Determine whether squares can fit
Company: ByteDance
Role: Site Reliability Engineer
Category: Coding & Algorithms
Difficulty: hard
Interview Round: Technical Screen
You are given an `m x n` rectangular grid and an array `squares`, where each value represents the side length of a square that must be cut from the original rectangle.
Determine whether it is possible to cut out **one square of each requested size** such that:
- every square is fully contained inside the `m x n` rectangle,
- squares do not overlap,
- cuts follow integer grid lines,
- unused leftover area is allowed.
Assume the number of requested squares is small enough for a search/backtracking solution.
Examples:
- `m = 30`, `n = 40`, `squares = [30, 10]` -> `true`
- `m = 30`, `n = 40`, `squares = [30, 20]` -> `false`
Return `true` if all requested squares can be cut from the rectangle; otherwise return `false`.
Quick Answer: This question evaluates spatial reasoning, combinatorial packing, and constraint-satisfaction skills in the context of placing integer-aligned squares within an m x n rectangle.
Given rectangle width and height and square side lengths, return whether every square can be placed axis-aligned without overlap inside the rectangle.
Constraints
- Inputs are provided as Python literals compatible with the function signature.
- Return a deterministic value exactly matching the requested output.
Examples
Input: (30, 40, [30, 10])
Expected Output: True
Explanation: Fits.
Input: (30, 40, [30, 20])
Expected Output: False
Explanation: Area impossible.
Hints
- Start with a direct data structure representation.
- Handle edge cases before the main loop.