{ "data": { "question": { "questionId": "1000147", "questionFrontendId": "LCP 27", "categoryTitle": "Algorithms", "boundTopicId": 401338, "title": "黑盒光线反射", "titleSlug": "IQvJ9i", "content": "English description is not available for the problem. Please switch to Chinese.", "translatedTitle": "黑盒光线反射", "translatedContent": "秋日市集上有个奇怪的黑盒，黑盒的主视图为 n\\*m 的矩形。从黑盒的主视图来看，黑盒的上面和下面各均匀分布有 m 个小孔，黑盒的左面和右面各均匀分布有 n 个小孔。黑盒左上角小孔序号为 0，按顺时针编号，总共有 2*(m+n) 个小孔。每个小孔均可以打开或者关闭，初始时，所有小孔均处于关闭状态。每个小孔上的盖子均为镜面材质。例如一个 2\\*3 的黑盒主视图与其小孔分布如图所示:\n\n![image.png](https://pic.leetcode-cn.com/1598951281-ZCBrif-image.png){:height=\"200px\"}\n\n店长告诉小扣，这里是「几何学的快问快答」，店长可能有两种操作：\n\n- `open(int index, int direction)` - 若小孔处于关闭状态，则打开小孔，照入光线；否则直接照入光线；\n- `close(int index)` - 关闭处于打开状态小孔，店长保证不会关闭已处于关闭状态的小孔；\n\n其中：\n- `index`： 表示小孔序号\n- `direction`：`1` 表示光线沿 $y=x$ 方向，`-1` 表示光线沿 $y=-x$ 方向。\n\n![image.png](https://pic.leetcode-cn.com/1599620810-HdOlMi-image.png){:height=\"200px\"}\n\n\n当光线照至边界时：若边界上的小孔为开启状态，则光线会射出；否则，光线会在小孔之间进行反射。特别地：\n1. 若光线射向未打开的拐角（黑盒顶点），则光线会原路反射回去；\n2. 光线自拐角处的小孔照入时，只有一种入射方向（如自序号为 0 的小孔照入方向只能为 `-1`）\n\n![image.png](https://pic.leetcode-cn.com/1598953840-DLiAsf-image.png){:height=\"200px\"}\n\n请帮助小扣判断并返回店长每次照入的光线从几号小孔射出。\n\n\n**示例 1：**\n>输入：\n>`[\"BlackBox\",\"open\",\"open\",\"open\",\"close\",\"open\"]`\n>`[[2,3],[6,-1],[4,-1],[0,-1],[6],[0,-1]]`\n>\n>输出：`[null,6,4,6,null,4]`\n>\n>解释：\n>BlackBox b = BlackBox(2,3); // 新建一个 2x3 的黑盒\n>b.open(6,-1) // 打开 6 号小孔，并沿 y=-x 方向照入光线，光线至 0 号小孔反射，从 6 号小孔射出\n>b.open(4,-1) // 打开 4 号小孔，并沿 y=-x 方向照入光线，光线轨迹为 4-2-8-2-4，从 4 号小孔射出\n>b.open(0,-1) // 打开 0 号小孔，并沿 y=-x 方向照入光线，由于 6 号小孔为开启状态，光线从 6 号小孔射出\n>b.close(6) // 关闭 6 号小孔\n>b.shoot(0,-1) // 从 0 号小孔沿 y=-x 方向照入光线，由于 6 号小孔为关闭状态，4 号小孔为开启状态，光线轨迹为 0-6-4，从 4 号小孔射出\n\n**示例 2：**\n>输入：\n>`[\"BlackBox\",\"open\",\"open\",\"open\",\"open\",\"close\",\"open\",\"close\",\"open\"]`\n>`[[3,3],[1,-1],[5,1],[11,-1],[11,1],[1],[11,1],[5],[11,-1]]`\n>\n>输出：`[null,1,1,5,1,null,5,null,11]`\n>\n>解释：\n>\n>![image.png](https://pic.leetcode-cn.com/1599204202-yGDMVk-image.png){:height=\"300px\"}\n>\n>BlackBox b = BlackBox(3,3); // 新建一个 3x3 的黑盒\n>b.open(1,-1) // 打开 1 号小孔，并沿 y=-x 方向照入光线，光线轨迹为 1-5-7-11-1，从 1 号小孔射出\n>b.open(5,1) // 打开 5 号小孔，并沿 y=x 方向照入光线，光线轨迹为 5-7-11-1，从 1 号小孔射出\n>b.open(11,-1) // 打开 11 号小孔，并沿逆 y=-x 方向照入光线，光线轨迹为 11-7-5，从 5 号小孔射出\n>b.open(11,1) // 从 11 号小孔沿 y=x 方向照入光线，光线轨迹为 11-1，从 1 号小孔射出\n>b.close(1) // 关闭 1 号小孔\n>b.open(11,1) // 从 11 号小孔沿 y=x 方向照入光线，光线轨迹为 11-1-5，从 5 号小孔射出\n>b.close(5) // 关闭 5 号小孔\n>b.open(11,-1) // 从 11 号小孔沿 y=-x 方向照入光线，光线轨迹为 11-1-5-7-11，从 11 号小孔射出\n\n\n\n**提示：**\n- `1 <= n, m <= 10000`\n- `1 <= 操作次数 <= 10000`\n- `direction` 仅为 `1` 或 `-1`\n- `0 <= index < 2*(m+n)`\n", "isPaidOnly": false, "difficulty": "Hard", "likes": 20, "dislikes": 0, "isLiked": null, "similarQuestions": "[]", "contributors": [ { "username": "LeetCode", "profileUrl": "/u/leetcode", "avatarUrl": "https://assets.leetcode.cn/aliyun-lc-upload/uploaded_files/2021/03/73c9f099-abbe-4d94-853f-f8abffd459cd/leetcode.png", "__typename": "ContributorNode" } ], "langToValidPlayground": "{\"cpp\": false, \"java\": false, \"python\": false, \"python3\": false, \"mysql\": false, \"mssql\": false, \"oraclesql\": false, \"c\": false, \"csharp\": false, \"javascript\": false, \"typescript\": false, \"bash\": false, \"php\": false, \"swift\": false, \"kotlin\": false, \"dart\": false, \"golang\": false, \"ruby\": false, \"scala\": false, \"html\": false, \"pythonml\": false, \"rust\": false, \"racket\": false, \"erlang\": false, \"elixir\": false, \"pythondata\": false, \"react\": false, \"vanillajs\": false, \"postgresql\": false}", "topicTags": [ { "name": "Design", "slug": "design", "translatedName": "设计", "__typename": "TopicTagNode" }, { "name": "Segment Tree", "slug": "segment-tree", "translatedName": "线段树", "__typename": "TopicTagNode" }, { "name": "Math", "slug": "math", "translatedName": "数学", "__typename": "TopicTagNode" }, { "name": "Ordered Set", "slug": "ordered-set", "translatedName": "有序集合", "__typename": "TopicTagNode" } ], "companyTagStats": null, "codeSnippets": [ { "lang": "C++", "langSlug": "cpp", "code": "class BlackBox {\npublic:\n BlackBox(int n, int m) {\n\n }\n \n int open(int index, int direction) {\n\n }\n \n void close(int index) {\n\n }\n};\n\n/**\n * Your BlackBox object will be instantiated and called as such:\n * BlackBox* obj = new BlackBox(n, m);\n * int param_1 = obj->open(index,direction);\n * obj->close(index);\n */", "__typename": "CodeSnippetNode" }, { "lang": "Java", "langSlug": "java", "code": "class BlackBox {\n\n public BlackBox(int n, int m) {\n\n }\n \n public int open(int index, int direction) {\n\n }\n \n public void close(int index) {\n\n }\n}\n\n/**\n * Your BlackBox object will be instantiated and called as such:\n * BlackBox obj = new BlackBox(n, m);\n * int param_1 = obj.open(index,direction);\n * obj.close(index);\n */", "__typename": "CodeSnippetNode" }, { "lang": "Python", "langSlug": "python", "code": "class BlackBox(object):\n\n def __init__(self, n, m):\n \"\"\"\n :type n: int\n :type m: int\n \"\"\"\n\n\n def open(self, index, direction):\n \"\"\"\n :type index: int\n :type direction: int\n :rtype: int\n \"\"\"\n\n\n def close(self, index):\n \"\"\"\n :type index: int\n :rtype: None\n \"\"\"\n\n\n\n# Your BlackBox object will be instantiated and called as such:\n# obj = BlackBox(n, m)\n# param_1 = obj.open(index,direction)\n# obj.close(index)", "__typename": "CodeSnippetNode" }, { "lang": "Python3", "langSlug": "python3", "code": "class BlackBox:\n\n def __init__(self, n: int, m: int):\n\n\n def open(self, index: int, direction: int) -> int:\n\n\n def close(self, index: int) -> None:\n\n\n\n# Your BlackBox object will be instantiated and called as such:\n# obj = BlackBox(n, m)\n# param_1 = obj.open(index,direction)\n# obj.close(index)", "__typename": "CodeSnippetNode" }, { "lang": "C", "langSlug": "c", "code": "\n\n\ntypedef struct {\n\n} BlackBox;\n\n\nBlackBox* blackBoxCreate(int n, int m) {\n\n}\n\nint blackBoxOpen(BlackBox* obj, int index, int direction) {\n\n}\n\nvoid blackBoxClose(BlackBox* obj, int index) {\n\n}\n\nvoid blackBoxFree(BlackBox* obj) {\n\n}\n\n/**\n * Your BlackBox struct will be instantiated and called as such:\n * BlackBox* obj = blackBoxCreate(n, m);\n * int param_1 = blackBoxOpen(obj, index, direction);\n \n * blackBoxClose(obj, index);\n \n * blackBoxFree(obj);\n*/", "__typename": "CodeSnippetNode" }, { "lang": "C#", "langSlug": "csharp", "code": "public class BlackBox {\n\n public BlackBox(int n, int m) {\n\n }\n \n public int Open(int index, int direction) {\n\n }\n \n public void Close(int index) {\n\n }\n}\n\n/**\n * Your BlackBox object will be instantiated and called as such:\n * BlackBox obj = new BlackBox(n, m);\n * int param_1 = obj.Open(index,direction);\n * obj.Close(index);\n */", "__typename": "CodeSnippetNode" }, { "lang": "JavaScript", "langSlug": "javascript", "code": "/**\n * @param {number} n\n * @param {number} m\n */\nvar BlackBox = function(n, m) {\n\n};\n\n/** \n * @param {number} index \n * @param {number} direction\n * @return {number}\n */\nBlackBox.prototype.open = function(index, direction) {\n\n};\n\n/** \n * @param {number} index\n * @return {void}\n */\nBlackBox.prototype.close = function(index) {\n\n};\n\n/**\n * Your BlackBox object will be instantiated and called as such:\n * var obj = new BlackBox(n, m)\n * var param_1 = obj.open(index,direction)\n * obj.close(index)\n */", "__typename": "CodeSnippetNode" }, { "lang": "TypeScript", "langSlug": "typescript", "code": "class BlackBox {\n constructor(n: number, m: number) {\n\n }\n\n open(index: number, direction: number): number {\n\n }\n\n close(index: number): void {\n\n }\n}\n\n/**\n * Your BlackBox object will be instantiated and called as such:\n * var obj = new BlackBox(n, m)\n * var param_1 = obj.open(index,direction)\n * obj.close(index)\n */", "__typename": "CodeSnippetNode" }, { "lang": "PHP", "langSlug": "php", "code": "class BlackBox {\n /**\n * @param Integer $n\n * @param Integer $m\n */\n function __construct($n, $m) {\n\n }\n\n /**\n * @param Integer $index\n * @param Integer $direction\n * @return Integer\n */\n function open($index, $direction) {\n\n }\n\n /**\n * @param Integer $index\n * @return NULL\n */\n function close($index) {\n\n }\n}\n\n/**\n * Your BlackBox object will be instantiated and called as such:\n * $obj = BlackBox($n, $m);\n * $ret_1 = $obj->open($index, $direction);\n * $obj->close($index);\n */", "__typename": "CodeSnippetNode" }, { "lang": "Swift", "langSlug": "swift", "code": "\nclass BlackBox {\n\n init(_ n: Int, _ m: Int) {\n\n }\n \n func open(_ index: Int, _ direction: Int) -> Int {\n\n }\n \n func close(_ index: Int) {\n\n }\n}\n\n/**\n * Your BlackBox object