{
    "data": {
        "question": {
            "questionId": "1733",
            "questionFrontendId": "1610",
            "boundTopicId": null,
            "title": "Maximum Number of Visible Points",
            "titleSlug": "maximum-number-of-visible-points",
            "content": "<p>You are given an array <code>points</code>, an integer <code>angle</code>, and your <code>location</code>, where <code>location = [pos<sub>x</sub>, pos<sub>y</sub>]</code> and <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> both denote <strong>integral coordinates</strong> on the X-Y plane.</p>\n\n<p>Initially, you are facing directly east from your position. You <strong>cannot move</strong> from your position, but you can <strong>rotate</strong>. In other words, <code>pos<sub>x</sub></code> and <code>pos<sub>y</sub></code> cannot be changed. Your field of view in <strong>degrees</strong> is represented by <code>angle</code>, determining how wide you can see from any given view direction. Let <code>d</code> be the amount in degrees that you rotate counterclockwise. Then, your field of view is the <strong>inclusive</strong> range of angles <code>[d - angle/2, d + angle/2]</code>.</p>\n\n<p>\n<video autoplay=\"\" controls=\"\" height=\"360\" muted=\"\" style=\"max-width:100%;height:auto;\" width=\"480\"><source src=\"https://assets.leetcode.com/uploads/2020/09/30/angle.mp4\" type=\"video/mp4\" />Your browser does not support the video tag or this video format.</video>\n</p>\n\n<p>You can <strong>see</strong> some set of points if, for each point, the <strong>angle</strong> formed by the point, your position, and the immediate east direction from your position is <strong>in your field of view</strong>.</p>\n\n<p>There can be multiple points at one coordinate. There may be points at your location, and you can always see these points regardless of your rotation. Points do not obstruct your vision to other points.</p>\n\n<p>Return <em>the maximum number of points you can see</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/09/30/89a07e9b-00ab-4967-976a-c723b2aa8656.png\" style=\"width: 400px; height: 300px;\" />\n<pre>\n<strong>Input:</strong> points = [[2,1],[2,2],[3,3]], angle = 90, location = [1,1]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> The shaded region represents your field of view. All points can be made visible in your field of view, including [3,3] even though [2,2] is in front and in the same line of sight.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> points = [[2,1],[2,2],[3,4],[1,1]], angle = 90, location = [1,1]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> All points can be made visible in your field of view, including the one at your location.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/09/30/5010bfd3-86e6-465f-ac64-e9df941d2e49.png\" style=\"width: 690px; height: 348px;\" />\n<pre>\n<strong>Input:</strong> points = [[1,0],[2,1]], angle = 13, location = [1,1]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> You can only see one of the two points, as shown above.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= points.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>points[i].length == 2</code></li>\n\t<li><code>location.length == 2</code></li>\n\t<li><code>0 &lt;= angle &lt; 360</code></li>\n\t<li><code>0 &lt;= pos<sub>x</sub>, pos<sub>y</sub>, x<sub>i</sub>, y<sub>i</sub> &lt;= 100</code></li>\n</ul>\n",
            "translatedTitle": null,
            "translatedContent": null,
            "isPaidOnly": false,
            "difficulty": "Hard",
            "likes": 358,
            "dislikes": 485,
            "isLiked": null,
            "similarQuestions": "[]",
            "exampleTestcases": "[[2,1],[2,2],[3,3]]\n90\n[1,1]\n[[2,1],[2,2],[3,4],[1,1]]\n90\n[1,1]\n[[1,0],[2,1]]\n13\n[1,1]",
            "categoryTitle": "Algorithms",
            "contributors": [],
            "topicTags": [
                {
                    "name": "Array",
                    "slug": "array",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                },
                {
                    "name": "Math",
                    "slug": "math",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                },
                {
                    "name": "Geometry",
                    "slug": "geometry",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                },
                {
                    "name": "Sliding Window",
                    "slug": "sliding-window",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                },
                {
                    "name": "Sorting",
                    "slug": "sorting",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                }
            ],
            "companyTagStats": null,
            "codeSnippets": [
                {
                    "lang": "C++",
                    "langSlug": "cpp",
                    "code": "class Solution {\npublic:\n    int visiblePoints(vector<vector<int>>& points, int angle, vector<int>& location) {\n        \n    }\n};",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Java",
