Detect Squares

Detect Squares is a Medium Data Structures and Algorithms interview problem you can solve, run and submit on Thita.ai. It belongs to the Design Patterns pattern, in the Design (General/Specific) subpattern.

Problem statement

You are given a stream of points on the X-Y plane. Design an algorithm that:

- Adds new points from the stream into a data structure. Duplicate points are allowed and should be treated as different points.

- Given a query point, counts the number of ways to choose three points from the data structure such that the three points and the query point form an axis-aligned square with positive area.

An axis-aligned square is a square whose edges are all the same length and are either parallel or perpendicular to the x-axis and y-axis.

Implement the DetectSquares class:

- DetectSquares() Initializes the object with an empty data structure.

- void add(int[] point) Adds a new point point = [x, y] to the data structure.

- int count(int[] point) Counts the number of ways to form axis-aligned squares with point point = [x, y] as described above.

Example 1:

Input ["DetectSquares", "add", "add", "add", "count", "count", "add", "count"] [[], [[3, 10]], [[11, 2]], [[3, 2]], [[11, 10]], [[14, 8]], [[11, 2]], [[11, 10]]] Output [null, null, null, null, 1, 0, null, 2]

Explanation DetectSquares detectSquares = new DetectSquares(); detectSquares.add([3, 10]); detectSquares.add([11, 2]); detectSquares.add([3, 2]); detectSquares.count([11, 10]); // return 1. You can choose: // - The first, second, and third points detectSquares.count([14, 8]); // return 0. The query point cannot form a square with any points in the data structure. detectSquares.add([11, 2]); // Adding duplicate points is allowed. detectSquares.count([11, 10]); // return 2. You can choose: // - The first, second, and third points // - The first, third, and fourth points

Constraints:

- point.length == 2

- 0 <= x, y <= 1000

- At most 3000 calls in total will be made to add and count.

Topics and companies

Topics: Array, Hash Table, Design, Counting.

How to practise Detect Squares on Thita.ai

Starter code is provided in C, C#, C++, Go, Java, JavaScript and Python. Your solution runs against 5 test cases for this problem, with the AI coach available for a hint when you are stuck rather than a finished answer. The reference solution runs in O(N) per count, O(1) per add. Here, N is the number of unique x-coordinates stored. For each count query, we iterate over all unique x (columns) to check possible squares. time and O(U), where U is the number of unique (x, y) points ever added (including duplicates, as we store counts). space.

Open Detect Squares in the code editor, or read the Detect Squares editorial for a worked solution with its approach and complexity analysis.

Where Detect Squares sits in the DSA pattern sheet

Problems related to Detect Squares

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