Factorial 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, Mathematical Problems, Factorials

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: How should the function handle negative inputs?
  • A: The factorial function is traditionally defined for non-negative integers, so a negative input could either not be allowed or handled separately.

HAPPY CASE
Input: 5
Output: 120
Explanation: The factorial of 5 is 5 * 4 * 3 * 2 * 1 = 120.

EDGE CASE
Input: 0
Output: 1
Explanation: The factorial of 0 is defined as 1.

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.

For factorial computation problems, we can use:

• Direct recursive function calls implementing the mathematical definition of factorial.
• Consideration of special cases like the factorial of 0.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Use recursion to compute the factorial based on its definition.

1) Base Case: If `n` is 0, return 1 (since 0! = 1).
2) Recursive Case: Return `n * factorial(n - 1)`.

⚠️ Common Mistakes

• Forgetting the base case for 0 which might result in an incorrect or infinite recursion.

4: I-mplement

Implement the code to solve the algorithm.

def factorial(n):
    if n == 0:
        return 1
    return n * factorial(n-1)

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 each recursive call is calculated correctly and aggregates to 120.
• Validate the base case with input 0, which should return 1 directly.

6: E-valuate

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

• Time Complexity: O(n) because we make n recursive calls.
• Space Complexity: O(n) because each recursive call adds a layer to the call stack, using more memory.