Two Sigma·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

Two Sigma data scientist interview, got hit with a grid/island problem that felt more like a competitive programming warmup than anything data-sciency. Not a bad experience, just unexpected territory.

Questions Asked (1)

Given a binary grid of 0s and 1s, find the number of distinct island shapes, where two islands count as the same shape if one can be translated (no rotation or reflection) to exactly overlap the other.

Algorithms & Data Structures

Author's notes

My first instinct was to just count connected components, which is obviously wrong.

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AI HintsAI Generated

Suggested Approach

Use DFS/BFS to find each island and compute a canonical representation of its shape by normalizing the coordinates relative to the island's top-left bounding box. Store these canonical forms in a set to count distinct shapes. This approach efficiently handles translation invariance and avoids explicit rotation/reflection checks.

Pro tip: Emphasize that the canonical representation must be invariant to translation but not rotation/reflection, and discuss how to handle large grids by using a set for O(1) lookups. Mention that the time complexity is O(R*C) and space O(R*C) in the worst case.

1. Traverse the grid

Iterate through each cell; when encountering an unvisited '1', start a DFS/BFS to explore the entire island.

2. Collect island coordinates

During traversal, record the relative coordinates of each cell in the island (e.g., row and column offsets from the starting cell).

3. Normalize the shape

Compute the minimum row and column among the coordinates and subtract them to shift the island to the origin, ensuring translation invariance.

4. Canonicalize and store

Convert the normalized coordinates into a hashable form (e.g., a sorted tuple of coordinates or a string) and add it to a set of distinct shapes.

5. Count distinct shapes

After processing all islands, the size of the set gives the number of distinct island shapes.

Key Points to Mention

Translation invariance: normalize coordinates by subtracting the minimum row and column.
Use DFS or BFS for island traversal, marking visited cells to avoid revisiting.
Canonical representation: sorted list of relative coordinates or a string encoding.
Hash set for O(1) average-time insertion and lookup to count distinct shapes.
Time complexity: O(R*C) for grid traversal, space O(R*C) for visited and set storage.
Edge cases: empty grid, no islands, all water, or all land (one island).

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