What is the algorithm to check if four points form a square?
A geometry problem requiring distance calculations and property verification. It tests spatial reasoning and math logic.
Why Interviewers Ask This
This question tests the candidate's ability to translate geometric properties into code. Interviewers look for a robust solution that checks side lengths and diagonals. It also checks handling of coordinate systems and floating-point precision.
How to Answer This Question
Explain calculating the distances between all pairs of points. A square has four equal sides and two equal diagonals which are longer than the sides. Check if there are exactly two distinct distance values with the correct multiplicities. Alternatively, use vector dot products to check perpendicularity.
Key Points to Cover
- Distance calculation
- Side and diagonal counts
- Squared distance usage
- Geometric properties
Sample Answer
To check if four points form a square, I calculate the squared Euclidean distance between all six pairs of points. In a valid square, there should be four equal smaller distances (sides) and two equal larger distances (d…
Common Mistakes to Avoid
- Checking only side lengths
- Ignoring diagonal length
- Floating-point precision issues
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