{ "data": { "question": { "questionId": "2583", "questionFrontendId": "2493", "categoryTitle": "Algorithms", "boundTopicId": 2000454, "title": "Divide Nodes Into the Maximum Number of Groups", "titleSlug": "divide-nodes-into-the-maximum-number-of-groups", "content": "

You are given a positive integer n representing the number of nodes in an undirected graph. The nodes are labeled from 1 to n.

\n\n

You are also given a 2D integer array edges, where edges[i] = [ai, bi] indicates that there is a bidirectional edge between nodes ai and bi. Notice that the given graph may be disconnected.

\n\n

Divide the nodes of the graph into m groups (1-indexed) such that:

\n\n\n\n

Return the maximum number of groups (i.e., maximum m) into which you can divide the nodes. Return -1 if it is impossible to group the nodes with the given conditions.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: n = 6, edges = [[1,2],[1,4],[1,5],[2,6],[2,3],[4,6]]\nOutput: 4\nExplanation: As shown in the image we:\n- Add node 5 to the first group.\n- Add node 1 to the second group.\n- Add nodes 2 and 4 to the third group.\n- Add nodes 3 and 6 to the fourth group.\nWe can see that every edge is satisfied.\nIt can be shown that that if we create a fifth group and move any node from the third or fourth group to it, at least on of the edges will not be satisfied.\n
\n\n

Example 2:

\n\n
\nInput: n = 3, edges = [[1,2],[2,3],[3,1]]\nOutput: -1\nExplanation: If we add node 1 to the first group, node 2 to the second group, and node 3 to the third group to satisfy the first two edges, we can see that the third edge will not be satisfied.\nIt can be shown that no grouping is possible.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "将节点分成尽可能多的组", "translatedContent": "

给你一个正整数 n ，表示一个 无向 图中的节点数目，节点编号从 1 到 n 。

\n\n

同时给你一个二维整数数组 edges ，其中 edges[i] = [ai, bi] 表示节点 ai 和 bi 之间有一条 双向 边。注意给定的图可能是不连通的。

\n\n

请你将图划分为 m 个组（编号从 1 开始），满足以下要求：

\n\n\n\n

请你返回最多可以将节点分为多少个组（也就是最大的 m ）。如果没办法在给定条件下分组，请你返回 -1 。

\n\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
输入：n = 6, edges = [[1,2],[1,4],[1,5],[2,6],[2,3],[4,6]]\n输出：4\n解释：如上图所示，\n- 节点 5 在第一个组。\n- 节点 1 在第二个组。\n- 节点 2 和节点 4 在第三个组。\n- 节点 3 和节点 6 在第四个组。\n所有边都满足题目要求。\n如果我们创建第五个组，将第三个组或者第四个组中任何一个节点放到第五个组，至少有一条边连接的两个节点所属的组编号不符合题目要求。\n
\n\n

示例 2：

\n\n
输入：n = 3, edges = [[1,2],[2,3],[3,1]]\n输出：-1\n解释：如果我们将节点 1 放入第一个组，节点 2 放入第二个组，节点 3 放入第三个组，前两条边满足题目要求，但第三条边不满足题目要求。\n没有任何符合题目要求的分组方式。\n
\n\n

 

