The positive case felt trivial and I almost rushed past it, which was a mistake because the negative case is where the real logic lives.
First clarify the problem: for positive resize, simply add resize/count to each rectangle; for negative, you need to reduce as evenly as possible while respecting the minimum height of 1. Then design an algorithm that iteratively distributes the reduction among rectangles that can still be reduced, ensuring fairness and correctness.
Pro tip: Discuss edge cases like when the total reduction exceeds the total available height (sum of heights - count), and mention that the order of reduction can affect the result if not careful—use a priority queue or sort to always reduce the tallest first to maintain evenness.
Ask about the exact meaning of 'evenly as possible' for negative resize, and confirm constraints like minimum height 1. Discuss what happens if resize is so negative that it would require reducing below 1 for all.
For positive resize, simply add resize/count to each rectangle. Mention that this is straightforward and no minimum constraint applies.
For negative resize, compute the total reduction needed. Use a greedy approach: repeatedly reduce the tallest rectangles by 1 until the total reduction is met, but never below 1. Alternatively, sort and distribute proportionally.
Use a max-heap or sort to efficiently find the tallest rectangles. For large inputs, consider a binary search on the final heights to achieve O(n log n) or better.
Verify with the given example and edge cases like resize=0, resize larger than total available reduction, and all heights at 1.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify that preserving relative positions means maintaining the vertical ordering and gaps between rectangles, where gaps are measured from the bottom of the upper rectangle to the top of the lower rectangle. Then, propose a two-phase algorithm: compute the new heights and y-coordinates by processing rectangles in vertical order, ensuring that the gap between each consecutive pair remains proportional to the original gap (or unchanged if only heights change). Finally, discuss trade-offs such as whether to scale gaps proportionally or keep them fixed, and how to handle overlapping rectangles.
Pro tip: Demonstrate maturity by explicitly asking whether the resizing should preserve absolute gaps or scale them proportionally, and mention that in a real design tool like Figma, constraints and auto-layout often dictate this behavior.
Confirm that relative position includes both the vertical ordering and the gaps between rectangles, where a gap is the distance from the bottom edge of one rectangle to the top edge of the next. Ask if gaps should remain constant or scale with resizing.
Sort the rectangles based on their original y-coordinates to establish their vertical order. This order must be preserved after resizing.
Starting from the topmost rectangle, assign its new y-coordinate (e.g., keep the topmost y fixed). For each subsequent rectangle, set its new y-coordinate as the previous rectangle's new bottom plus the preserved gap (either constant or scaled).
Discuss cases like overlapping rectangles, negative gaps, or when scaling gaps might cause collisions. Mention alternative approaches such as maintaining center-to-center distances or using a constraint-based solver.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.