Determine whether squares can fit
Problem Description
You are given the dimensions of a rectangular grid, m (height) and n (width), and an array squares. Each value in the squares array represents the side length of a square that must be cut from the original m x n rectangle.
Your task is to determine whether it is possible to cut out one square corresponding to each requested side length such that all the following conditions are met:
- Every square is fully contained within the
m x nrectangle. - No two squares overlap.
- All cuts must align with integer grid lines.
- Unused leftover area within the
m x nrectangle is permitted.
Assume that the total number of requested squares is sufficiently small to allow for a search or backtracking-based solution.
Examples
m = 30,n = 40,squares = [30, 10]->truem = 30,n = 40,squares = [30, 20]->false
Return true if all requested squares can be successfully cut from the rectangle; otherwise, return false.
AI interview prep
Core dilemma
The central dilemma is efficiently navigating an extremely large search space for optimal 2D packing, which is an NP-hard problem, while leveraging the 'small number of squares' constraint to make a backtracking solution feasible.
3 tradeoffs and 2 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Determine whether squares can fit
Problem Description
You are given the dimensions of a rectangular grid, m (height) and n (width), and an array squares. Each value in the squares array represents the side length of a square that must be cut from the original m x n rectangle.
Your task is to determine whether it is possible to cut out one square corresponding to each requested side length such that all the following conditions are met:
- Every square is fully contained within the
m x nrectangle. - No two squares overlap.
- All cuts must align with integer grid lines.
- Unused leftover area within the
m x nrectangle is permitted.
Assume that the total number of requested squares is sufficiently small to allow for a search or backtracking-based solution.
Examples
m = 30,n = 40,squares = [30, 10]->truem = 30,n = 40,squares = [30, 20]->false
Return true if all requested squares can be successfully cut from the rectangle; otherwise, return false.