{ "data": { "question": { "questionId": "3439", "questionFrontendId": "3203", "boundTopicId": null, "title": "Find Minimum Diameter After Merging Two Trees", "titleSlug": "find-minimum-diameter-after-merging-two-trees", "content": "

There exist two undirected trees with n and m nodes, numbered from 0 to n - 1 and from 0 to m - 1, respectively. You are given two 2D integer arrays edges1 and edges2 of lengths n - 1 and m - 1, respectively, where edges1[i] = [ai, bi] indicates that there is an edge between nodes ai and bi in the first tree and edges2[i] = [ui, vi] indicates that there is an edge between nodes ui and vi in the second tree.

\n\n

You must connect one node from the first tree with another node from the second tree with an edge.

\n\n

Return the minimum possible diameter of the resulting tree.

\n\n

The diameter of a tree is the length of the longest path between any two nodes in the tree.

\n\n

 

\n

Example 1:\"\"

\n\n
\n

Input: edges1 = [[0,1],[0,2],[0,3]], edges2 = [[0,1]]

\n\n

Output: 3

\n\n

Explanation:

\n\n

We can obtain a tree of diameter 3 by connecting node 0 from the first tree with any node from the second tree.

\n
\n\n

Example 2:

\n\"\"\n
\n

Input: edges1 = [[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]], edges2 = [[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]]

\n\n

Output: 5

\n\n

Explanation:

\n\n

We can obtain a tree of diameter 5 by connecting node 0 from the first tree with node 0 from the second tree.

