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 
// 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 
?> 

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 
?> 

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

My Personal Notes

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

C++

Java

Python 3

C#

PHP

C++

Java

Python3

C#

PHP

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