C++ Program for How to check if a given number is Fibonacci number?

Given a number ‘n’, how to check if n is a Fibonacci number. First few Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 141, .. 
Examples : 

Input : 8
Output : Yes

Input : 34
Output : Yes

Input : 41
Output : No

Following is an interesting property about Fibonacci numbers that can also be used to check if a given number is Fibonacci or not. 
A number is Fibonacci if and only if one or both of (5*n² + 4) or (5*n² – 4) is a perfect square (Source: Wiki). 

CPP

// C++ program to check if x is a perfect square
#include <iostream>
#include <math.h>
using namespace std;

// A utility function that returns true if x is perfect square
bool isPerfectSquare(int x)
{
    int s = sqrt(x);
    return (s * s == x);
}

// Returns true if n is a Fibonacci Number, else false
bool isFibonacci(int n)
{
    // n is Fibonacci if one of 5*n*n + 4 or 5*n*n - 4 or both
    // is a perfect square
    return isPerfectSquare(5 * n * n + 4) || isPerfectSquare(5 * n * n - 4);
}

// A utility function to test above functions
int main()
{
    for (int i = 1; i <= 10; i++)
        isFibonacci(i) ? cout << i << " is a Fibonacci Number \n"
                       : cout << i << " is a not Fibonacci Number \n";
    return 0;
}

Output:

1 is a Fibonacci Number 
2 is a Fibonacci Number 
3 is a Fibonacci Number 
4 is a not Fibonacci Number 
5 is a Fibonacci Number 
6 is a not Fibonacci Number 
7 is a not Fibonacci Number 
8 is a Fibonacci Number 
9 is a not Fibonacci Number 
10 is a not Fibonacci Number

Time complexity: O(logn)

As sqrt() function takes O(logn) time.

Auxiliary space: O(1)

As constant extra space is used.

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