\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": null, "translatedContent": null, "isPaidOnly": false, "difficulty": "Hard", "likes": 114, "dislikes": 5, "isLiked": null, "similarQuestions": "[{\"title\": \"Minimum Height Trees\", \"titleSlug\": \"minimum-height-trees\", \"difficulty\": \"Medium\", \"translatedTitle\": null}, {\"title\": \"Tree Diameter\", \"titleSlug\": \"tree-diameter\", \"difficulty\": \"Medium\", \"translatedTitle\": null}]", "exampleTestcases": "[[0,1],[0,2],[0,3]]\n[[0,1]]\n[[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]]\n[[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]]", "categoryTitle": "Algorithms", "contributors": [], "topicTags": [ { "name": "Tree", "slug": "tree", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Depth-First Search", "slug": "depth-first-search", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Breadth-First Search", "slug": "breadth-first-search", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Graph", "slug": "graph", "translatedName": null, "__typename": "TopicTagNode" } ], "companyTagStats": null, "codeSnippets": [ { "lang": "C++", "langSlug": "cpp", "code": "class Solution {\npublic:\n int minimumDiameterAfterMerge(vector>& edges1, vector>& edges2) {\n \n }\n};", "__typename": "CodeSnippetNode" }, { "lang": "Java", "langSlug": "java", "code": "class Solution {\n public int minimumDiameterAfterMerge(int[][] edges1, int[][] edges2) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Python", "langSlug": "python", "code": "class Solution(object):\n def minimumDiameterAfterMerge(self, edges1, edges2):\n \"\"\"\n :type edges1: List[List[int]]\n :type edges2: List[List[int]]\n :rtype: int\n \"\"\"\n ", "__typename": "CodeSnippetNode" }, { "lang": "Python3", "langSlug": "python3", "code": "class Solution:\n def minimumDiameterAfterMerge(self, edges1: List[List[int]], edges2: List[List[int]]) -> int:\n ", "__typename": "CodeSnippetNode" }, { "lang": "C", "langSlug": "c", "code": "int minimumDiameterAfterMerge(int** edges1, int edges1Size, int* edges1ColSize, int** edges2, int edges2Size, int* edges2ColSize) {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "C#", "langSlug": "csharp", "code": "public class Solution {\n public int MinimumDiameterAfterMerge(int[][] edges1, int[][] edges2) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "JavaScript", "langSlug": "javascript", "code": "/**\n * @param {number[][]} edges1\n * @param {number[][]} edges2\n * @return {number}\n */\nvar minimumDiameterAfterMerge = function(edges1, edges2) {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "TypeScript", "langSlug": "typescript", "code": "function minimumDiameterAfterMerge(edges1: number[][], edges2: number[][]): number {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "PHP", "langSlug": "php", "code": "class Solution {\n\n /**\n * @param Integer[][] $edges1\n * @param Integer[][] $edges2\n * @return Integer\n */\n function minimumDiameterAfterMerge($edges1, $edges2) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Swift", "langSlug": "swift", "code": "class Solution {\n func minimumDiameterAfterMerge(_ edges1: [[Int]], _ edges2: [[Int]]) -> Int {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Kotlin", "langSlug": "kotlin", "code": "class Solution {\n fun minimumDiameterAfterMerge(edges1: Array, edges2: Array): Int {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Dart", "langSlug": "dart", "code": "class Solution {\n int minimumDiameterAfterMerge(List> edges1, List> edges2) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Go", "langSlug": "golang", "code": "func minimumDiameterAfterMerge(edges1 [][]int, edges2 [][]int) int {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "Ruby", "langSlug": "ruby", "code": "# @param {Integer[][]} edges1\n# @param {Integer[][]} edges2\n# @return {Integer}\ndef minimum_diameter_after_merge(edges1, edges2)\n \nend", "__typename": "CodeSnippetNode" }, { "lang": "Scala", "langSlug": "scala", "code": "object Solution {\n def minimumDiameterAfterMerge(edges1: Array[Array[Int]], edges2: Array[Array[Int]]): Int = {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Rust", "langSlug": "rust", "code": "impl Solution {\n pub fn minimum_diameter_after_merge(edges1: Vec>, edges2: Vec>) -> i32 {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Racket", "langSlug": "racket", "code": "(define/contract (minimum-diameter-after-merge edges1 edges2)\n (-> (listof (listof exact-integer?)) (listof (listof exact-integer?)) exact-integer?)\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec minimum_diameter_after_merge(Edges1 :: [[integer()]], Edges2 :: [[integer()]]) -> integer().\nminimum_diameter_after_merge(Edges1, Edges2) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec minimum_diameter_after_merge(edges1 :: [[integer]], edges2 :: [[integer]]) :: integer\n def minimum_diameter_after_merge(edges1, edges2) do\n \n end\nend", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"7.4K\", \"totalSubmission\": \"21.2K\", \"totalAcceptedRaw\": 7370, \"totalSubmissionRaw\": 21187, \"acRate\": \"34.8%\"}", "hints": [ "Suppose that we connected node a in tree1 with node b in tree2. The diameter length of the resulting tree will be the largest of the following 3 values: \r\n
    \r\n
  1. The diameter of tree 1.
  2. \r\n
  3. The diameter of tree 2.
  4. \r\n
  5. The length of the longest path that starts at node a and that is completely within Tree 1 + The length of the longest path that starts at node b and that is completely within Tree 2 + 1.
  6. \r\n
\r\nThe added one in the third value is due to the additional edge that we have added between trees 1 and 2.", "Values 1 and 2 are constant regardless of our choice of a and b. Therefore, we need to pick a and b in such a way that minimizes value 3.", "If we pick a and b optimally, they will be in the diameters of Tree 1 and Tree 2, respectively. Exactly which nodes of the diameter should we pick?", "a is the center of the diameter of tree 1, and b is the center of the diameter of tree 2." ], "solution": null, "status": null, "sampleTestCase": "[[0,1],[0,2],[0,3]]\n[[0,1]]", "metaData": "{\n \"name\": \"minimumDiameterAfterMerge\",\n \"params\": [\n {\n \"name\": \"edges1\",\n \"type\": \"integer[][]\"\n },\n {\n \"type\": \"integer[][]\",\n \"name\": \"edges2\"\n }\n ],\n \"return\": {\n \"type\": \"integer\"\n }\n}", "judgerAvailable": true, "judgeType": "large", "mysqlSchemas": [], "enableRunCode": true, "enableTestMode": false, "enableDebugger": true, "envInfo": "{\"cpp\": [\"C++\", \"

Compiled with clang 17 using the latest C++ 23 standard, and libstdc++ provided by GCC 13.

\\r\\n\\r\\n

Your code is compiled with level two optimization (-O2). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.

\\r\\n\\r\\n

Most standard library headers are already included automatically for your convenience.

\"], \"java\": [\"Java\", \"

OpenJDK 21. Using compile arguments: --enable-preview --release 21

\\r\\n\\r\\n

Most standard library headers are already included automatically for your convenience.

