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"questionId": "2139",
"questionFrontendId": "2013",
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"title": "Detect Squares",
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"content": "<p>You are given a stream of points on the X-Y plane. Design an algorithm that:</p>\n\n<ul>\n\t<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>\n\t<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>\n</ul>\n\n<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>\n\n<p>Implement the <code>DetectSquares</code> class:</p>\n\n<ul>\n\t<li><code>DetectSquares()</code> Initializes the object with an empty data structure.</li>\n\t<li><code>void add(int[] point)</code> Adds a new point <code>point = [x, y]</code> to the data structure.</li>\n\t<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>\n</ul>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/09/01/image.png\" style=\"width: 869px; height: 504px;\" />\n<pre>\n<strong>Input</strong>\n["DetectSquares", "add", "add", "add", "count", "count", "add", "count"]\n[[], [[3, 10]], [[11, 2]], [[3, 2]], [[11, 10]], [[14, 8]], [[11, 2]], [[11, 10]]]\n<strong>Output</strong>\n[null, null, null, null, 1, 0, null, 2]\n\n<strong>Explanation</strong>\nDetectSquares detectSquares = new DetectSquares();\ndetectSquares.add([3, 10]);\ndetectSquares.add([11, 2]);\ndetectSquares.add([3, 2]);\ndetectSquares.count([11, 10]); // return 1. You can choose:\n // - The first, second, and third points\ndetectSquares.count([14, 8]); // return 0. The query point cannot form a square with any points in the data structure.\ndetectSquares.add([11, 2]); // Adding duplicate points is allowed.\ndetectSquares.count([11, 10]); // return 2. You can choose:\n // - The first, second, and third points\n // - The first, third, and fourth points\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>point.length == 2</code></li>\n\t<li><code>0 <= x, y <= 1000</code></li>\n\t<li>At most <code>3000</code> calls <strong>in total</strong> will be made to <code>add</code> and <code>count</code>.</li>\n</ul>\n",
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"lang": "C++",
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"code": "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 */",
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"lang": "Java",
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"code": "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 */",
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"lang": "Python",
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"code": "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)",
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"lang": "Python3",
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"code": "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)",
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"lang": "C",
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"code": "\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*/",
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"lang": "C#",
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"code": "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 */",
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"code": "\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 */",
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"lang": "Ruby",
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"code": "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)",
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"lang": "Swift",
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"code": "\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 */",
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"lang": "Go",
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"code": "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 */",
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"lang": "Scala",
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"code": "class DetectSquares() {\n\n def add(point: Array[Int]) {\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 * var obj = new DetectSquares()\n * obj.add(point)\n * var param_2 = obj.count(point)\n */",
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"lang": "Kotlin",
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"code": "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 */",
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"lang": "Rust",
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"code": "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 */",
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"lang": "PHP",
"langSlug": "php",
"code": "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 */",
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"lang": "TypeScript",
"langSlug": "typescript",
"code": "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 */",
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"lang": "Racket",
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"code": "(define detect-squares%\n (class object%\n (super-new)\n (init-field)\n \n ; add : (listof exact-integer?) -> void?\n (define/public (add point)\n\n )\n ; count : (listof exact-integer?) -> exact-integer?\n (define/public (count point)\n\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))",
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"lang": "Erlang",
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"code": "-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.",
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"lang": "Elixir",
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"code": "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.",
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"hints": [
"Maintain the frequency of all the points in a hash map.",
"Traverse the hash map and if any point has the same y-coordinate as the query point, consider this point and the query point to form one of the horizontal lines of the square."
],
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"sampleTestCase": "[\"DetectSquares\",\"add\",\"add\",\"add\",\"count\",\"count\",\"add\",\"count\"]\n[[],[[3,10]],[[11,2]],[[3,2]],[[11,10]],[[14,8]],[[11,2]],[[11,10]]]",
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Java 8 features such as lambda expressions and stream API can be used. </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 2.7.12</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\\\">will not be maintained past 2020</a>. For the latest Python, please choose Python3 instead.</p>\"], \"c\": [\"C\", \"<p>Compiled with <code>gcc 8.2</code> using the gnu99 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level one optimization (<code>-O1</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. 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