Detect Squares
<p>You are given a stream of points on the X-Y plane. Design an algorithm that:</p>

<ul>
	<li><strong>Adds</strong> new points from the stream into a data structure. <strong>Duplicate</strong> points are allowed and should be treated as different points.</li>
	<li>Given a query point, <strong>counts</strong> the number of ways to choose three points from the data structure such that the three points and the query point form an <strong>axis-aligned square</strong> with <strong>positive area</strong>.</li>
</ul>

<p>An <strong>axis-aligned square</strong> is a square whose edges are all the same length and are either parallel or perpendicular to the x-axis and y-axis.</p>

<p>Implement the <code>DetectSquares</code> class:</p>

<ul>
	<li><code>DetectSquares()</code> Initializes the object with an empty data structure.</li>
	<li><code>void add(int[] point)</code> Adds a new point <code>point = [x, y]</code> to the data structure.</li>
	<li><code>int count(int[] point)</code> Counts the number of ways to form <strong>axis-aligned squares</strong> with point <code>point = [x, y]</code> as described above.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/09/01/image.png" style="width: 869px; height: 504px;" />
<pre>
<strong>Input</strong>
[&quot;DetectSquares&quot;, &quot;add&quot;, &quot;add&quot;, &quot;add&quot;, &quot;count&quot;, &quot;count&quot;, &quot;add&quot;, &quot;count&quot;]
[[], [[3, 10]], [[11, 2]], [[3, 2]], [[11, 10]], [[14, 8]], [[11, 2]], [[11, 10]]]
<strong>Output</strong>
[null, null, null, null, 1, 0, null, 2]

<strong>Explanation</strong>
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
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>point.length == 2</code></li>
	<li><code>0 &lt;= x, y &lt;= 1000</code></li>
	<li>At most <code>3000</code> calls <strong>in total</strong> will be made to <code>add</code> and <code>count</code>.</li>
</ul>

[]
[]
[{"value": "cpp", "text": "C++", "defaultCode": "class DetectSquares {\npublic:\n    DetectSquares() {\n        \n    }\n    \n    void add(vector<int> point) {\n        \n    }\n    \n    int count(vector<int> point) {\n        \n    }\n};\n\n/**\n * Your DetectSquares object will be instantiated and called as such:\n * DetectSquares* obj = new DetectSquares();\n * obj->add(point);\n * int param_2 = obj->count(point);\n */"}, {"value": "java", "text": "Java", "defaultCode": "class DetectSquares {\n\n    public DetectSquares() {\n        \n    }\n    \n    public void add(int[] point) {\n        \n    }\n    \n    public int count(int[] point) {\n        \n    }\n}\n\n/**\n * Your DetectSquares object will be instantiated and called as such:\n * DetectSquares obj = new DetectSquares();\n * obj.add(point);\n * int param_2 = obj.count(point);\n */"}, {"value": "python", "text": "Python", "defaultCode": "class DetectSquares(object):\n\n    def __init__(self):\n        \n\n    def add(self, point):\n        \"\"\"\n        :type point: List[int]\n        :rtype: None\n        \"\"\"\n        \n\n    def count(self, point):\n        \"\"\"\n        :type point: List[int]\n        :rtype: int\n        \"\"\"\n        \n\n\n# Your DetectSquares object will be instantiated and called as such:\n# obj = DetectSquares()\n# obj.add(point)\n# param_2 = obj.count(point)"}, {"value": "python3", "text": "Python3", "defaultCode": "class DetectSquares:\n\n    def __init__(self):\n        \n\n    def add(self, point: List[int]) -> None:\n        \n\n    def count(self, point: List[int]) -> int:\n        \n\n\n# Your DetectSquares object will be instantiated and called as such:\n# obj = DetectSquares()\n# obj.add(point)\n# param_2 = obj.count(point)"}, {"value": "c", "text": "C", "defaultCode": "\n\n\ntypedef struct {\n    \n} DetectSquares;\n\n\nDetectSquares* detectSquaresCreate() {\n    \n}\n\nvoid detectSquaresAdd(DetectSquares* obj, int* point, int pointSize) {\n    \n}\n\nint detectSquaresCount(DetectSquares* obj, int* point, int pointSize) {\n    \n}\n\nvoid detectSquaresFree(DetectSquares* obj) {\n    \n}\n\n/**\n * Your DetectSquares struct will be instantiated and called as such:\n * DetectSquares* obj = detectSquaresCreate();\n * detectSquaresAdd(obj, point, pointSize);\n \n * int param_2 = detectSquaresCount(obj, point, pointSize);\n \n * detectSquaresFree(obj);\n*/"}, {"value": "csharp", "text": "C#", "defaultCode": "public class DetectSquares {\n\n    public DetectSquares() {\n        \n    }\n    \n    public void Add(int[] point) {\n        \n    }\n    \n    public int Count(int[] point) {\n        \n    }\n}\n\n/**\n * Your DetectSquares object will be instantiated and called as such:\n * DetectSquares obj = new DetectSquares();\n * obj.Add(point);\n * int param_2 = obj.Count(point);\n */"}, {"value": "javascript", "text": "JavaScript", "defaultCode": "\nvar DetectSquares = function() {\n    \n};\n\n/** \n * @param {number[]} point\n * @return {void}\n */\nDetectSquares.prototype.add = function(point) {\n    \n};\n\n/** \n * @param {number[]} point\n * @return {number}\n */\nDetectSquares.prototype.count = function(point) {\n    \n};\n\n/** \n * Your DetectSquares object will be instantiated and called as such:\n * var obj = new DetectSquares()\n * obj.add(point)\n * var param_2 = obj.count(point)\n */"}, {"value": "typescript", "text": "TypeScript", "defaultCode": "class DetectSquares {\n    constructor() {\n        \n    }\n\n    add(point: number[]): void {\n        \n    }\n\n    count(point: number[]): number {\n        \n    }\n}\n\n/**\n * Your DetectSquares object will be instantiated and called as such:\n * var obj = new DetectSquares()\n * obj.add(point)\n * var param_2 = obj.count(point)\n */"}, {"value": "php", "text": "PHP", "defaultCode": "class DetectSquares {\n    /**\n     */\n    function __construct() {\n        \n    }\n  \n    /**\n     * @param Integer[] $point\n     * @return NULL\n     */\n    function add($point) {\n        \n    }\n  \n    /**\n     * @param Integer[] $point\n     * @return Integer\n     */\n    function count($point) {\n        \n    }\n}\n\n/**\n * Your DetectSquares object will be instantiated and called as such:\n * $obj = DetectSquares();\n * $obj->add($point);\n * $ret_2 = $obj->count($point);\n */"}, {"value": "swift", "text": "Swift", "defaultCode": "\nclass DetectSquares {\n\n    init() {\n        \n    }\n    \n    func add(_ point: [Int]) {\n        \n    }\n    \n    func count(_ point: [Int]) -> Int {\n        \n    }\n}\n\n/**\n * Your DetectSquares object will be instantiated and called as such:\n * let obj = DetectSquares()\n * obj.add(point)\n * let ret_2: Int = obj.count(point)\n */"}, {"value": "kotlin", "text": "Kotlin", "defaultCode": "class DetectSquares() {\n\n    fun add(point: IntArray) {\n        \n    }\n\n    fun count(point: IntArray): Int {\n        \n    }\n\n}\n\n/**\n * Your DetectSquares object will be instantiated and called as such:\n * var obj = DetectSquares()\n * obj.add(point)\n * var param_2 = obj.count(point)\n */"}, {"value": "dart", "text": "Dart", "defaultCode": "class DetectSquares {\n\n  DetectSquares() {\n    \n  }\n  \n  void add(List<int> point) {\n    \n  }\n  \n  int count(List<int> point) {\n    \n  }\n}\n\n/**\n * Your DetectSquares object will be instantiated and called as such:\n * DetectSquares obj = DetectSquares();\n * obj.add(point);\n * int param2 = obj.count(point);\n */"}, {"value": "golang", "text": "Go", "defaultCode": "type DetectSquares struct {\n    \n}\n\n\nfunc Constructor() DetectSquares {\n    \n}\n\n\nfunc (this *DetectSquares) Add(point []int)  {\n    \n}\n\n\nfunc (this *DetectSquares) Count(point []int) int {\n    \n}\n\n\n/**\n * Your DetectSquares object will be instantiated and called as such:\n * obj := Constructor();\n * obj.Add(point);\n * param_2 := obj.Count(point);\n */"}, {"value": "ruby", "text": "Ruby", "defaultCode": "class DetectSquares\n    def initialize()\n        \n    end\n\n\n=begin\n    :type point: Integer[]\n    :rtype: Void\n=end\n    def add(point)\n        \n    end\n\n\n=begin\n    :type point: Integer[]\n    :rtype: Integer\n=end\n    def count(point)\n        \n    end\n\n\nend\n\n# Your DetectSquares object will be instantiated and called as such:\n# obj = DetectSquares.new()\n# obj.add(point)\n# param_2 = obj.count(point)"}, {"value": "scala", "text": "Scala", "defaultCode": "class DetectSquares() {\n\n    def add(point: Array[Int]): Unit = {\n        \n    }\n\n    def count(point: Array[Int]): Int = {\n        \n    }\n\n}\n\n/**\n * Your DetectSquares object will be instantiated and called as such:\n * val obj = new DetectSquares()\n * obj.add(point)\n * val param_2 = obj.count(point)\n */"}, {"value": "rust", "text": "Rust", "defaultCode": "struct DetectSquares {\n\n}\n\n\n/** \n * `&self` means the method takes an immutable reference.\n * If you need a mutable reference, change it to `&mut self` instead.\n */\nimpl DetectSquares {\n\n    fn new() -> Self {\n        \n    }\n    \n    fn add(&self, point: Vec<i32>) {\n        \n    }\n    \n    fn count(&self, point: Vec<i32>) -> i32 {\n        \n    }\n}\n\n/**\n * Your DetectSquares object will be instantiated and called as such:\n * let obj = DetectSquares::new();\n * obj.add(point);\n * let ret_2: i32 = obj.count(point);\n */"}, {"value": "racket", "text": "Racket", "defaultCode": "(define detect-squares%\n  (class object%\n    (super-new)\n    \n    (init-field)\n    \n    ; add : (listof exact-integer?) -> void?\n    (define/public (add point)\n      )\n    ; count : (listof exact-integer?) -> exact-integer?\n    (define/public (count point)\n      )))\n\n;; Your detect-squares% object will be instantiated and called as such:\n;; (define obj (new detect-squares%))\n;; (send obj add point)\n;; (define param_2 (send obj count point))"}, {"value": "erlang", "text": "Erlang", "defaultCode": "-spec detect_squares_init_() -> any().\ndetect_squares_init_() ->\n  .\n\n-spec detect_squares_add(Point :: [integer()]) -> any().\ndetect_squares_add(Point) ->\n  .\n\n-spec detect_squares_count(Point :: [integer()]) -> integer().\ndetect_squares_count(Point) ->\n  .\n\n\n%% Your functions will be called as such:\n%% detect_squares_init_(),\n%% detect_squares_add(Point),\n%% Param_2 = detect_squares_count(Point),\n\n%% detect_squares_init_ will be called before every test case, in which you can do some necessary initializations."}, {"value": "elixir", "text": "Elixir", "defaultCode": "defmodule DetectSquares do\n  @spec init_() :: any\n  def init_() do\n    \n  end\n\n  @spec add(point :: [integer]) :: any\n  def add(point) do\n    \n  end\n\n  @spec count(point :: [integer]) :: integer\n  def count(point) do\n    \n  end\nend\n\n# Your functions will be called as such:\n# DetectSquares.init_()\n# DetectSquares.add(point)\n# param_2 = DetectSquares.count(point)\n\n# DetectSquares.init_ will be called before every test case, in which you can do some necessary initializations."}]
{
  "classname": "DetectSquares",
  "constructor": {
    "params": []
  },
  "methods": [
    {
      "params": [
        {
          "type": "integer[]",
          "name": "point"
        }
      ],
      "name": "add",
      "return": {
        "type": "void"
      }
    },
    {
      "params": [
        {
          "type": "integer[]",
          "name": "point"
        }
      ],
      "name": "count",
      "return": {
        "type": "integer"
