Recursive Count 7s

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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, Number Manipulation

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 happen if n is zero?
  • A: The function should return 0 since there are no occurrences of any digits in 0.

HAPPY CASE
Input: 1727647
Output: 2
Explanation: The digit 7 appears twice in the number 1727647.

EDGE CASE
Input: 0
Output: 0
Explanation: The number 0 does not contain any digits of 7.

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 falls into a category of counting specific items within a larger structure, utilizing recursion for simplified breakdown:

• Using recursive function calls to peel off digits of the number and count occurrences.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Create a recursive function that checks if the last digit of a number is 7 and then recursively calls itself with the rest of the number.

1) Base Case: If `n` is 0, return 0.
2) Recursive Case: Check if the last digit is 7. If it is, add 1 and recurse with `n` divided by 10; otherwise, just recurse with `n` divided by 10.

⚠️ Common Mistakes

• Forgetting to handle the case where n becomes zero, which might lead to incorrect or endless recursion.

4: I-mplement

Implement the code to solve the algorithm.

def count_sevens(n):
    if n == 0:
        return 0  # Base case: no more digits to check
    elif n % 10 == 7:
        return 1 + count_sevens(n // 10)  # Increment count and recurse on the rest
    else:
        return count_sevens(n // 10)  # Just recurse without incrementing

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 1727647 to ensure it correctly counts two occurrences of the digit 7.
• Validate the base case with input 0 to confirm that it returns 0.

6: E-valuate

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

• Time Complexity: O(log n) because the function reduces n by a factor of 10 with each recursive call, effectively depending on the number of digits in n.
• Space Complexity: O(log n) due to the recursion stack depth also relating to the number of digits.