interview-file-3.md

Technical Interview Question: Counting Squares from Points

Prompt

You are given a vector of points in 2D space, represented as Vec<(i32, i32)>. Write a function that returns the number of distinct squares that can be formed using these points as vertices.

A square is defined as a quadrilateral with four equal sides and four right angles.

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Function Signature (Rust)

fn count_squares(points: &Vec<(i32, i32)>) -> usize

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Examples

Example 1

let points = vec![(0, 0), (1, 0), (0, 1), (1, 1)];
assert_eq!(count_squares(&points), 1);

Explanation: These four points form a unit square.

Example 2

let points = vec![
    (0, 0), (1, 0), (2, 0),
    (0, 1), (1, 1), (2, 1),
    (0, 2), (1, 2), (2, 2)
];
assert_eq!(count_squares(&points), 6);

Explanation:

• Four 1×1 squares
• One 2×2 square
• One √2×√2 rotated square (diamond)

Example 3

let points = vec![(0, 0), (1, 1), (2, 0)];
assert_eq!(count_squares(&points), 0);

Explanation: No four points form a square.