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.

This article is contributed by Sachin. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above