

// This code is contributed by subham348.
</script>

Output :

0 1 4 9 16

Time Complexity: O(n)

Auxiliary Space: O(1), since no extra space has been taken.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above