Instacart·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Instacart software engineer interview with a grid placement problem that sounds deceptively simple until you're actually implementing it. The non-rectangular shape handling is where things get interesting.

Questions Asked (1)

Given an empty 2D grid and four fixed shapes (each defined as a small 2D binary mask), place all four shapes onto the grid such that no two shapes overlap and each shape is placed greedily at the lexicographically smallest (row, col) origin that fits. One of the shapes is a T-shape (non-rectangular). Return the final grid or the chosen origin for each shape.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was to treat each shape as a bounding box, which completely breaks for the T-shape.

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AI HintsAI Generated

Suggested Approach

Clarify the problem constraints (grid size, shape definitions, ordering of shapes) and then propose a greedy algorithm that processes shapes in a fixed order, scanning the grid row-major to find the first valid placement for each shape. Discuss how to efficiently check for overlaps and handle the non-rectangular T-shape, and analyze the time complexity.

Pro tip: Mention that the greedy choice for each shape is independent of future shapes, but the order of shapes matters; if the order is not specified, ask or assume a given order and note that different orders can lead to different placements.

1. Clarify requirements and constraints

Ask about grid dimensions, shape definitions (including the T-shape), whether shapes can be rotated/reflected, and the order in which shapes should be placed. Confirm that 'lexicographically smallest' means row-major order.

2. Design the greedy placement algorithm

For each shape in the given order, scan the grid from top-left to bottom-right. At each cell, check if the shape fits entirely within the grid and does not overlap any already placed shape. Place the shape at the first valid cell.

3. Implement efficient overlap checking

Use a 2D boolean array to track occupied cells. For each candidate placement, iterate over the shape's mask and verify that all corresponding grid cells are within bounds and unoccupied. If valid, mark those cells as occupied.

4. Handle the non-rectangular T-shape

Treat the T-shape as a list of relative coordinates (e.g., (0,0), (0,1), (0,2), (1,1)). Ensure the overlap check works for arbitrary masks, not just rectangles.

5. Analyze complexity and discuss trade-offs

Time complexity is O(S * G * A) where S is number of shapes, G is grid cells, and A is shape area. Mention that scanning can be optimized by starting from the last placed position or using a set of free cells, but the simple approach is often sufficient.

Key Points to Mention

Greedy algorithm: process shapes in a fixed order, place each at the first valid position in row-major order.
Overlap detection using a boolean occupancy grid or set of occupied coordinates.
Handling non-rectangular shapes by representing them as a list of relative offsets.
Boundary checks: ensure shape fits within grid dimensions.
Time complexity: O(S * G * A) and potential optimizations.
Edge cases: no valid placement for a shape, grid too small, shapes with holes or disconnected parts.

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