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2013. Detect Squares

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 (Rust)

1. Solution

use std::collections::HashMap;structDetectSquares{points:HashMap<(i32,i32),i32>,diagonals:HashMap<(i32,i32),Vec<(i32,i32)>>,}/** * `&self` means the method takes an immutable reference. * If you need a mutable reference, change it to `&mut self` instead. */implDetectSquares{fnnew() -> Self{Self{points:HashMap::new(),diagonals:HashMap::new(),}}fnadd(&mutself,point:Vec<i32>){let(x, y) = (point[0], point[1]);*self.points.entry((x, y)).or_insert(0) += 1;self.diagonals.entry((1, y - x)).or_insert(vec![]).push((x, y));self.diagonals.entry((-1, y + x)).or_insert(vec![]).push((x, y));}fncount(&self,point:Vec<i32>) -> i32{let(x0, y0) = (point[0], point[1]);letmut ret = 0;for&(x1, y1)inself.diagonals.get(&(1, y0 - x0)).unwrap_or(&vec![]){if x1 == x0 {continue;}let count0 = *self.points.get(&(x0, y1)).unwrap_or(&0);let count1 = *self.points.get(&(x1, y0)).unwrap_or(&0); ret += count0 * count1;}for&(x1, y1)inself.diagonals.get(&(-1, y0 + x0)).unwrap_or(&vec![]){if x1 == x0 {continue;}let count0 = *self.points.get(&(x0, y1)).unwrap_or(&0);let count1 = *self.points.get(&(x1, y0)).unwrap_or(&0); ret += count0 * count1;} ret }}/** * Your DetectSquares object will be instantiated and called as such: * let obj = DetectSquares::new(); * obj.add(point); * let ret_2: i32 = obj.count(point); */
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