{ "data": { "question": { "questionId": "2597", "questionFrontendId": "2509", "categoryTitle": "Algorithms", "boundTopicId": 2022041, "title": "Cycle Length Queries in a Tree", "titleSlug": "cycle-length-queries-in-a-tree", "content": "

You are given an integer n. There is a complete binary tree with 2n - 1 nodes. The root of that tree is the node with the value 1, and every node with a value val in the range [1, 2n - 1 - 1] has two children where:

\n\n\n\n

You are also given a 2D integer array queries of length m, where queries[i] = [ai, bi]. For each query, solve the following problem:

\n\n
    \n\t
  1. Add an edge between the nodes with values ai and bi.
    2. \n\t
  2. Find the length of the cycle in the graph.
    3. \n\t
  3. Remove the added edge between nodes with values ai and bi.
    4. \n
\n\n

Note that:

\n\n\n\n

Return an array answer of length m where answer[i] is the answer to the ith query.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: n = 3, queries = [[5,3],[4,7],[2,3]]\nOutput: [4,5,3]\nExplanation: The diagrams above show the tree of 23 - 1 nodes. Nodes colored in red describe the nodes in the cycle after adding the edge.\n- After adding the edge between nodes 3 and 5, the graph contains a cycle of nodes [5,2,1,3]. Thus answer to the first query is 4. We delete the added edge and process the next query.\n- After adding the edge between nodes 4 and 7, the graph contains a cycle of nodes [4,2,1,3,7]. Thus answer to the second query is 5. We delete the added edge and process the next query.\n- After adding the edge between nodes 2 and 3, the graph contains a cycle of nodes [2,1,3]. Thus answer to the third query is 3. We delete the added edge.\n
\n\n

Example 2:

\n\"\"\n
\nInput: n = 2, queries = [[1,2]]\nOutput: [2]\nExplanation: The diagram above shows the tree of 22 - 1 nodes. Nodes colored in red describe the nodes in the cycle after adding the edge.\n- After adding the edge between nodes 1 and 2, the graph contains a cycle of nodes [2,1]. Thus answer for the first query is 2. We delete the added edge.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "查询树中环的长度", "translatedContent": "

给你一个整数 n ，表示你有一棵含有 2n - 1 个节点的 完全二叉树 。根节点的编号是 1 ，树中编号在[1, 2n - 1 - 1] 之间，编号为 val 的节点都有两个子节点，满足：

\n\n\n\n

给你一个长度为 m 的查询数组 queries ，它是一个二维整数数组，其中 queries[i] = [ai, bi] 。对于每个查询，求出以下问题的解：

\n\n
    \n\t
  1. 在节点编号为 ai 和 bi 之间添加一条边。
    2. \n\t
  2. 求出图中环的长度。
    3. \n\t
  3. 删除节点编号为 ai 和 bi 之间新添加的边。
    4. \n
\n\n

注意：

\n\n\n\n

请你返回一个长度为 m 的数组 answer ，其中 answer[i] 是第 i 个查询的结果。

\n\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
\n输入：n = 3, queries = [[5,3],[4,7],[2,3]]\n输出：[4,5,3]\n解释：上图是一棵有 23 - 1 个节点的树。红色节点表示添加额外边后形成环的节点。\n- 在节点 3 和节点 5 之间添加边后，环为 [5,2,1,3] ，所以第一个查询的结果是 4 。删掉添加的边后处理下一个查询。\n- 在节点 4 和节点 7 之间添加边后，环为 [4,2,1,3,7] ，所以第二个查询的结果是 5 。删掉添加的边后处理下一个查询。\n- 在节点 2 和节点 3 之间添加边后，环为 [2,1,3] ，所以第三个查询的结果是 3 。删掉添加的边。\n
\n\n

示例 2：

\n\n

\"\"

\n\n
\n输入：n = 2, queries = [[1,2]]\n输出：[2]\n解释：上图是一棵有 22 - 1 个节点的树。红色节点表示添加额外边后形成环的节点。\n- 在节点 1 和节点 2 之间添加边后，环为 [2,1] ，所以第一个查询的结果是 2 。删掉添加的边。\n
\n\n

 

