2013 - Detect Squares.

Medium

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.