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Print squares of first n natural numbers without using *, / and –
  • Difficulty Level : Medium
  • Last Updated : 06 Apr, 2021

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
// wothout 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
// wothout 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
// wothout 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
// wothout 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
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
// wothout 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
# wothout 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
// wothout 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
// wothout 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
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
 
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
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