                    "langSlug": "java",
                    "code": "class Solution {\n    public int visiblePoints(List<List<Integer>> points, int angle, List<Integer> location) {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Python",
                    "langSlug": "python",
                    "code": "class Solution(object):\n    def visiblePoints(self, points, angle, location):\n        \"\"\"\n        :type points: List[List[int]]\n        :type angle: int\n        :type location: List[int]\n        :rtype: int\n        \"\"\"\n        ",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Python3",
                    "langSlug": "python3",
                    "code": "class Solution:\n    def visiblePoints(self, points: List[List[int]], angle: int, location: List[int]) -> int:\n        ",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "C",
                    "langSlug": "c",
                    "code": "\n\nint visiblePoints(int** points, int pointsSize, int* pointsColSize, int angle, int* location, int locationSize){\n\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "C#",
                    "langSlug": "csharp",
                    "code": "public class Solution {\n    public int VisiblePoints(IList<IList<int>> points, int angle, IList<int> location) {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "JavaScript",
                    "langSlug": "javascript",
                    "code": "/**\n * @param {number[][]} points\n * @param {number} angle\n * @param {number[]} location\n * @return {number}\n */\nvar visiblePoints = function(points, angle, location) {\n    \n};",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Ruby",
                    "langSlug": "ruby",
                    "code": "# @param {Integer[][]} points\n# @param {Integer} angle\n# @param {Integer[]} location\n# @return {Integer}\ndef visible_points(points, angle, location)\n    \nend",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Swift",
                    "langSlug": "swift",
                    "code": "class Solution {\n    func visiblePoints(_ points: [[Int]], _ angle: Int, _ location: [Int]) -> Int {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Go",
                    "langSlug": "golang",
                    "code": "func visiblePoints(points [][]int, angle int, location []int) int {\n    \n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Scala",
                    "langSlug": "scala",
                    "code": "object Solution {\n    def visiblePoints(points: List[List[Int]], angle: Int, location: List[Int]): Int = {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Kotlin",
                    "langSlug": "kotlin",
                    "code": "class Solution {\n    fun visiblePoints(points: List<List<Int>>, angle: Int, location: List<Int>): Int {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Rust",
                    "langSlug": "rust",
                    "code": "impl Solution {\n    pub fn visible_points(points: Vec<Vec<i32>>, angle: i32, location: Vec<i32>) -> i32 {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "PHP",
                    "langSlug": "php",
                    "code": "class Solution {\n\n    /**\n     * @param Integer[][] $points\n     * @param Integer $angle\n     * @param Integer[] $location\n     * @return Integer\n     */\n    function visiblePoints($points, $angle, $location) {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "TypeScript",
                    "langSlug": "typescript",
                    "code": "function visiblePoints(points: number[][], angle: number, location: number[]): number {\n\n};",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Racket",
                    "langSlug": "racket",
                    "code": "(define/contract (visible-points points angle location)\n  (-> (listof (listof exact-integer?)) exact-integer? (listof exact-integer?) exact-integer?)\n\n  )",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Erlang",
                    "langSlug": "erlang",
                    "code": "-spec visible_points(Points :: [[integer()]], Angle :: integer(), Location :: [integer()]) -> integer().\nvisible_points(Points, Angle, Location) ->\n  .",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Elixir",
                    "langSlug": "elixir",
                    "code": "defmodule Solution do\n  @spec visible_points(points :: [[integer]], angle :: integer, location :: [integer]) :: integer\n  def visible_points(points, angle, location) do\n\n  end\nend",
                    "__typename": "CodeSnippetNode"
                }
            ],
            "stats": "{\"totalAccepted\": \"24.4K\", \"totalSubmission\": \"67.3K\", \"totalAcceptedRaw\": 24391, \"totalSubmissionRaw\": 67252, \"acRate\": \"36.3%\"}",
            "hints": [
                "Sort the points by polar angle with the original position. Now only a consecutive collection of points would be visible from any coordinate.",
                "We can use two pointers to keep track of visible points for each start point",
                "For handling the cyclic condition, it’d be helpful to append the point list to itself after sorting."
