How to Understand the Recursive Fibonacci Sequence in Java

Can you explain how the recursive Fibonacci algorithm works in Java?

public int fibonacci(int n) {
    if(n == 0)
        return 0;
    else if(n == 1)
        return 1;
    else
        return fibonacci(n - 1) + fibonacci(n - 2);
}

The recursive Fibonacci algorithm in Java calculates Fibonacci numbers by calling itself to evaluate smaller problems (i.e., finding Fibonacci of a smaller index) until it reaches the base cases. This approach is quite intuitive but not the most efficient due to overlapping subproblems.

public int fibonacciMemoization(int n, Integer[] memo) {
    if (memo[n] != null) return memo[n];

    if (n == 0) 
        return 0;
    else if (n == 1) 
        return 1;
    else
        memo[n] = fibonacciMemoization(n - 1, memo) + fibonacciMemoization(n - 2, memo);

    return memo[n];
}

Causes

• The function relies on recursion, where each call to 'fibonacci' calculates two additional calls until it reaches the base cases of 0 and 1.
• This leads to an exponential number of calls, causing inefficiency as n increases.

Solutions

• To compute Fibonacci numbers more efficiently, consider implementing memoization or an iterative approach instead.
• For example, using an array to store already computed Fibonacci numbers can drastically reduce redundant calculations.

Mistake: Not understanding base cases.

Solution: Always ensure you know when your recursion stops (i.e., when to return values without further calls).

Mistake: Assuming recursive calls only occur twice.

Solution: Recognize that the depth and amount of calls grow rapidly, especially for large values of n, leading to performance issues.