\n\n

提示：

\n\n\n", "isPaidOnly": false, "difficulty": "Hard", "likes": 15, "dislikes": 0, "isLiked": null, "similarQuestions": "[]", "contributors": [], "langToValidPlayground": "{\"cpp\": false, \"java\": true, \"python\": true, \"python3\": false, \"mysql\": false, \"mssql\": false, \"oraclesql\": false, \"c\": false, \"csharp\": false, \"javascript\": false, \"ruby\": false, \"bash\": false, \"swift\": false, \"golang\": false, \"scala\": false, \"html\": false, \"pythonml\": false, \"kotlin\": false, \"rust\": false, \"php\": false, \"typescript\": false, \"racket\": false, \"erlang\": false, \"elixir\": false, \"dart\": false}", "topicTags": [ { "name": "Tree", "slug": "tree", "translatedName": "树", "__typename": "TopicTagNode" }, { "name": "Binary Tree", "slug": "binary-tree", "translatedName": "二叉树", "__typename": "TopicTagNode" } ], "companyTagStats": null, "codeSnippets": [ { "lang": "C++", "langSlug": "cpp", "code": "class Solution {\npublic:\n vector cycleLengthQueries(int n, vector>& queries) {\n \n }\n};", "__typename": "CodeSnippetNode" }, { "lang": "Java", "langSlug": "java", "code": "class Solution {\n public int[] cycleLengthQueries(int n, int[][] queries) {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Python", "langSlug": "python", "code": "class Solution(object):\n def cycleLengthQueries(self, n, queries):\n \"\"\"\n :type n: int\n :type queries: List[List[int]]\n :rtype: List[int]\n \"\"\"", "__typename": "CodeSnippetNode" }, { "lang": "Python3", "langSlug": "python3", "code": "class Solution:\n def cycleLengthQueries(self, n: int, queries: List[List[int]]) -> List[int]:", "__typename": "CodeSnippetNode" }, { "lang": "C", "langSlug": "c", "code": "/**\n * Note: The returned array must be malloced, assume caller calls free().\n */\nint* cycleLengthQueries(int n, int** queries, int queriesSize, int* queriesColSize, int* returnSize){\n\n}", "__typename": "CodeSnippetNode" }, { "lang": "C#", "langSlug": "csharp", "code": "public class Solution {\n public int[] CycleLengthQueries(int n, int[][] queries) {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "JavaScript", "langSlug": "javascript", "code": "/**\n * @param {number} n\n * @param {number[][]} queries\n * @return {number[]}\n */\nvar cycleLengthQueries = function(n, queries) {\n\n};", "__typename": "CodeSnippetNode" }, { "lang": "Ruby", "langSlug": "ruby", "code": "# @param {Integer} n\n# @param {Integer[][]} queries\n# @return {Integer[]}\ndef cycle_length_queries(n, queries)\n\nend", "__typename": "CodeSnippetNode" }, { "lang": "Swift", "langSlug": "swift", "code": "class Solution {\n func cycleLengthQueries(_ n: Int, _ queries: [[Int]]) -> [Int] {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Go", "langSlug": "golang", "code": "func cycleLengthQueries(n int, queries [][]int) []int {\n\n}", "__typename": "CodeSnippetNode" }, { "lang": "Scala", "langSlug": "scala", "code": "object Solution {\n def cycleLengthQueries(n: Int, queries: Array[Array[Int]]): Array[Int] = {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Kotlin", "langSlug": "kotlin", "code": "class Solution {\n fun cycleLengthQueries(n: Int, queries: Array): IntArray {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Rust", "langSlug": "rust", "code": "impl Solution {\n pub fn cycle_length_queries(n: i32, queries: Vec>) -> Vec {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "PHP", "langSlug": "php", "code": "class Solution {\n\n /**\n * @param Integer $n\n * @param Integer[][] $queries\n * @return Integer[]\n */\n function cycleLengthQueries($n, $queries) {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "TypeScript", "langSlug": "typescript", "code": "function cycleLengthQueries(n: number, queries: number[][]): number[] {\n\n};", "__typename": "CodeSnippetNode" }, { "lang": "Racket", "langSlug": "racket", "code": "(define/contract (cycle-length-queries n queries)\n (-> exact-integer? (listof (listof exact-integer?)) (listof exact-integer?))\n\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec cycle_length_queries(N :: integer(), Queries :: [[integer()]]) -> [integer()].\ncycle_length_queries(N, Queries) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec cycle_length_queries(n :: integer, queries :: [[integer]]) :: [integer]\n def cycle_length_queries(n, queries) do\n\n end\nend", "__typename": "CodeSnippetNode" }, { "lang": "Dart", "langSlug": "dart", "code": "class Solution {\n List cycleLengthQueries(int n, List> queries) {\n\n }\n}", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"3.1K\", \"totalSubmission\": \"4.8K\", \"totalAcceptedRaw\": 3058, \"totalSubmissionRaw\": 4823, \"acRate\": \"63.4%\"}", "hints": [ "Find the distance between nodes “a” and “b”.", "distance(a, b) = depth(a) + depth(b) - 2 * LCA(a, b). Where depth(a) denotes depth from root to node “a” and LCA(a, b) denotes the lowest common ancestor of nodes “a” and “b”.", "To find LCA(a, b), iterate over all ancestors of node “a” and check if it is the ancestor of node “b” too. If so, take the one with maximum depth." ], "solution": null, "status": null, "sampleTestCase": "3\n[[5,3],[4,7],[2,3]]", "metaData": "{\n \"name\": \"cycleLengthQueries\",\n \"params\": [\n {\n \"type\": \"integer\",\n \"name\": \"n\"\n },\n {\n \"type\": \"integer[][]\",\n \"name\": \"queries\"\n }\n ],\n \"return\": {\n \"type\": \"integer[]\"\n }\n}", "judgerAvailable": true, "judgeType": "large", "mysqlSchemas": [], "enableRunCode": true, "envInfo": "{\"cpp\":[\"C++\",\"

\\u7248\\u672c\\uff1aclang 11<\\/code> \\u91c7\\u7528\\u6700\\u65b0C++ 17\\u6807\\u51c6\\u3002<\\/p>\\r\\n\\r\\n

\\u7f16\\u8bd1\\u65f6\\uff0c\\u5c06\\u4f1a\\u91c7\\u7528-O2<\\/code>\\u7ea7\\u4f18\\u5316\\u3002AddressSanitizer<\\/a> \\u4e5f\\u88ab\\u5f00\\u542f\\u6765\\u68c0\\u6d4bout-of-bounds<\\/code>\\u548cuse-after-free<\\/code>\\u9519\\u8bef\\u3002<\\/p>\\r\\n\\r\\n

\\u4e3a\\u4e86\\u4f7f\\u7528\\u65b9\\u4fbf\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8\\u5bfc\\u5165\\u3002<\\/p>\"],\"java\":[\"Java\",\"

\\u7248\\u672c\\uff1aOpenJDK 17<\\/code>\\u3002\\u53ef\\u4ee5\\u4f7f\\u7528Java 8\\u7684\\u7279\\u6027\\u4f8b\\u5982\\uff0clambda expressions \\u548c stream API\\u3002<\\/p>\\r\\n\\r\\n

\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u88ab\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n

\\u5305\\u542b Pair \\u7c7b: https:\\/\\/docs.oracle.com\\/javase\\/8\\/javafx\\/api\\/javafx\\/util\\/Pair.html <\\/p>\"],\"python\":[\"Python\",\"

\\u7248\\u672c\\uff1a Python 2.7.12<\\/code><\\/p>\\r\\n\\r\\n

\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982\\uff1aarray<\\/a>, bisect<\\/a>, collections<\\/a>\\u3002\\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n

\\u6ce8\\u610f Python 2.7 \\u5c06\\u57282020\\u5e74\\u540e\\u4e0d\\u518d\\u7ef4\\u62a4<\\/a>\\u3002 \\u5982\\u60f3\\u4f7f\\u7528\\u6700\\u65b0\\u7248\\u7684Python\\uff0c\\u8bf7\\u9009\\u62e9Python 3\\u3002<\\/p>\"],\"c\":[\"C\",\"

\\u7248\\u672c\\uff1aGCC 8.2<\\/code>\\uff0c\\u91c7\\u7528GNU11\\u6807\\u51c6\\u3002<\\/p>\\r\\n\\r\\n

\\u7f16\\u8bd1\\u65f6\\uff0c\\u5c06\\u4f1a\\u91c7\\u7528-O1<\\/code>\\u7ea7\\u4f18\\u5316\\u3002 AddressSanitizer<\\/a>\\u4e5f\\u88ab\\u5f00\\u542f\\u6765\\u68c0\\u6d4bout-of-bounds<\\/code>\\u548cuse-after-free<\\/code>\\u9519\\u8bef\\u3002<\\/p>\\r\\n\\r\\n

\\u4e3a\\u4e86\\u4f7f\\u7528\\u65b9\\u4fbf\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n

\\u5982\\u60f3\\u4f7f\\u7528\\u54c8\\u5e0c\\u8868\\u8fd0\\u7b97, \\u60a8\\u53ef\\u4ee5\\u4f7f\\u7528 uthash<\\/a>\\u3002 \\\"uthash.h\\\"\\u5df2\\u7ecf\\u9ed8\\u8ba4\\u88ab\\u5bfc\\u5165\\u3002\\u8bf7\\u770b\\u5982\\u4e0b\\u793a\\u4f8b:<\\/p>\\r\\n\\r\\n

1. \\u5f80\\u54c8\\u5e0c\\u8868\\u4e2d\\u6dfb\\u52a0\\u4e00\\u4e2a\\u5bf9\\u8c61\\uff1a<\\/b>\\r\\n