      }
    }
  ],
  "return": {
    "type": "boolean"
  },
  "systemdesign": true
}
{"cpp": ["C++", "<p>Compiled with <code> clang 19 </code> using the latest C++ 23 standard, and <code>libstdc++</code> provided by GCC 14.</p>\r\n\r\n<p>Your code is compiled with level two optimization (<code>-O2</code>). <a href=\"https://github.com/google/sanitizers/wiki/AddressSanitizer\" target=\"_blank\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\r\n\r\n<p>Most standard library headers are already included automatically for your convenience.</p>"], "java": ["Java", "<p><code>OpenJDK 21</code>. Using compile arguments: <code>--enable-preview --release 21</code></p>\r\n\r\n<p>Most standard library headers are already included automatically for your convenience.</p>\r\n<p>Includes <code>Pair</code> class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.</p>"], "python": ["Python", "<p><code>Python 2.7.18</code>.</p>\r\n\r\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\"https://docs.python.org/2/library/array.html\" target=\"_blank\">array</a>, <a href=\"https://docs.python.org/2/library/bisect.html\" target=\"_blank\">bisect</a>, <a href=\"https://docs.python.org/2/library/collections.html\" target=\"_blank\">collections</a>. If you need more libraries, you can import it yourself.</p>\r\n\r\n<p>For Map/TreeMap data structure, you may use <a href=\"http://www.grantjenks.com/docs/sortedcontainers/\" target=\"_blank\">sortedcontainers</a> library.</p>\r\n\r\n<p>Note that Python 2.7 <a href=\"https://www.python.org/dev/peps/pep-0373/\" target=\"_blank\">is not maintained anymore</a>. For the latest Python, please choose Python3 instead.</p>"], "c": ["C", "<p>Compiled with <code>gcc 14</code> using the gnu11 standard.</p>\r\n\r\n<p>Your code is compiled with level one optimization (<code>-O2</code>). <a href=\"https://github.com/google/sanitizers/wiki/AddressSanitizer\" target=\"_blank\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\r\n\r\n<p>Most standard library headers are already included automatically for your convenience.</p>\r\n\r\n<p>For hash table operations, you may use <a href=\"https://troydhanson.github.io/uthash/\" target=\"_blank\">uthash</a>. \"uthash.h\" is included by default. Below are some examples:</p>\r\n\r\n<p><b>1. Adding an item to a hash.</b>\r\n<pre>\r\nstruct hash_entry {\r\n    int id;            /* we'll use this field as the key */\r\n    char name[10];\r\n    UT_hash_handle hh; /* makes this structure hashable */\r\n};\r\n\r\nstruct hash_entry *users = NULL;\r\n\r\nvoid add_user(struct hash_entry *s) {\r\n    HASH_ADD_INT(users, id, s);\r\n}\r\n</pre>\r\n</p>\r\n\r\n<p><b>2. Looking up an item in a hash:</b>\r\n<pre>\r\nstruct hash_entry *find_user(int user_id) {\r\n    struct hash_entry *s;\r\n    HASH_FIND_INT(users, &user_id, s);\r\n    return s;\r\n}\r\n</pre>\r\n</p>\r\n\r\n<p><b>3. Deleting an item in a hash:</b>\r\n<pre>\r\nvoid delete_user(struct hash_entry *user) {\r\n    HASH_DEL(users, user);  \r\n}\r\n</pre>\r\n</p>"], "csharp": ["C#", "<p><a href=\"https://learn.microsoft.com/en-us/dotnet/csharp/whats-new/csharp-13\" target=\"_blank\">C# 13</a> with .NET 9 runtime</p>"], "javascript": ["JavaScript", "<p><code>Node.js 22.14.0</code>.</p>\r\n\r\n<p>Your code is run with <code>--harmony</code> flag, enabling <a href=\"http://node.green/\" target=\"_blank\">new ES6 features</a>.</p>\r\n\r\n<p><a href=\"https://lodash.com\" target=\"_blank\">lodash.js</a> library is included by default.</p>\r\n\r\n<p>For Priority Queue / Queue data structures, you may use 6.3.2 version of <a href=\"https://github.com/datastructures-js/priority-queue/tree/v6.3.2\" target=\"_blank\">datastructures-js/priority-queue</a> and 4.2.3 version of <a href=\"https://github.com/datastructures-js/queue/tree/v4.2.3\" target=\"_blank\">datastructures-js/queue</a> and 1.0.4 version of <a href=\"https://github.com/datastructures-js/deque/tree/v1.0.4\" target=\"_blank\">datastructures-js/deque</a>.