Lonely Pixel I

Lonely Pixel I

What is this problem about?

The Lonely Pixel I interview question involves analyzing a 2D grid or matrix consisting of two types of characters: 'B' for black pixels and 'W' for white pixels. The goal is to determine the total number of "lonely" black pixels in the image. A black pixel 'B' is considered lonely if and only if it is the absolute only 'B' in its entire row AND its entire column. This requires scanning the matrix to understand the distribution of pixels across both dimensions.

Why is this asked in interviews?

This matrix coding problem is frequently asked because it perfectly tests a candidate's ability to traverse 2D arrays efficiently and manage state. It requires transforming a naive, slow approach into an optimized solution by precomputing data. Interviewers look for this progression to evaluate your understanding of time versus space complexity trade-offs, which is critical for optimizing graphics processing or tabular data analysis in real engineering tasks.

Algorithmic pattern used

The ideal approach applies a Precomputation / Hash Table pattern to Arrays. Instead of checking the entire row and column for every single 'B' we encounter (which would result in a sluggish O(N^2 * M^2) time complexity), we can iterate through the matrix once to count the number of 'B's in every row and every column, storing these in two separate 1D arrays. Then, we perform a second pass: if we see a 'B', we simply check our precomputed arrays to see if rowCount[row] == 1 and colCount[col] == 1. This brings the time complexity down to O(N * M).

Example explanation

Consider a 3x3 matrix:

W W B
W B W
B W W

First, we count the 'B's per row and column:

• Row counts: Row 0 has 1, Row 1 has 1, Row 2 has 1.
• Col counts: Col 0 has 1, Col 1 has 1, Col 2 has 1.

Next, we evaluate each 'B'.

• The 'B' at (0, 2) is in a row with exactly 1 'B' and a col with exactly 1 'B'. It is lonely.
• The 'B' at (1, 1) is also lonely.
• The 'B' at (2, 0) is also lonely. Total lonely pixels: 3. If row 0 had another 'B' at (0,1), then neither the 'B' at (0,1) nor (0,2) would be lonely, and the column counts would change too, rippling the effect.

Common mistakes candidates make

The most common mistake candidates make is jumping straight into the brute-force nested loop solution without considering precomputation. They find a 'B', and then write two while loops to scan that specific row and column. This leads to redundant work and often triggers Time Limit Exceeded errors in tests. Another mistake is forgetting to check both the row count AND the column count during the verification phase.

Interview preparation tip

To ace the Lonely Pixel I interview question, deeply internalize the concept of precomputing row and column states when dealing with matrix problems. Whenever a problem asks you to validate a condition based on an entire row and column, your first instinct should be to ask, "Can I count or flag these rows and columns in a single initial pass?"