\\r\\n

Includes Pair class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.

\"], \"python\": [\"Python\", \"

Python 2.7.12.

\\r\\n\\r\\n

Most libraries are already imported automatically for your convenience, such as array, bisect, collections. If you need more libraries, you can import it yourself.

\\r\\n\\r\\n

For Map/TreeMap data structure, you may use sortedcontainers library.

\\r\\n\\r\\n

Note that Python 2.7 will not be maintained past 2020. For the latest Python, please choose Python3 instead.

\"], \"c\": [\"C\", \"

Compiled with gcc 13 using the gnu11 standard.

\\r\\n\\r\\n

Your code is compiled with level one optimization (-O2). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.

\\r\\n\\r\\n

Most standard library headers are already included automatically for your convenience.

\\r\\n\\r\\n

For hash table operations, you may use uthash. \\\"uthash.h\\\" is included by default. Below are some examples:

\\r\\n\\r\\n

1. Adding an item to a hash.\\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
\\r\\n

\\r\\n\\r\\n

2. Looking up an item in a hash:\\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
\\r\\n

\\r\\n\\r\\n

3. Deleting an item in a hash:\\r\\n

\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n    HASH_DEL(users, user);  \\r\\n}\\r\\n
\\r\\n

\"], \"csharp\": [\"C#\", \"

C# 12 with .NET 8 runtime

\"], \"javascript\": [\"JavaScript\", \"

Node.js 20.10.0.

\\r\\n\\r\\n

Your code is run with --harmony flag, enabling new ES6 features.

\\r\\n\\r\\n

lodash.js library is included by default.

\\r\\n\\r\\n

For Priority Queue / Queue data structures, you may use 5.4.0 version of datastructures-js/priority-queue and 4.2.3 version of datastructures-js/queue.

\"], \"ruby\": [\"Ruby\", \"

Ruby 3.2

\\r\\n\\r\\n

Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms

\"], \"swift\": [\"Swift\", \"

Swift 5.9.

\\r\\n\\r\\n

You may use swift-algorithms 1.2.0 and swift-collections 1.1.0.

\"], \"golang\": [\"Go\", \"

Go 1.21

\\r\\n

Support https://pkg.go.dev/github.com/emirpasic/gods@v1.18.1 and https://pkg.go.dev/github.com/emirpasic/gods/v2@v2.0.0-alpha library.

\"], \"python3\": [\"Python3\", \"

Python 3.11.

\\r\\n\\r\\n

Most libraries are already imported automatically for your convenience, such as array, bisect, collections. If you need more libraries, you can import it yourself.

\\r\\n\\r\\n

For Map/TreeMap data structure, you may use sortedcontainers library.

\"], \"scala\": [\"Scala\", \"

Scala 3.3.1.

\"], \"kotlin\": [\"Kotlin\", \"

Kotlin 1.9.0.

\\r\\n\\r\\n

We are using an experimental compiler provided by JetBrains.

\"], \"rust\": [\"Rust\", \"

Rust 1.79.0. Your code will be compiled with opt-level 2.

\\r\\n\\r\\n

Supports rand v0.8 and regex\\u00a0v1 from crates.io

\"], \"php\": [\"PHP\", \"

PHP 8.2.

\\r\\n

With bcmath module

\"], \"typescript\": [\"Typescript\", \"

TypeScript 5.1.6, Node.js 20.10.0.

\\r\\n\\r\\n

Compile Options: --alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2022

\\r\\n\\r\\n

Your code is run with --harmony flag, enabling new ES2022 features.

\\r\\n\\r\\n

lodash.js library is included by default.

\"], \"racket\": [\"Racket\", \"

Racket CS v8.11

\\r\\n\\r\\n

Using #lang racket

\\r\\n\\r\\n

Required data/gvector data/queue data/order data/heap automatically for your convenience

\"], \"erlang\": [\"Erlang\", \"Erlang/OTP 26\"], \"elixir\": [\"Elixir\", \"Elixir 1.15 with Erlang/OTP 26\"], \"dart\": [\"Dart\", \"

Dart 3.2. You may use package collection

\\r\\n\\r\\n

Your code will be run directly without compiling

\"]}", "libraryUrl": null, "adminUrl": null, "challengeQuestion": null, "__typename": "QuestionNode" } } }