chalk·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

Chalk had me work through a grid simulation problem that looked deceptively clean on the surface. The tie-breaking wrinkle and the efficiency constraint are where it actually gets interesting.

Questions Asked (1)

Given a 2D elevation grid where each cell receives one unit of rain, simulate water flow where water moves downhill via steepest descent among 4-directional neighbors until reaching a local minimum. When multiple neighbors tie for steepest descent, split water equally among them. Return the total water collected at each cell, and aim for O(N log N) overall.

Algorithms & Data StructuresSystem Design

Author's notes

The basic flow logic clicked pretty fast, sort cells by elevation descending, push water forward.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Model the grid as a directed graph where each cell points to its steepest downhill neighbor(s), then process cells in increasing elevation order to accumulate water from higher to lower cells. Use a priority queue to efficiently process cells and handle ties by splitting water equally among multiple steepest neighbors.

Pro tip: Clarify whether water can flow off the grid edges (treat outside as a global minimum) and confirm if local minima can be multiple cells; this shows attention to edge cases and prevents incorrect assumptions.

1. Clarify problem constraints and edge cases

Ask about grid boundaries, whether water can exit the grid, and if multiple local minima can exist. Confirm that each cell starts with 1 unit of rain and that water splits equally on ties.

2. Model flow as a directed graph

For each cell, determine its steepest descent neighbor(s) among 4-directional neighbors. If a cell is a local minimum, it retains its water; otherwise, it has outgoing edges to one or more neighbors.

3. Process cells in topological order

Since water flows from higher to lower elevations, sort cells by elevation descending (or use a priority queue). Process each cell, distributing its accumulated water equally to its outgoing neighbors.

4. Accumulate and return results

Initialize each cell with 1 unit of water. As you process cells, add the distributed amounts to neighbors. After processing all cells, the water at each cell is the total collected.

5. Analyze complexity and optimize

Sorting cells takes O(N log N) where N is the number of cells. Processing each cell and its neighbors is O(N). Overall O(N log N) time and O(N) space.

Key Points to Mention

Graph representation: each cell as a node with directed edges to steepest descent neighbors.
Topological order processing: water flows from higher to lower elevations, so process in descending elevation order.
Handling ties: split water equally among multiple steepest descent neighbors.
Local minima: cells with no lower neighbors retain all incoming water.
Complexity: O(N log N) due to sorting, O(N) space for storing water amounts and graph.
Edge cases: grid boundaries, multiple local minima, and uniform elevation plateaus.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.