Programming Example

Check if a Number is a Fibonacci Number in Range using Java

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Information & Algorithm

Given Input:

range [1, 100]
55

Expected Output:

55 is a Fibonacci number within the range [1, 100].
Fibonacci numbers within the range [1, 100]: [1, 2, 3, 5, 8, 13, 21, 34, 55, 89]

Program Code

import java.util.*;

public class FibonacciInRangeChecker {

    // Function to check if a number is a perfect square
    public static boolean isPerfectSquare(int x) {
        int s = (int) Math.sqrt(x);
        return s * s == x;
    }

    // Function to check if a number is a Fibonacci number
    public static boolean isFibonacci(int number) {
        // A number is Fibonacci if one of 5*n*n + 4 or 5*n*n - 4 or both is a perfect square
        return isPerfectSquare(5 * number * number + 4) || isPerfectSquare(5 * number * number - 4);
    }

    // Function to find all Fibonacci numbers in a given range
    public static List<Integer> findFibonacciNumbersInRange(int start, int end) {
        List<Integer> fibonacciNumbers = new ArrayList<>();

        int currentFibonacci = 0;
        int n1 = 0, n2 = 1;

        while (currentFibonacci <= end) {
            if (currentFibonacci >= start) {
                fibonacciNumbers.add(currentFibonacci);
            }

            // Calculate next Fibonacci number
            currentFibonacci = n1 + n2;
            n1 = n2;
            n2 = currentFibonacci;
        }

        return fibonacciNumbers;
    }

    public static void main(String[] args) {
        int start = 1; // Example start of range
        int end = 100; // Example end of range

        List<Integer> fibonacciNumbersInRange = findFibonacciNumbersInRange(start, end);

        // Check if a specific number is Fibonacci and within the range
        int numberToCheck = 55; // Example number to check
        if (fibonacciNumbersInRange.contains(numberToCheck) && isFibonacci(numberToCheck)) {
            System.out.println(numberToCheck + " is a Fibonacci number within the range [" + start + ", " + end + "].");
        } else {
            System.out.println(numberToCheck + " is not a Fibonacci number within the range [" + start + ", " + end + "].");
        }

        // Print all Fibonacci numbers found within the range
        System.out.println("Fibonacci numbers within the range [" + start + ", " + end + "]: " + fibonacciNumbersInRange);
    }
}

Output

55 is a Fibonacci number within the range [1, 100].
Fibonacci numbers within the range [1, 100]: [1, 2, 3, 5, 8, 13, 21, 34, 55, 89]

Explanation

isPerfectSquare(int x): Helper function to check if x is a perfect square.
isFibonacci(int number): Function to check if number is a Fibonacci number using the mathematical property discussed earlier.
findFibonacciNumbersInRange(int start, int end): Function to find all Fibonacci numbers within the specified range [start, end]. It iterates through Fibonacci numbers until the current Fibonacci number exceeds end, storing those that fall within the range.
main(String[] args): In the main method, specify the start and end of the range. It calculates all Fibonacci numbers in the range and checks if a specific numberToCheck is both a Fibonacci number and within the range.

How to learn from this program

First read the algorithm, then study the program code line by line. After that, compare the code with the output and finally go through the explanation. This approach helps learners understand both the logic and the implementation properly.

Practice suggestion

After understanding this example, try to rewrite the same program without looking at the code. Then change some values or logic and run it again. This helps improve confidence and keeps learners engaged on the page for longer.