Lonely Pixel II

Lonely Pixel II

What is this problem about?

The Lonely Pixel II coding problem is a step up in complexity from its predecessor. You are again given a 2D matrix of 'B' (black) and 'W' (white) pixels, along with an integer target N. A black pixel at (row, col) is now considered "lonely" under strict, multi-layered conditions: First, its row must contain exactly N black pixels. Second, its column must contain exactly N black pixels. Third, and most challengingly, for every other row that has a black pixel in this exact same column, that row must be completely identical to our starting row.

Why is this asked in interviews?

Interviewers ask this question to evaluate your ability to handle complex logical constraints and data modeling. While the first variation only required simple counting, this problem demands that you compare entire rows of a matrix efficiently. It tests your skills with Hash Tables, String manipulation (for row hashing), and Matrix traversal, revealing if you can write clean, modular code when the rules get complicated.

Algorithmic pattern used

This problem utilizes Hashing and Counting. To efficiently compare if entire rows are identical, you can convert each row into a string (or tuple) representation and use it as a key in a Hash Table, keeping track of how many times that exact row pattern appears. You also use 1D arrays to track the count of 'B's in each column. By combining these precomputed counts and hashes, you can evaluate the complex conditions in optimal time.

Example explanation

Imagine a matrix with target N = 2:

Row 0: W B W B
Row 1: W B W B
Row 2: B W W W

First, we map the string representation of rows:

• "WBWB" appears 2 times.
• "BWWW" appears 1 time. We also count 'B's per column: Col 0 has 1, Col 1 has 2, Col 2 has 0, Col 3 has 2.

Let's check the 'B' at (0, 1):

• Does Row 0 have N (2) black pixels? Yes.
• Does Col 1 have N (2) black pixels? Yes.
• Are all rows that have a 'B' in Col 1 identical to Row 0? The hash map tells us that the row pattern "WBWB" occurs exactly 2 times. Since Col 1 has 2 'B's, and both belong to this exact row pattern, the condition holds! This 'B' is lonely.

Common mistakes candidates make

Candidates often fail to realize that comparing arrays element-by-element repeatedly will cause a massive performance hit. Brute-forcing the row-matching condition leads to messy, deeply nested code. Another trap is misinterpreting the third condition—candidates sometimes try to check every single row in the matrix rather than just the rows that share a 'B' in the current column.

Interview preparation tip

When dealing with the Lonely Pixel II interview pattern or similar matrix grouping problems, practice serializing arrays into strings so they can be hashed. By grouping identical rows into a dictionary mapping RowString -> Count, you can eliminate manual row-to-row comparisons, making your logic vastly simpler and your execution time much faster.