Recursive Product

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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, 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.