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


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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:

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// 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);
}
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// 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
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# 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
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// 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
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<?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
?>
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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.

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// 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);
}
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// 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
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# 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
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// 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..
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<?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
?>
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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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