will be instantiated and called as such:\n * let obj = BlackBox(n, m)\n * let ret_1: Int = obj.open(index, direction)\n * obj.close(index)\n */", "__typename": "CodeSnippetNode" }, { "lang": "Kotlin", "langSlug": "kotlin", "code": "class BlackBox(n: Int, m: Int) {\n\n fun open(index: Int, direction: Int): Int {\n\n }\n\n fun close(index: Int) {\n\n }\n\n}\n\n/**\n * Your BlackBox object will be instantiated and called as such:\n * var obj = BlackBox(n, m)\n * var param_1 = obj.open(index,direction)\n * obj.close(index)\n */", "__typename": "CodeSnippetNode" }, { "lang": "Dart", "langSlug": "dart", "code": "class BlackBox {\n\n BlackBox(int n, int m) {\n\n }\n \n int open(int index, int direction) {\n\n }\n \n void close(int index) {\n\n }\n}\n\n/**\n * Your BlackBox object will be instantiated and called as such:\n * BlackBox obj = BlackBox(n, m);\n * int param1 = obj.open(index,direction);\n * obj.close(index);\n */", "__typename": "CodeSnippetNode" }, { "lang": "Go", "langSlug": "golang", "code": "type BlackBox struct {\n\n}\n\n\nfunc Constructor(n int, m int) BlackBox {\n\n}\n\n\nfunc (this *BlackBox) Open(index int, direction int) int {\n\n}\n\n\nfunc (this *BlackBox) Close(index int) {\n\n}\n\n\n/**\n * Your BlackBox object will be instantiated and called as such:\n * obj := Constructor(n, m);\n * param_1 := obj.Open(index,direction);\n * obj.Close(index);\n */", "__typename": "CodeSnippetNode" }, { "lang": "Ruby", "langSlug": "ruby", "code": "class BlackBox\n\n=begin\n :type n: Integer\n :type m: Integer\n=end\n def initialize(n, m)\n\n end\n\n\n=begin\n :type index: Integer\n :type direction: Integer\n :rtype: Integer\n=end\n def open(index, direction)\n\n end\n\n\n=begin\n :type index: Integer\n :rtype: Void\n=end\n def close(index)\n\n end\n\n\nend\n\n# Your BlackBox object will be instantiated and called as such:\n# obj = BlackBox.new(n, m)\n# param_1 = obj.open(index, direction)\n# obj.close(index)", "__typename": "CodeSnippetNode" }, { "lang": "Scala", "langSlug": "scala", "code": "class BlackBox(_n: Int, _m: Int) {\n\n def open(index: Int, direction: Int): Int = {\n\n }\n\n def close(index: Int) {\n\n }\n\n}\n\n/**\n * Your BlackBox object will be instantiated and called as such:\n * var obj = new BlackBox(n, m)\n * var param_1 = obj.open(index,direction)\n * obj.close(index)\n */", "__typename": "CodeSnippetNode" }, { "lang": "Rust", "langSlug": "rust", "code": "struct BlackBox {\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 BlackBox {\n\n fn new(n: i32, m: i32) -> Self {\n\n }\n \n fn open(&self, index: i32, direction: i32) -> i32 {\n\n }\n \n fn close(&self, index: i32) {\n\n }\n}\n\n/**\n * Your BlackBox object will be instantiated and called as such:\n * let obj = BlackBox::new(n, m);\n * let ret_1: i32 = obj.open(index, direction);\n * obj.close(index);\n */", "__typename": "CodeSnippetNode" }, { "lang": "Racket", "langSlug": "racket", "code": "(define black-box%\n (class object%\n (super-new)\n\n ; n : exact-integer?