Check if a Given Number is a Fibonacci Number in Java

For a given input number, write a Java program to check if it is a Fibonacci number. Any number that belongs to Fibonacci series is called as Fibonacci number. The Fibonacci series is a sequence of numbers formed by the sum of its two previous integers. The first two terms of this series are 0 and 1 and further terms go like 1, 2, 3, 5, 8 and so on. This series was named after a famous Italian mathematician, Leonardo Fibonacci.

Example Scenario 1

Input: num1 = 8;
Output: 8 is a Fibonacci number 

8 comes into Fibonacci series

Example Scenario 2

Input: num2 = 9;
Output: 9 is not a Fibonacci number

How to Check Fibonacci Number in Java?

Use the below approaches to check whether a given number is Fibonacci ?

• Iterative approach
• Mathematical approach
• Recursive approach

Using Iterative Approach

In the iterative approach, find Fibonacci numbers iteratively until the loop reaches or surpasses the given number. However, it is not efficient for large numbers due to its linear time complexity.

Program

In this Java program, we are using iterative approach to check whether the given input is Fibonacci number or not.

public class CheckerClass {
   // function to check fibonacci
   public static boolean fibonacci_num_check(int number) {
      if (number == 0 || number == 1) 
         return true;
      int prev = 0, next = 1, sum;
      while (next < number) {
         sum = prev + next;
         prev = next;
         next = sum;
      }
      return number == next;
   }
   public static void main(String[] args) {
      // given input number
      int inputNum = 8; 
      // checking if given number is fibonacci
      boolean isFibonacciNumber = fibonacci_num_check(inputNum);
      if (isFibonacciNumber) {
         System.out.println(inputNum + " is a Fibonacci number.");
      } else {
         System.out.println(inputNum + " is not a Fibonacci number.");
      }
   }
}

On executing, this code will show below result ?

8 is a Fibonacci number.

Using Mathematical Approach

In this approach, calculate the perfect square to check whether the given number is Fibonacci or not. A given number is said to be Fibonacci number if and only if one or both of (5 times n^2 + 4) or (5 times n^2 - 4) is a perfect square.

Program

Following is the Java program to check if a given number is Fibonacci with the help of the above discussed Mathematical approach.

public class Demo{
   static boolean perfect_square_check(int val){
      int s = (int) Math.sqrt(val);
      return (s*s == val);
   }
   static boolean fibonacci_num_check(int n){
      return perfect_square_check(5*n*n + 4) || perfect_square_check(5*n*n - 4);
   }
   public static void main(String[] args){
      for (int i = 6; i <= 17; i++)
      System.out.println(fibonacci_num_check(i) ? i + " is a Fibonacci number" :
      i + " is a not Fibonacci number");
   }
}

On running the code, following output will be displayed ?

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
11 is a not Fibonacci number
12 is a not Fibonacci number
13 is a Fibonacci number
14 is a not Fibonacci number
15 is a not Fibonacci number
16 is a not Fibonacci number
17 is a not Fibonacci number

Using Recursive Approach

To check Fibonacci number recursively, follow the given steps −

• Step 1: Calculate the n-th Fibonacci number recursively.
• Step 2: Compare the calculated Fibonacci with the given input.
• Step 3: If both numbers are equal, return TRUE otherwise FALSE.

Program

The following Java program demonstrates how to check Fibonacci number using recursive approach.

public class CheckerClass {
   // calculate n-th Fibonacci number recursively
   public static int fibonacci_num_check(int n) {
      if (n <= 1) return n;
      return fibonacci_num_check(n-1) + fibonacci_num_check(n-2);
   }
   // check Fibonacci number
   public static boolean checkFibonacci(int number) {
      int fib = 0;
      int i = 0;
      while ((fib = fibonacci_num_check(i)) < number) {
         i++;
      }
      return number == fib;
   }
   public static void main(String[] args) {
      // given input number
      int inputNum = 21; 
      // checking if given number is fibonacci
      boolean isFibonacciNumber = checkFibonacci(inputNum);
      if (isFibonacciNumber) {
         System.out.println(inputNum + " is a Fibonacci number.");
      } else {
         System.out.println(inputNum + " is not a Fibonacci number.");
      }
   }
}

On running the code, following output will be displayed −

21 is a Fibonacci number.