A) Dynamically Programming Fibonnacci

Here is the dynamic programming definition that can be provided by someone who learned about the concept yesterday:

Quote

Dynamic programming is a recursive pattern in which the return values of a function are saved to be reused by later functions.

Calculating the value of an index in the fibonacci sequence is a perfect application for dynamic programming because each index of the Fibonacci sequence is a function of the two previous items in the sequence.

Implementation I created organically

const fibonacci = function(n, seq=[1, 1]){

  if (n < 2) return 1

  if (seq.length-1 < n){
    seq.push(seq[seq.length-1] + seq[seq.length-2])
    return fibonacci(n, seq)
  }

  return seq[n]
}

console.log(fibonacci(4))

Implementation I found online:

function fibonacci(n) {
  // Declare the memo object once
  const memo = {};
 
  // Inner recursive function that uses the memo object
  function fib(n) {
    // Base cases
    if (n <= 1) return n;
 
    // Check if the value is already computed
    if (memo[n]) return memo[n];
 
    // Compute the value and store it in the memo object
    memo[n] = fib(n - 1) + fib(n - 2);
 
    return memo[n];
  }
 
  // Call the inner recursive function
  return fib(n);
}
 
// Example usage
console.log(fibonacci(10)); // Outputs: 55
console.log(fibonacci(50)); // Outputs: 12586269025