</p>"], "ruby": ["Ruby", "<p><code>Ruby 3.2</code></p>\r\n\r\n<p>Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms</p>"], "swift": ["Swift", "<p><code>Swift 6.0</code>.</p>\r\n\r\n<p>You may use the following packages:<br/>\r\n<a href=\"https://github.com/apple/swift-algorithms/tree/1.2.0\" target=\"_blank\">swift-algorithms 1.2.0</a><br/>\r\n<a href=\"https://github.com/apple/swift-collections/tree/1.1.4\" target=\"_blank\">swift-collections 1.1.4</a><br/>\r\n<a href=\"https://github.com/apple/swift-numerics/tree/1.0.2\" target=\"_blank\">swift-numerics 1.0.2</a></p>"], "golang": ["Go", "<p><code>Go 1.23</code></p>\r\n<p>Support <a href=\"https://pkg.go.dev/github.com/emirpasic/gods@v1.18.1\" target=\"_blank\">https://pkg.go.dev/github.com/emirpasic/gods@v1.18.1</a> and <a href=\"https://pkg.go.dev/github.com/emirpasic/gods/v2@v2.0.0-alpha\" target=\"_blank\">https://pkg.go.dev/github.com/emirpasic/gods/v2@v2.0.0-alpha</a> library.</p>"], "python3": ["Python3", "<p><code>Python 3.11</code>.</p>\r\n\r\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\"https://docs.python.org/3/library/array.html\" target=\"_blank\">array</a>, <a href=\"https://docs.python.org/3/library/bisect.html\" target=\"_blank\">bisect</a>, <a href=\"https://docs.python.org/3/library/collections.html\" target=\"_blank\">collections</a>. If you need more libraries, you can import it yourself.</p>\r\n\r\n<p>For Map/TreeMap data structure, you may use <a href=\"http://www.grantjenks.com/docs/sortedcontainers/\" target=\"_blank\">sortedcontainers</a> library.</p>"], "scala": ["Scala", "<p><code>Scala 3.3.1</code>.</p>"], "kotlin": ["Kotlin", "<p><code>Kotlin 2.1.10</code>.</p>"], "rust": ["Rust", "<p><code>Rust 1.85.0</code>. Your code will be compiled with <code>opt-level</code> 2.</p>\r\n\r\n<p>Supports <a href=\"https://crates.io/crates/rand\" target=\"_blank\">rand v0.8</a> and <a href=\"https://crates.io/crates/regex\" target=\"_blank\">regex\u00a0v1</a> and <a href=\"https://crates.io/crates/itertools\" target=\"_blank\">itertools\u00a0v0.14</a> from crates.io</p>"], "php": ["PHP", "<p><code>PHP 8.2</code>.</p>\r\n<p>With bcmath module</p>"], "typescript": ["Typescript", "<p><code>TypeScript 5.7.3, Node.js 22.14.0</code>.</p>\r\n\r\n<p>Compile Options: <code>--alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2024</code></p>\r\n\r\n<p><a href=\"https://lodash.com\" target=\"_blank\">lodash.js</a> library is included by default.</p>\r\n\r\n<p>For Priority Queue / Queue data structures, you may use 6.3.2 version of <a href=\"https://github.com/datastructures-js/priority-queue/tree/v6.3.2\" target=\"_blank\">datastructures-js/priority-queue</a> and 4.2.3 version of <a href=\"https://github.com/datastructures-js/queue/tree/v4.2.3\" target=\"_blank\">datastructures-js/queue</a> and 1.0.4 version of <a href=\"https://github.com/datastructures-js/deque/tree/v1.0.4\" target=\"_blank\">datastructures-js/deque</a>.</p>"], "racket": ["Racket", "<p><a href=\"https://docs.racket-lang.org/guide/performance.html#%28tech._c%29\" target=\"_blank\">Racket CS</a> v8.15</p>\r\n\r\n<p>Using <code>#lang racket</code></p>\r\n\r\n<p>Required <code>data/gvector data/queue data/order data/heap</code> automatically for your convenience</p>"], "erlang": ["Erlang", "Erlang/OTP 26"], "elixir": ["Elixir", "Elixir 1.17 with Erlang/OTP 26"], "dart": ["Dart", "<p>Dart 3.2. You may use package <a href=\"https://pub.dev/packages/collection/versions/1.18.0\" target=\"_blank\">collection</a></p>\r\n\r\n<p>Your code will be run directly without compiling</p>"]}
['Array', 'Hash Table', 'Design', 'Counting']