打印前n个自然数的平方，而不使用*，/和–

给定自然数’n’，不使用*，/和-打印前n个自然数的平方。
例子 ：

Input:  n = 5
Output: 0 1 4 9 16

Input:  n = 6
Output: 0 1 4 9 16 25

强烈建议您最小化浏览器，然后自己尝试。
方法1：想法是使用先前的平方值计算下一个平方。考虑x和(x-1)的平方之间的以下关系。我们知道(x-1)的平方是(x-1) ² – 2 * x +1。我们可以将x ²写成

x2 = (x-1)2 + 2*x - 1 
x2 = (x-1)2 + x + (x - 1)

在编写迭代程序时，我们可以跟踪x的先前值，并将x的当前值和先前值添加到square的当前值。这样，我们甚至不使用’-‘运算符。
下面是上述方法的实现：

C++

// C++ program to print squares of first 'n' natural numbers
// wothout using *, / and -
#include
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

Javascript

// 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
 

输出：

0 1 4 9 16

方法2：前n个奇数之和是从1到n的自然数的平方。例如1、1 + 3、1 + 3 + 5、1 + 3 + 5 + 7、1 + 3 + 5 + 7 + 9，…。
以下是基于上述概念的程序。感谢Aadithya Umashanker和raviteja提出了这种方法。

C++

// C++ program to print squares of first 'n' natural numbers
// wothout using *, / and -
#include
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..

Java脚本

// 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.

输出 ：

0 1 4 9 16