Recursive Product - codepath/compsci_guides GitHub Wiki

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

Problem Highlights

  • 💡 Difficulty: Easy
  • ⏰ Time to complete: 10 mins
  • 🛠️ Topics: Recursion, List Operations, Product Calculation

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 an empty list?
    • A: The function should return 1 for an empty list, as the product of no elements is typically considered 1 (neutral element for multiplication).
HAPPY CASE
Input: [1, 2, 3, 4, 5]
Output: 120
Explanation: The product of all elements in the list is 1 * 2 * 3 * 4 * 5 = 120.

EDGE CASE
Input: []
Output: 1
Explanation: An empty list returns a product of 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.

This problem is a typical example of using recursion for aggregation:

  • Recursive decomposition to calculate a product.
  • Handling base cases in recursion to correctly terminate and aggregate results.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Develop a recursive function that calculates the product of all values in a list by recursively multiplying the first element by the product of the remaining list.

1) Base Case: If the list is empty, return 1.
2) Recursive Case: Return the first element multiplied by the recursive call for the rest of the list.

⚠️ Common Mistakes

  • Forgetting the base case which might lead to an error when trying to access elements of an empty list.

4: I-mplement

Implement the code to solve the algorithm.

def list_product(lst):
    if not lst:
        return 1
    else:
        return lst[0] * list_product(lst[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 [1, 2, 3, 4, 5] to check for the expected output of 120.
  • Validate the base case with an empty list to ensure it returns 1.

6: E-valuate

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

  • Time Complexity: O(n) because each function call processes one element of the list.
  • Space Complexity: O(n) due to the recursion depth being equal to the number of elements in the list.