Counting Black Holes with Quadtree Binary Search

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Interview Summary

Problem type

Counting Black Holes with Quadtree Binary Search

Interview question

Given the bottom-left and top-right coordinates of a 2D region of space (with coordinate values ranging from 0 to 1,000), and a black-box helper function blackhole_present(bottom_left, top_right) that returns true if one or more black holes exist within a given sub-region, design an efficient algorithm to count the total number of black holes in the region. The challenge is that each call to the helper function is expensive, so a brute-force, cell-by-cell scan is impractical; the solution must minimize the number of calls using a divide-and-conquer, quad-search strategy.

Interview Feedback

Feedback about Distinguished Dromedary (the interviewee)

• Advance this person to the next round?
  • Yes
• How were their technical skills? 4/4
• How was their problem solving ability? 4/4
• What about their communication ability? 4/4

Strengths and what went well:

• Communication:

  • At all time I could understand your thought process. You did very well in explaining the different approaches for a solution as well as pros and cons. You did a good job in writing your thinking on the IDE for the interviewer to see as well as going over the examples, edge cases, etc...
  • You received my feedback candidly and applied it right away, as well as asking clarifying questions.

• Problem Solving

  • You did an excellent progression from proposing a brute force solution to an optimized binary search.
  • Great job in figuring out the particular quad-binary search variant as well as the formula for dividing the coordinates in squares
  • You proactively identified the base cases of the recursive solution and how to go about counting the black holes

• Coding

  • Code was syntactically correct, extensible, and well formatted.
  • You dry ran the solution with example inputs to demonstrate it works and has no bugs

Areas of Improvement:

• Communication: Write down the approach of every proposed solution concisely.

• Problem solving:

  • Review problems that have complex recursive branching and their time and space complexity.
  • Ask clarifying questions more thoroughly.

• Coding:

  • Add a validation step to discard bad inputs.
  • Add minimal comments to the code.

Advise for Future interviews

• Track practice on a spreadsheet and identify areas for improvement.
• Be proactive in asking clarifying questions about variables, edge cases, expected outcomes, etc...

Interview Transcript

Ferocious Lightning:

Hello. Hi, can you hear me?

Distinguished Dromedary:

Good, how are you?

Ferocious Lightning:

Not bad. Let's proceed.

Distinguished Dromedary:

Sure, I'm a software engineer. I've been working for about 3.5 years now. I'm focusing on time management and edge cases for technical problems.

Ferocious Lightning:

Okay, let's go straight into a hard problem.

Problem Details

Given: bottom-left and top-right coordinates with black holes present. Task: Design an efficient algorithm using divide-and-conquer to count them.

Proposed Solution

1. Base Cases:
   • Return 0 if blackhole_present returns false.
   • Return 1 if coordinates are the same.
2. *Divide the Region into Quadrants:
   • Recursively call count_blackholes for four quadrants.
3. Summation: Return total count from all four quadrants.

Time and Space Complexity

• Time Complexity: O(m log n)
• Space Complexity: O(M)

Final Remarks

• Regular practice and understanding of algorithm patterns is crucial.

Thank you for your feedback: Keep practicing!