\n\n

提示：

\n\n\n", "isPaidOnly": false, "difficulty": "Hard", "likes": 21, "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, \"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": "Breadth-First Search", "slug": "breadth-first-search", "translatedName": "广度优先搜索", "__typename": "TopicTagNode" }, { "name": "Union Find", "slug": "union-find", "translatedName": "并查集", "__typename": "TopicTagNode" }, { "name": "Graph", "slug": "graph", "translatedName": "图", "__typename": "TopicTagNode" } ], "companyTagStats": null, "codeSnippets": [ { "lang": "C++", "langSlug": "cpp", "code": "class Solution {\npublic:\n int magnificentSets(int n, vector>& edges) {\n \n }\n};", "__typename": "CodeSnippetNode" }, { "lang": "Java", "langSlug": "java", "code": "class Solution {\n public int magnificentSets(int n, int[][] edges) {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Python", "langSlug": "python", "code": "class Solution(object):\n def magnificentSets(self, n, edges):\n \"\"\"\n :type n: int\n :type edges: List[List[int]]\n :rtype: int\n \"\"\"", "__typename": "CodeSnippetNode" }, { "lang": "Python3", "langSlug": "python3", "code": "class Solution:\n def magnificentSets(self, n: int, edges: List[List[int]]) -> int:", "__typename": "CodeSnippetNode" }, { "lang": "C", "langSlug": "c", "code": "int magnificentSets(int n, int** edges, int edgesSize, int* edgesColSize) {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "C#", "langSlug": "csharp", "code": "public class Solution {\n public int MagnificentSets(int n, int[][] edges) {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "JavaScript", "langSlug": "javascript", "code": "/**\n * @param {number} n\n * @param {number[][]} edges\n * @return {number}\n */\nvar magnificentSets = function(n, edges) {\n\n};", "__typename": "CodeSnippetNode" }, { "lang": "TypeScript", "langSlug": "typescript", "code": "function magnificentSets(n: number, edges: number[][]): number {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "PHP", "langSlug": "php", "code": "class Solution {\n\n /**\n * @param Integer $n\n * @param Integer[][] $edges\n * @return Integer\n */\n function magnificentSets($n, $edges) {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Swift", "langSlug": "swift", "code": "class Solution {\n func magnificentSets(_ n: Int, _ edges: [[Int]]) -> Int {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Kotlin", "langSlug": "kotlin", "code": "class Solution {\n fun magnificentSets(n: Int, edges: Array): Int {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Dart", "langSlug": "dart", "code": "class Solution {\n int magnificentSets(int n, List> edges) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Go", "langSlug": "golang", "code": "func magnificentSets(n int, edges [][]int) int {\n\n}", "__typename": "CodeSnippetNode" }, { "lang": "Ruby", "langSlug": "ruby", "code": "# @param {Integer} n\n# @param {Integer[][]} edges\n# @return {Integer}\ndef magnificent_sets(n, edges)\n\nend", "__typename": "CodeSnippetNode" }, { "lang": "Scala", "langSlug": "scala", "code": "object Solution {\n def magnificentSets(n: Int, edges: Array[Array[Int]]): Int = {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Rust", "langSlug": "rust", "code": "impl Solution {\n pub fn magnificent_sets(n: i32, edges: Vec>) -> i32 {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Racket", "langSlug": "racket", "code": "(define/contract (magnificent-sets n edges)\n (-> exact-integer? (listof (listof exact-integer?)) exact-integer?)\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec magnificent_sets(N :: integer(), Edges :: [[integer()]]) -> integer().\nmagnificent_sets(N, Edges) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec magnificent_sets(n :: integer, edges :: [[integer]]) :: integer\n def magnificent_sets(n, edges) do\n \n end\nend", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"3.1K\", \"totalSubmission\": \"7.1K\", \"totalAcceptedRaw\": 3140, \"totalSubmissionRaw\": 7093, \"acRate\": \"44.3%\"}", "hints": [ "If the graph is not bipartite, it is not possible to group the nodes.", "Notice that we can solve the problem for each connected component independently, and the final answer will be just the sum of the maximum number of groups in each component.", "Finally, to solve the problem for each connected component, we can notice that if for some node v we fix its position to be in the leftmost group, then we can also evaluate the position of every other node. That position is the depth of the node in a bfs tree after rooting at node v." ], "solution": null, "status": null, "sampleTestCase": "6\n[[1,2],[1,4],[1,5],[2,6],[2,3],[4,6]]", "metaData": "{\n \"name\": \"magnificentSets\",\n \"params\": [\n {\n \"type\": \"integer\",\n \"name\": \"n\"\n },\n {\n \"type\": \"integer[][]\",\n \"name\": \"edges\"\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++ 20\\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 1.21<\\/code><\\/p>\\r\\n\\r\\n
\\u652f\\u6301 https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods@v1.18.1<\\/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 1.9.0<\\/code><\\/p>\\r\\n\\r\\n
\\u6211\\u4eec\\u4f7f\\u7528\\u7684\\u662f JetBrains \\u63d0\\u4f9b\\u7684 experimental compiler\\u3002\\u5982\\u679c\\u60a8\\u8ba4\\u4e3a\\u60a8\\u9047\\u5230\\u4e86\\u7f16\\u8bd1\\u5668\\u76f8\\u5173\\u7684\\u95ee\\u9898\\uff0c\\u8bf7\\u5411\\u6211\\u4eec\\u53cd\\u9988<\\/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 5.1.6<\\/p>\\r\\n\\r\\n
Compile Options: --alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2022<\\/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": "6\n[[1,2],[1,4],[1,5],[2,6],[2,3],[4,6]]\n3\n[[1,2],[2,3],[3,1]]",
            "__typename": "QuestionNode"
        }
    }
}