Check if a Given Number is Fibonacci number?

Given a number n, check if n is a Fibonacci number. First few Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ..

Examples :

Input: n = 34
Output: true
Explanation: 34 is one of the numbers of the Fibonacci series.

Input: n = 41
Output: false
Explanation: 41 is not in the numbers of the Fibonacci series.

Generate Fibonacci Numbers Iteratively - O(log n) Time O(1) Space

The idea is to generate Fibonacci numbers one by one starting from 0 and 1 until the generated number becomes greater than or equal to n.

• If the generated Fibonacci number becomes equal to n, then n is a Fibonacci number.
• Otherwise, n is not a Fibonacci number.

true

Time Complexity: O(log n)
Space Complexity: O(1)

Using Perfect Square Property - O(1) Time O(1) Space

A number n is a Fibonacci number if either of the following is a perfect square: 5n² + 4 or 5n² − 4. So, we calculate both values and check if any one of them is a perfect square. If any one of them is a perfect square, then n is a Fibonacci number.

This is a mathematical property of Fibonacci numbers: 5n² + 4 or 5n² − 4.

true

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