findNthFibonacciNumber()

Step 1: Understand the Problem

The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... The next number is found by adding up the two numbers before it.

We are tasked to write a Javascript function that, given an order number, n, returns the corresponding Fibonacci sequence number.

Step 2: Start With the Base Case

The lowest two elements of the sequence are always 0 and 1, so we'll start defining these as our base cases.

function fibonacci(n) {
  if (n === 0) {
    return 0;
  }
  if (n === 1) {
    return 1;
  }
}

Step 3: Implement the Recursion

After the first two elements, every element in the sequence is the sum of the previous two. We'll implement this rule by making a recursive call to the function.

function fibonacci(n) {
  if (n === 0) {
    return 0;
  }
  if (n === 1) {
    return 1;
  }

  return fibonacci(n - 1) + fibonacci(n - 2);
}

Step 4: Consider Efficiency

Although the above solution works, it is not very effective for large n, because the same Fibonacci numbers are calculated multiple times. We can optimise this by using dynamic programming. Here's a new version of the function that utilizes an array to store previously calculated values.

function fibonacci(n) {
  let fibSequence = [0, 1];

  for (let i = 2; i <= n; i++) {
    fibSequence[i] = fibSequence[i - 1] + fibSequence[i - 2];
  }

  return fibSequence[n];
}

Conclusion

This function calculates the nth Fibonacci number efficiently, even for large n. It uses an iterative approach with dynamic programming, instead of recursive, to make it more efficient.

Here is the complete function:

function fibonacci(n) {
  let fibSequence = [0, 1];

  for (let i = 2; i <= n; i++) {
    fibSequence[i] = fibSequence[i - 1] + fibSequence[i - 2];
  }

  return fibSequence[n];
}