:orphan:

Detect Squares
==============

.. highlight:: none

Problem
-------
https://leetcode.com/problems/detect-squares/

You are given a stream of points on the X-Y plane. Design a data
structure 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.



**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]



**Constraints:**

- ``point.length == 2``
- ``0 <= x, y <= 1000``
- At most ``3000`` calls in total will be made to ``add`` and ``count``.

.. highlight:: python

Pattern
-------
Hash Table, Math

Approaches
----------

.. tab-set::

    .. tab-item:: Hash Map

        **Code**

        .. literalinclude:: ../problems/medium/detect-squares/detect_squares__hash_map.py
            :language: python
            :lines: 16-

        **Test**

        >>> from detect_squares__hash_map import DetectSquares
        >>> ds = DetectSquares()
        >>> ds.add([3, 10])
        >>> ds.add([11, 2])
        >>> ds.add([3, 2])
        >>> ds.count([11, 10])
        1
        >>> ds.count([14, 8])
        0
        >>> ds.add([11, 2])
        >>> ds.count([11, 10])
        2

        .. autoclass:: detect_squares__hash_map.DetectSquares
           :members:
           :show-inheritance:
           :undoc-members: