{ "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.
You must connect one node from the first tree with another node from the second tree with an edge.
\n\nReturn the minimum possible diameter of the resulting tree.
\n\nThe diameter of a tree is the length of the longest path between any two nodes in the tree.
\n\n\n
Example 1:
\n\nInput: edges1 = [[0,1],[0,2],[0,3]], edges2 = [[0,1]]
\n\nOutput: 3
\n\nExplanation:
\n\nWe can obtain a tree of diameter 3 by connecting node 0 from the first tree with any node from the second tree.
\nExample 2:
\n\nInput: 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\nOutput: 5
\n\nExplanation:
\n\nWe can obtain a tree of diameter 5 by connecting node 0 from the first tree with node 0 from the second tree.
\n\n
Constraints:
\n\n1 <= n, m <= 105
edges1.length == n - 1
edges2.length == m - 1
edges1[i].length == edges2[i].length == 2
edges1[i] = [ai, bi]
0 <= ai, bi < n
edges2[i] = [ui, vi]
0 <= ui, vi < m
edges1
and edges2
represent valid trees.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\na
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.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.
Your code is compiled with level two optimization (-O2
). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.
Most standard library headers are already included automatically for your convenience.
\"], \"java\": [\"Java\", \"OpenJDK 21
. Using compile arguments: --enable-preview --release 21
Most standard library headers are already included automatically for your convenience.
\\r\\nIncludes Pair
class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.
Python 2.7.12
.
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\\nFor Map/TreeMap data structure, you may use sortedcontainers library.
\\r\\n\\r\\nNote 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.
Your code is compiled with level one optimization (-O2
). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.
Most standard library headers are already included automatically for your convenience.
\\r\\n\\r\\nFor hash table operations, you may use uthash. \\\"uthash.h\\\" is included by default. Below are some examples:
\\r\\n\\r\\n1. 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
.
Your code is run with --harmony
flag, enabling new ES6 features.
lodash.js library is included by default.
\\r\\n\\r\\nFor 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
Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms
\"], \"swift\": [\"Swift\", \"Swift 5.9
.
You may use swift-algorithms 1.2.0 and swift-collections 1.1.0.
\"], \"golang\": [\"Go\", \"Go 1.21
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
.
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\\nFor Map/TreeMap data structure, you may use sortedcontainers library.
\"], \"scala\": [\"Scala\", \"Scala 3.3.1
.
Kotlin 1.9.0
.
We are using an experimental compiler provided by JetBrains.
\"], \"rust\": [\"Rust\", \"Rust 1.79.0
. Your code will be compiled with opt-level
2.
Supports rand v0.8 and regex\\u00a0v1 from crates.io
\"], \"php\": [\"PHP\", \"PHP 8.2
.
With bcmath module
\"], \"typescript\": [\"Typescript\", \"TypeScript 5.1.6, Node.js 20.10.0
.
Compile Options: --alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2022
Your code is run with --harmony
flag, enabling new ES2022 features.
lodash.js library is included by default.
\"], \"racket\": [\"Racket\", \"Racket CS v8.11
\\r\\n\\r\\nUsing #lang racket
Required data/gvector data/queue data/order data/heap
automatically for your convenience
Dart 3.2. You may use package collection
\\r\\n\\r\\nYour code will be run directly without compiling
\"]}", "libraryUrl": null, "adminUrl": null, "challengeQuestion": null, "__typename": "QuestionNode" } } }