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Google·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Jun 2026

Summary

Google SWE coding round with a graph/pathfinding problem. Pretty standard algorithmic interview but the twist on Dijkstra threw me a bit.

Questions Asked (1)

Q1

Given an m x n grid where each cell has a unique height value, find a path from the top-left to the bottom-right corner such that the maximum height encountered along the path is as small as possible. Solve it using Dijkstra's algorithm.

Algorithms & Data Structures
Author's notes

My first instinct was binary search on the answer, which probably would've worked too, but they nudged me toward Dijkstra.

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AI HintsAI Generated

Suggested Approach

Model the grid as a graph where each cell is a node and edges connect adjacent cells. Use Dijkstra's algorithm with a modified cost function: the cost to reach a cell is the maximum height along the path. The answer is the minimum possible maximum height to reach the bottom-right cell.

Pro tip: Clarify that while Dijkstra typically minimizes sum of weights, here we minimize the maximum edge weight, which still works because the 'max' operation is monotonic and the greedy property holds. Mention that this is equivalent to finding the minimum bottleneck path.

1. Understand the problem

Restate the problem: find a path from (0,0) to (m-1,n-1) minimizing the maximum height along the path. Confirm that heights are unique and positive.

2. Model as a graph

Treat each cell as a node. Edges connect 4-directionally adjacent cells. The weight of an edge is the height of the destination cell (or the maximum of the two cells).

3. Adapt Dijkstra's algorithm

Use a priority queue storing (max_height_so_far, row, col). Initialize with (grid[0][0], 0, 0). For each neighbor, compute new_max = max(current_max, neighbor_height). If new_max is less than the best known for that neighbor, update and push.

4. Implement and analyze

Write code using a min-heap. Track visited cells to avoid reprocessing. Time complexity O(mn log(mn)), space O(mn).

5. Test and discuss

Walk through a small example, e.g., 3x3 grid, to verify correctness. Discuss edge cases: 1x1 grid, large grids, and why Dijkstra works despite non-standard cost.

Key Points to Mention

  • Dijkstra's algorithm can be adapted to minimize the maximum edge weight along a path, not just the sum.
  • The cost function is monotonic: extending a path cannot decrease the maximum height.
  • Use a priority queue to always expand the path with the smallest current maximum height.
  • Maintain a distance array (or visited set) to store the minimum maximum height found so far for each cell.
  • Time complexity is O(mn log(mn)) with a binary heap, which is efficient for grid sizes up to 10^5 cells.
  • This problem is equivalent to finding the minimum bottleneck path, and can also be solved with binary search + BFS, but Dijkstra is more direct.

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