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

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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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