24.1.1. Lecture - 45

Try these first

1. 1.

   What is a recursive function?

   Hint

   Think of how factorials are computed.

2. 2.

   What is memoization?

   Hint

   Remember it helps avoid repeated calculations.

3. 3.

   What is the time complexity of naive recursive Fibonacci?

   • O(n)
   • O(log n)
   • O(2^n)

   Hint

   Consider how many calls are made in a recursion tree.

4. 4.

   True or False: Memoization can reduce the time complexity of recursive functions.

   • True
   • False

   Hint

   Remember how it stores values.

5. 5.

   Using dynamic programming, create an algorithm to compute the nth Fibonacci number and count how many times the function was called.

   Hint

   Use an array to hold computed Fibonacci values and loop through for the final result.

6. 6.

   Propose a new recursive function incorporating memoization to compute the nth Fibonacci number in Python. Show the implementation.

   Hint

   Choose a dictionary to map inputs to Fibonacci results.