Certainly! The Fibonacci series is a sequence of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. Let's write a JavaScript function to generate the nth Fibonacci number.

Brute Force Solution:

// Brute Force Solution
function fibonacciBruteForce(n) {
  if (n <= 1) {
    return n;
  } else {
    return fibonacciBruteForce(n - 1) + fibonacciBruteForce(n - 2);
  }
}
 
// Example usage
console.log(fibonacciBruteForce(5)); // Output: 5

This solution uses recursion to calculate Fibonacci numbers. However, it's not optimal because it recalculates the same Fibonacci numbers multiple times, leading to exponential time complexity.

Optimal Solution (Dynamic Programming - Memoization):

// Optimal Solution using Memoization
function fibonacciOptimal(n, memo = {}) {
  if (n <= 1) {
    return n;
  }
 
  if (memo[n]) {
    return memo[n];
  } else {
    memo[n] = fibonacciOptimal(n - 1, memo) + fibonacciOptimal(n - 2, memo);
    return memo[n];
  }
}
 
// Example usage
console.log(fibonacciOptimal(5)); // Output: 5

This solution uses memoization to store the results of previously calculated Fibonacci numbers, preventing redundant calculations. It has a time complexity of O(n) because each Fibonacci number is calculated only once.

Feel free to ask if you have any questions or if you'd like explanations for any part of the code!