How to Check if a Given Number is Fibonacci Number in JavaScript ?

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, starting from 0 and 1. Checking for Fibonacci numbers involves verifying whether a given number appears in this sequence. The first few Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and 89, and so on. There are various approaches to check if a number is a Fibonacci number in Javascript or not which are as follows:

Iterative Fibonacci Number Checking

This approach involves iterating through generating Fibonacci numbers until we either find a match with the given number or reach a Fibonacci number greater than the given number.

Example: To check if a number is a Fibonacci number using iterations in Javascript.

Javascript

function isFibonacci(N) {
  if (N == 0 || N == 1) {
    return true;
  }

  let a = 0,
    b = 1,
    c;

  while (true) {
    c = a + b;
    a = b;
    b = c;

    if (c == N) {
      return true;
    } else if (c >= N) {
      return false;
    }
  }
}

let i = 8;
if (isFibonacci(i)) {
  console.log(i + " is a Fibonacci number.");
} else {
  console.log(i + " is not a Fibonacci number.");
}

Output

8 is a Fibonacci number.

Using the Golden Ratio Formula

In this approach, we use the property that a number is a Fibonacci number if and only if one of (5 * n^2 + 4) or (5 * n^2 – 4) is a perfect square. We implement a function to check for a perfect square and then use it in the main function to determine if the given number is a Fibonacci number or not.

Example: To check if a number is Fibonacci number or not using golden ratio.

Javascript

// A function that returns true if x is a perfect square

function isPerfectSquare(x) {
  let sqrt = parseInt(Math.sqrt(x));
  return sqrt * sqrt == x;
}

// Returns true if n is a Fibonacci Number, else false

function isFibonacci(n) {
  return isPerfectSquare(5 * n * n + 4) || isPerfectSquare(5 * n * n - 4);
}

// Example usage:
let i = 54;
if (isFibonacci(i)) {
  console.log(i + " is a Fibonacci number.");
} else {
  console.log(i + " is not a Fibonacci number.");
}

Output

54 is not a Fibonacci number.

Iterative On-the-Fly Fibonacci Generation

In this approach, we first handle the special case where the input number is 0 (which is a Fibonacci number). Then, we use a while loop to generate Fibonacci numbers until we find a Fibonacci number greater than or equal to the input number.

If the generated Fibonacci number is equal to the input number, we return true. Otherwise, we check if either (5 * n * n + 4) or (5 * n * n – 4) is a perfect square, as per the formula mentioned in the original code.

This approach may be more efficient than the original code in some cases, especially for larger input values, as it generates Fibonacci numbers on-the-fly and stops as soon as it finds a Fibonacci number greater than or equal to the input number.

Example: To check if a number is fibonacci number or not using on the fly method.

Javascript

function isPerfectSquare(n) {
  let root = parseInt(Math.sqrt(n));
  return root * root == n;
}

function isFibonacci(n) {
  if (n == 0) {
    return true;
  }
  let a = 0,
    b = 1,
    c = 1;
  while (c < n) {
    a = b;
    b = c;
    c = a + b;
  }
  return (
    c == n
    || isPerfectSquare(5 * n * n + 4)
    || isPerfectSquare(5 * n * n - 4)
  );
}

for (let i = 1; i <= 10; i++) {
  if (isFibonacci(i)) {
    console.log(i + " is a Fibonacci number.");
  } else {
    console.log(i + " is not a Fibonacci number.");
  }
}

Output

1 is a Fibonacci number.
2 is a Fibonacci number.
3 is a Fibonacci number.
4 is not a Fibonacci number.
5 is a Fibonacci number.
6 is not a Fibonacci number.
7 is not a Fibonacci number.
8 is a Fibona...