            ],
            "solution": null,
            "status": null,
            "sampleTestCase": "[[2,1],[2,2],[3,3]]\n90\n[1,1]",
            "metaData": "{\n  \"name\": \"visiblePoints\",\n  \"params\": [\n    {\n      \"name\": \"points\",\n      \"type\": \"list<list<integer>>\"\n    },\n    {\n      \"type\": \"integer\",\n      \"name\": \"angle\"\n    },\n    {\n      \"type\": \"list<integer>\",\n      \"name\": \"location\"\n    }\n  ],\n  \"return\": {\n    \"type\": \"integer\"\n  }\n}",
            "judgerAvailable": true,
            "judgeType": "large",
            "mysqlSchemas": [],
            "enableRunCode": true,
            "enableTestMode": false,
            "enableDebugger": true,
            "envInfo": "{\"cpp\": [\"C++\", \"<p>Compiled with <code> clang 11 </code> using the latest C++ 17 standard.</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 17 </code>. 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. 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://docs.microsoft.com/en-us/dotnet/csharp/whats-new/csharp-9\\\" target=\\\"_blank\\\">C# 10 with .NET 6 runtime</a></p>\\r\\n\\r\\n<p>Your code is compiled with debug flag enabled (<code>/debug</code>).</p>\"], \"javascript\": [\"JavaScript\", \"<p><code>Node.js 16.13.2</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 <a href=\\\"https://github.com/datastructures-js/priority-queue\\\" target=\\\"_blank\\\">datastructures-js/priority-queue</a> and <a href=\\\"https://github.com/datastructures-js/queue\\\" target=\\\"_blank\\\">datastructures-js/queue</a>.</p>\"], \"ruby\": [\"Ruby\", \"<p><code>Ruby 3.1</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 5.5.2</code>.</p>\"], \"golang\": [\"Go\", \"<p><code>Go 1.17.6</code>.</p>\\r\\n\\r\\n<p>Support <a href=\\\"https://godoc.org/github.com/emirpasic/gods\\\" target=\\\"_blank\\\">https://godoc.org/github.com/emirpasic/gods</a> library.</p>\"], \"python3\": [\"Python3\", \"<p><code>Python 3.10</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 2.13.7</code>.</p>\"], \"kotlin\": [\"Kotlin\", \"<p><code>Kotlin 1.3.10</code>.</p>\"], \"rust\": [\"Rust\", \"<p><code>Rust 1.58.1</code></p>\\r\\n\\r\\n<p>Supports <a href=\\\"https://crates.io/crates/rand\\\" target=\\\"_blank\\\">rand </a> v0.6\\u00a0from crates.io</p>\"], \"php\": [\"PHP\", \"<p><code>PHP 8.1</code>.</p>\\r\\n<p>With bcmath module</p>\"], \"typescript\": [\"Typescript\", \"<p><code>TypeScript 4.5.4, Node.js 16.13.2</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 ES2020 features</a>.</p>\\r\\n\\r\\n<p><a href=\\\"https://lodash.com\\\" target=\\\"_blank\\\">lodash.js</a> library is included by default.</p>\"], \"racket\": [\"Racket\", \"<p>Run with <code>Racket 8.3</code>.</p>\"], \"erlang\": [\"Erlang\", \"Erlang/OTP 24.2\"], \"elixir\": [\"Elixir\", \"Elixir 1.13.0 with Erlang/OTP 24.2\"]}",
            "libraryUrl": null,
            "adminUrl": null,
            "challengeQuestion": null,
            "__typename": "QuestionNode"
        }
    }
}