2013. Detect Squares

Description

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.

 

Solutions

Solution: Hash Table

• Time complexity: O(n)
• Space complexity: O(n)

 

JavaScript

const DetectSquares = function () {
  this.coordinateMap = new Map();
};

/**
 * @param {number[]} point
 * @return {void}
 */
DetectSquares.prototype.add = function (point) {
  const [x, y] = point;
  const key = `${x},${y}`;
  const coordinate = this.coordinateMap.get(key) ?? { point, count: 0 };

  coordinate.count += 1;
  this.coordinateMap.set(key, coordinate);
};

/**
 * @param {number[]} point
 * @return {number}
 */
DetectSquares.prototype.count = function (point) {
  const [px, py] = point;
  let result = 0;

  for (const { point: coordinate, count } of this.coordinateMap.values()) {
    const [x, y] = coordinate;

    if (px === x || py === y) continue;
    if (Math.abs(px - x) !== Math.abs(py - y)) continue;
    const a = this.coordinateMap.get(`${px},${y}`)?.count ?? 0;
    const b = this.coordinateMap.get(`${x},${py}`)?.count ?? 0;

    result += a * b * count;
  }
  return result;
};

/**
 * Your DetectSquares object will be instantiated and called as such:
 * var obj = new DetectSquares()
 * obj.add(point)
 * var param_2 = obj.count(point)
 */