Fibonacci Cases

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Unit 7 Session 1 (Click for link to problem statements)

Problem Highlights

• 💡 Difficulty: Easy
• ⏰ Time to complete: 10 mins
• 🛠️ Topics: Recursion, Fibonacci Sequence, Mathematics

1: U-nderstand

Understand what the interviewer is asking for by using test cases and questions about the problem.

• Established a set (2-3) of test cases to verify their own solution later.
• Established a set (1-2) of edge cases to verify their solution handles complexities.
• Have fully understood the problem and have no clarifying questions.
• Have you verified any Time/Space Constraints for this problem?

• Q: What should the function return for n = 0 and n = 1?
  • A: According to Fibonacci sequence rules, for n = 0, return 0, and for n = 1, return 1.

HAPPY CASE
Input: 5
Output: 5
Explanation: The 5th Fibonacci number is 5 (sequence: 0, 1, 1, 2, 3, 5).

EDGE CASE
Input: 0
Output: 0
Explanation: The 0th Fibonacci number is defined as 0.

2: M-atch

Match what this problem looks like to known categories of problems, e.g. Linked List or Dynamic Programming, and strategies or patterns in those categories.

This is a classic recursive problem related to number sequences:

• Utilizing the definition of Fibonacci sequence to create recursive function calls.
• Handling multiple base cases as the sequence has specific values defined for the first two indices.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Develop a recursive function to return the nth Fibonacci number using its mathematical definition.

1) Base Case 1: If `n` is 0, return 0.
2) Base Case 2: If `n` is 1, return 1.
3) Recursive Case: Return `fibonacci(n-1) + fibonacci(n-2)`.

⚠️ Common Mistakes

• Forgetting to implement both base cases, which are crucial for the recursive logic to terminate properly.

4: I-mplement

Implement the code to solve the algorithm.

def fibonacci(n):
    if n == 0:
        return 0
    elif n == 1:
        return 1
    else:
        return fibonacci(n-1) + fibonacci(n-2)

5: R-eview

Review the code by running specific example(s) and recording values (watchlist) of your code's variables along the way.

• Trace through your code with an input of 5 to ensure it correctly computes the Fibonacci number as 5.
• Validate the base cases with input 0 and 1 to confirm correct returns of 0 and 1, respectively.

6: E-valuate

Evaluate the performance of your algorithm and state any strong/weak or future potential work.

• Time Complexity: O(2^n) due to the exponential number of function calls.
• Space Complexity: O(n) due to the maximum height of the recursion tree, which equals n.