Package g2001_2100.s2013_detect_squares

Class DetectSquares

  • public class DetectSquares
extends Object
    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.

    • Constructor Detail

      • DetectSquares

        public DetectSquares()

    • Method Detail

      • add

        public void add​(int[] point)

      • count

        public int count​(int[] point)