\\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
2. \\u5728\\u54c8\\u5e0c\\u8868\\u4e2d\\u67e5\\u627e\\u4e00\\u4e2a\\u5bf9\\u8c61\\uff1a<\\/b>\\r\\n
\\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
3. \\u4ece\\u54c8\\u5e0c\\u8868\\u4e2d\\u5220\\u9664\\u4e00\\u4e2a\\u5bf9\\u8c61\\uff1a<\\/b>\\r\\n
\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n    HASH_DEL(users, user);  \\r\\n}\\r\\n<\\/pre>\\r\\n<\\/p>\"],\"csharp\":[\"C#\",\"
C# 10<\\/a> \\u8fd0\\u884c\\u5728 .NET 6 \\u4e0a<\\/p>\"],\"javascript\":[\"JavaScript\",\"
\\u7248\\u672c\\uff1aNode.js 16.13.2<\\/code><\\/p>\\r\\n\\r\\n
\\u60a8\\u7684\\u4ee3\\u7801\\u5728\\u6267\\u884c\\u65f6\\u5c06\\u5e26\\u4e0a --harmony<\\/code> \\u6807\\u8bb0\\u6765\\u5f00\\u542f \\u65b0\\u7248ES6\\u7279\\u6027<\\/a>\\u3002<\\/p>\\r\\n\\r\\n
lodash.js<\\/a> \\u5e93\\u5df2\\u7ecf\\u9ed8\\u8ba4\\u88ab\\u5305\\u542b\\u3002<\\/p>\\r\\n\\r\\n
 \\u5982\\u9700\\u4f7f\\u7528\\u961f\\u5217\\/\\u4f18\\u5148\\u961f\\u5217\\uff0c\\u60a8\\u53ef\\u4f7f\\u7528  datastructures-js\\/priority-queue@5.3.0<\\/a> \\u548c  datastructures-js\\/queue@4.2.1<\\/a>\\u3002<\\/p>\"],\"ruby\":[\"Ruby\",\"
\\u4f7f\\u7528Ruby 3.1<\\/code>\\u6267\\u884c<\\/p>\\r\\n\\r\\n
\\u4e00\\u4e9b\\u5e38\\u7528\\u7684\\u6570\\u636e\\u7ed3\\u6784\\u5df2\\u5728 Algorithms \\u6a21\\u5757\\u4e2d\\u63d0\\u4f9b\\uff1ahttps:\\/\\/www.rubydoc.info\\/github\\/kanwei\\/algorithms\\/Algorithms<\\/p>\"],\"swift\":[\"Swift\",\"
\\u7248\\u672c\\uff1aSwift 5.5.2<\\/code><\\/p>\\r\\n\\r\\n
\\u6211\\u4eec\\u901a\\u5e38\\u4fdd\\u8bc1\\u66f4\\u65b0\\u5230 Apple\\u653e\\u51fa\\u7684\\u6700\\u65b0\\u7248Swift<\\/a>\\u3002\\u5982\\u679c\\u60a8\\u53d1\\u73b0Swift\\u4e0d\\u662f\\u6700\\u65b0\\u7248\\u7684\\uff0c\\u8bf7\\u8054\\u7cfb\\u6211\\u4eec\\uff01\\u6211\\u4eec\\u5c06\\u5c3d\\u5feb\\u66f4\\u65b0\\u3002<\\/p>\"],\"golang\":[\"Go\",\"
\\u7248\\u672c\\uff1aGo 1.17<\\/code><\\/p>\\r\\n\\r\\n
\\u652f\\u6301 https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods<\\/a> \\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\"
\\u7248\\u672c\\uff1aPython 3.10<\\/code><\\/p>\\r\\n\\r\\n
\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982array<\\/a>, bisect<\\/a>, collections<\\/a>\\u3002 \\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n
\\u5982\\u9700\\u4f7f\\u7528 Map\\/TreeMap \\u6570\\u636e\\u7ed3\\u6784\\uff0c\\u60a8\\u53ef\\u4f7f\\u7528 sortedcontainers<\\/a> \\u5e93\\u3002<\\/p>\"],\"scala\":[\"Scala\",\"
\\u7248\\u672c\\uff1aScala 2.13<\\/code><\\/p>\"],\"kotlin\":[\"Kotlin\",\"
\\u7248\\u672c\\uff1aKotlin 1.3.10<\\/code><\\/p>\"],\"rust\":[\"Rust\",\"
\\u7248\\u672c\\uff1arust 1.58.1<\\/code><\\/p>\\r\\n\\r\\n
\\u652f\\u6301 crates.io \\u7684 rand<\\/a><\\/p>\"],\"php\":[\"PHP\",\"
PHP 8.1<\\/code>.<\\/p>\\r\\n\\r\\n
With bcmath module.<\\/p>\"],\"typescript\":[\"TypeScript\",\"
TypeScript 4.5.4<\\/p>\\r\\n\\r\\n
Compile Options: --alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2020<\\/p>\\r\\n\\r\\n
lodash.js<\\/a> \\u5e93\\u5df2\\u7ecf\\u9ed8\\u8ba4\\u88ab\\u5305\\u542b\\u3002<\\/p>\\r\\n\\r\\n
 \\u5982\\u9700\\u4f7f\\u7528\\u961f\\u5217\\/\\u4f18\\u5148\\u961f\\u5217\\uff0c\\u60a8\\u53ef\\u4f7f\\u7528  datastructures-js\\/priority-queue@5.3.0<\\/a> \\u548c  datastructures-js\\/queue@4.2.1<\\/a>\\u3002<\\/p>\"],\"racket\":[\"Racket\",\"
Racket CS<\\/a> v8.3<\\/p>\\r\\n\\r\\n
\\u4f7f\\u7528 #lang racket<\\/p>\\r\\n\\r\\n
\\u5df2\\u9884\\u5148 (require data\\/gvector data\\/queue data\\/order data\\/heap). \\u82e5\\u9700\\u4f7f\\u7528\\u5176\\u5b83\\u6570\\u636e\\u7ed3\\u6784\\uff0c\\u53ef\\u81ea\\u884c require\\u3002<\\/p>\"],\"erlang\":[\"Erlang\",\"Erlang\\/OTP 24.2\"],\"elixir\":[\"Elixir\",\"Elixir 1.13.0 with Erlang\\/OTP 24.2\"],\"dart\":[\"Dart\",\"
Dart 2.17.3<\\/p>\\r\\n\\r\\n
\\u60a8\\u7684\\u4ee3\\u7801\\u5c06\\u4f1a\\u88ab\\u4e0d\\u7f16\\u8bd1\\u76f4\\u63a5\\u8fd0\\u884c<\\/p>\"]}",
            "book": null,
            "isSubscribed": false,
            "isDailyQuestion": false,
            "dailyRecordStatus": null,
            "editorType": "CKEDITOR",
            "ugcQuestionId": null,
            "style": "LEETCODE",
            "exampleTestcases": "3\n[[5,3],[4,7],[2,3]]\n2\n[[1,2]]",
            "__typename": "QuestionNode"
        }
    }
}