Find the Grid of Region Average

Find the Grid of Region Average

What is this problem about?

The Find the Grid of Region Average interview question is an image-processing simulation. You are given a grid of intensities. A $3 imes 3$ subgrid is a "region" if the absolute difference between any two adjacent cells in that region is $\leq$ threshold. For each cell in the original grid, you need to calculate its "region average": the average of the averages of all $3 imes 3$ regions that contain this cell.

Why is this asked in interviews?

Companies like Apple ask the Find the Grid of Region Average coding problem to test a candidate's ability to manage complex 2D traversals and nested aggregations. It requires careful bookkeeping to track which regions are valid and which cells belong to which regions. It evaluations your proficiency with Matrix interview patterns and multi-pass algorithms.

Algorithmic pattern used

This problem is solved using a Multi-pass Matrix Simulation.

1. Identify Valid Regions: Iterate through all possible $3 imes 3$ subgrids.
2. Validate: For each subgrid, check all pairs of adjacent cells. If every pair's difference is $\leq$ threshold, calculate the average of the 9 cells.
3. Accumulate: For every cell $(r, c)$ in a valid region, add that region's average to a sumGrid[r][c] and increment a countGrid[r][c].
4. Calculate Final Grid: For each cell, if countGrid[r][c] > 0, the final value is sumGrid[r][c] / countGrid[r][c]. If it wasn't part of any valid region, keep its original value (or use a problem-specific default).

Example explanation

Imagine a $4 imes 4$ grid. There are four possible $3 imes 3$ regions.

• Region 1 (top-left): Valid? Yes. Avg = 10.
• Region 2 (top-right): Valid? No.
• Cells in Region 1 get 10 added to their sum and 1 to their count.
• The cell at (1, 1) is in all four regions. Its final value will be the average of the averages of all valid ones among those four.

Common mistakes candidates make

• Redundant Checks: Checking adjacency for the entire $3 imes 3$ grid multiple times instead of reusing results.
• Integer Truncation: Forgetting that "averages of averages" usually requires integer division at each step according to specific rounding rules.
• Boundary Errors: Incorrectly calculating the range of $3 imes 3$ top-left corners.

Interview preparation tip

Practice "Convolution" style problems. Working with a moving window over a 2D grid is a standard skill for computer vision and graphics roles. Be organized with your loops: for r in 0..rows-3 and for c in 0..cols-3.