2013. Detect Squares

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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:

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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.

Hints/Notes

  • 2024/12/26
  • hashmap
  • No solution from 0x3F

Solution

Language: C++

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class DetectSquares {
public:
    unordered_map<int, unordered_map<int, int>> cols, rows;
    unordered_map<int, int> m;

    DetectSquares() {
    }

    void add(vector<int> point) {
        int i = point[0], j = point[1];
        cols[i][j]++;
        rows[j][i]++;
        m[encode(i, j)]++;
    }

    int count(vector<int> point) {
        int i = point[0], j = point[1], res = 0;
        for (auto& [row, v1] : cols[i]) {
            if (row == j) {
                continue;
            }
            for (auto& [col, v2] : rows[j]) {
                if (col == i) {
                    continue;
                }
                if (abs(row - j) == abs(i - col)) {
                    res += m[encode(col, row)] * v1 * v2;
                }
            }
        }
        return res;
    }


    int encode(int x, int y) {
        return x * 1000 + y;
    }


};

/**
 * Your DetectSquares object will be instantiated and called as such:
 * DetectSquares* obj = new DetectSquares();
 * obj->add(point);
 * int param_2 = obj->count(point);
 */