How do I approach Coding & Algorithms interview questions?

Coding & Algorithms questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master coding & algorithms interviews.

What difficulty level is this interview question?

This is a medium difficulty Coding & Algorithms question, commonly asked during Onsite rounds at Purestorage.

What role is this question designed for?

This question is commonly asked for Software Engineer candidates at Purestorage during technical interviews.

Determine whether points form squares | Purestorage Interview Question

Quick Overview

This question evaluates computational geometry, combinatorial counting, and algorithmic optimization skills by requiring validation of a non-degenerate square from four 2D integer points and counting distinct squares in a larger point set, and it falls under the Coding & Algorithms category.

Problem: Square detection and counting from point coordinates

You are given points on a 2D plane with integer coordinates.

Part A — Validate a single square

Given exactly 4 points [(x1,y1), (x2,y2), (x3,y3), (x4,y4)], determine whether these 4 points can be the vertices of a non-degenerate square (square may be rotated; sides are not necessarily axis-aligned).

Output: true if they form a square, otherwise false.

Part B — Count squares in a set (with optimization)

Given N points (may contain duplicates; treat duplicates as separate inputs but they should not create degenerate “squares”), count how many distinct squares can be formed whose 4 vertices are all present in the set.

A square is considered the same regardless of the order of its vertices.
Squares may be rotated.

Follow-up:

Describe a brute-force approach (e.g., around $O(n^4)$ ).
Improve it to about $O(n^3)$ .
Further improve to about $O(n^2)$ time (assume hash set / hash map lookups are $O(1)$ average).

Constraints (assume typical interview constraints)

1 <= N <= 2e4 (for the optimized discussion)
Coordinates fit in 32-bit signed integers

Clarify any additional assumptions you need (e.g., whether duplicates should be ignored by converting to a set).

Quick Overview

Problem: Square detection and counting from point coordinates

You are given points on a 2D plane with integer coordinates.

Part A — Validate a single square

Output: true if they form a square, otherwise false.

Part B — Count squares in a set (with optimization)

A square is considered the same regardless of the order of its vertices.

Squares may be rotated.

Follow-up:

Describe a brute-force approach (e.g., around

O(n^4)

Improve it to about

O(n^3)

Further improve to about

O(n^2)

time (assume hash set / hash map lookups are

O(1)

average).

Constraints (assume typical interview constraints)

1 <= N <= 2e4 (for the optimized discussion)

Coordinates fit in 32-bit signed integers

Clarify any additional assumptions you need (e.g., whether duplicates should be ignored by converting to a set).

Determine whether points form squares

Quick Overview

Problem: Square detection and counting from point coordinates

Part A — Validate a single square

Part B — Count squares in a set (with optimization)

Constraints (assume typical interview constraints)

Comments (0)

Determine whether points form squares

Quick Overview

Problem: Square detection and counting from point coordinates

Part A — Validate a single square

Part B — Count squares in a set (with optimization)

Constraints (assume typical interview constraints)

Comments (0)