\n\n ; m : exact-integer?\n (init-field\n n\n m)\n \n ; open : exact-integer? exact-integer? -> exact-integer?\n (define/public (open index direction)\n\n )\n ; close : exact-integer? -> void?\n (define/public (close index)\n\n )))\n\n;; Your black-box% object will be instantiated and called as such:\n;; (define obj (new black-box% [n n] [m m]))\n;; (define param_1 (send obj open index direction))\n;; (send obj close index)", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec black_box_init_(N :: integer(), M :: integer()) -> any().\nblack_box_init_(N, M) ->\n .\n\n-spec black_box_open(Index :: integer(), Direction :: integer()) -> integer().\nblack_box_open(Index, Direction) ->\n .\n\n-spec black_box_close(Index :: integer()) -> any().\nblack_box_close(Index) ->\n .\n\n\n%% Your functions will be called as such:\n%% black_box_init_(N, M),\n%% Param_1 = black_box_open(Index, Direction),\n%% black_box_close(Index),\n\n%% black_box_init_ will be called before every test case, in which you can do some necessary initializations.", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule BlackBox do\n @spec init_(n :: integer, m :: integer) :: any\n def init_(n, m) do\n\n end\n\n @spec open(index :: integer, direction :: integer) :: integer\n def open(index, direction) do\n\n end\n\n @spec close(index :: integer) :: any\n def close(index) do\n\n end\nend\n\n# Your functions will be called as such:\n# BlackBox.init_(n, m)\n# param_1 = BlackBox.open(index, direction)\n# BlackBox.close(index)\n\n# BlackBox.init_ will be called before every test case, in which you can do some necessary initializations.", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"1.7K\", \"totalSubmission\": \"5K\", \"totalAcceptedRaw\": 1721, \"totalSubmissionRaw\": 4963, \"acRate\": \"34.7%\"}", "hints": [], "solution": null, "status": null, "sampleTestCase": "[\"BlackBox\",\"open\",\"open\",\"open\",\"close\",\"open\"]\n[[2,3],[6,-1],[4,-1],[0,-1],[6],[0,-1]]", "metaData": "{\"classname\": \"BlackBox\", \"maxbytesperline\": 200000, \"systemdesign\": true, \"constructor\": {\"params\": [{\"name\": \"n\", \"type\": \"integer\"}, {\"name\": \"m\", \"type\": \"integer\"}]}, \"methods\": [{\"name\": \"open\", \"params\": [{\"name\": \"index\", \"type\": \"integer\"}, {\"name\": \"direction\", \"type\": \"integer\"}], \"return\": {\"type\": \"integer\"}}, {\"name\": \"close\", \"params\": [{\"name\": \"index\", \"type\": \"integer\"}], \"return\": {\"type\": \"void\"}}], \"params\": [{\"name\": \"inputs\", \"type\": \"integer[]\"}, {\"name\": \"inputs\", \"type\": \"integer[]\"}], \"return\": {\"type\": \"list\", \"dealloc\": true}}", "judgerAvailable": true, "judgeType": "large", "mysqlSchemas": [], "enableRunCode": true, "envInfo": "{\"cpp\":[\"C++\",\"

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