Check whether the number can be made perfect square after adding 1

Last Updated : 16 Oct, 2022

Given an integer N, the task is to check whether N the given number can be made a perfect square after adding 1 to it.

Examples:

Input: 3
Output: Yes
3 + 1 = 4 which is a perfect square i.e. 2²

Input: 5
Output: No
5 + 1 = 6 which is not a perfect square.

Approach: Check whether n + 1 is a perfect square or not by taking the square root of n + 1 and checking whether it is an integer. If it is then n + 1 is a perfect square and n is a sunny number.

Below is the implementation of the above approach:

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;

// Function that returns true
// if x is a perfect square
bool isPerfectSquare(long double x)
{

    // Find floating point value of
    // square root of x
    long double sr = sqrt(x);

    // If square root is an integer
    return ((sr - floor(sr)) == 0);
}

// Function that returns true
// if n is a sunny number
bool isSunnyNum(int n)
{

    // If (n + 1) is a perfect square
    if (isPerfectSquare(n + 1))
        return true;
    return false;
}

// Driver code
int main()
{
    int n = 3;

    if (isSunnyNum(n))
        cout << "Yes";
    else
        cout << "No";

    return 0;
}

Java

// Java implementation of the approach 

class GFG 
{
    
    // Function that returns true 
    // if x is a perfect square 
    static boolean isPerfectSquare(double x) 
    { 
    
        // Find floating point value of 
        // square root of x 
        double sr = Math.sqrt(x); 
    
        // If square root is an integer 
        return ((sr - Math.floor(sr)) == 0); 
    } 
    
    // Function that returns true 
    // if n is a sunny number 
    static boolean isSunnyNum(int n) 
    { 
    
        // If (n + 1) is a perfect square 
        if (isPerfectSquare(n + 1)) 
            return true; 
        return false; 
    } 
    
    // Driver code 
    public static void main (String[] args)
    { 
        int n = 3; 
    
        if (isSunnyNum(n)) 
            System.out.println("Yes"); 
        else
            System.out.println("No"); 
    
    } 
}

// This code is contributed by Ryuga

Python3

# Python3 implementation of the approach
import math as mt

# Function that returns true
# if x is a perfect square
def isPerfectSquare(x):

    # Find floating po value of
    # square root of x
    sr = mt.sqrt(x)

    # If square root is an eger
    return ((sr - mt.floor(sr)) == 0)

# Function that returns true
# if n is a sunny number
def isSunnyNum(n):

    # If (n + 1) is a perfect square
    if (isPerfectSquare(n + 1)):
        return True
    return False

# Driver code
n = 3

if (isSunnyNum(n)):
    print("Yes")
else:
    print("No")

# This code is contributed 
# by Mohit Kumar

// C# implementation of the approach 
using System;
class GFG 
{
    
    // Function that returns true 
    // if x is a perfect square 
    static bool isPerfectSquare(double x) 
    { 
    
        // Find floating point value of 
        // square root of x 
        double sr = Math.Sqrt(x); 
    
        // If square root is an integer 
        return ((sr - Math.Floor(sr)) == 0); 
    } 
    
    // Function that returns true 
    // if n is a sunny number 
    static bool isSunnyNum(int n) 
    { 
    
        // If (n + 1) is a perfect square 
        if (isPerfectSquare(n + 1)) 
            return true; 
        return false; 
    } 
    
    // Driver code 
    public static void Main ()
    { 
        int n = 3; 
    
        if (isSunnyNum(n)) 
            Console.WriteLine("Yes"); 
        else
            Console.WriteLine("No"); 
    } 
}

// This code is contributed by Code_Mech.

PHP

<?php
// PHP implementation of the approach

// Function that returns true
// if x is a perfect square
function isPerfectSquare($x)
{

    // Find floating point value of
    // square root of x
    $sr = sqrt($x);

    // If square root is an integer
    return (($sr - floor($sr)) == 0);
}

// Function that returns true
// if n is a sunny number
function isSunnyNum($n)
{

    // If (n + 1) is a perfect square
    if (isPerfectSquare($n + 1))
        return true;
    return false;
}

// Driver code
$n = 3;

if (isSunnyNum($n))
    echo "Yes";
else
    echo "No";

// This code is contributed
// by Akanksha Rai
?>

JavaScript

<script>

// Javascript implementation of the approach

// Function that returns true
// if x is a perfect square
function isPerfectSquare(x)
{
    
    // Find floating point value of
    // square root of x
    let sr = Math.sqrt(x);

    // If square root is an integer
    return ((sr - Math.floor(sr)) == 0);
}

// Function that returns true
// if n is a sunny number
function isSunnyNum(n)
{
    
    // If (n + 1) is a perfect square
    if (isPerfectSquare(n + 1))
        return true;
        
    return false;
}

// Driver code
let n = 3;

if (isSunnyNum(n))
    document.write("Yes");
else
    document.write("No");
    
// This code is contributed by rishavmahato348

</script>

Output:

Yes

Time Complexity: O(logn)
Auxiliary Space: O(1)

Check whether the number can be made perfect square after adding 1

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Check whether the number can be made perfect square after adding 1

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