Closest Nodes Queries in a Binary Search Tree
<p>You are given the <code>root</code> of a <strong>binary search tree </strong>and an array <code>queries</code> of size <code>n</code> consisting of positive integers.</p>

<p>Find a <strong>2D</strong> array <code>answer</code> of size <code>n</code> where <code>answer[i] = [min<sub>i</sub>, max<sub>i</sub>]</code>:</p>

<ul>
	<li><code>min<sub>i</sub></code> is the <strong>largest</strong> value in the tree that is smaller than or equal to <code>queries[i]</code>. If a such value does not exist, add <code>-1</code> instead.</li>
	<li><code>max<sub>i</sub></code> is the <strong>smallest</strong> value in the tree that is greater than or equal to <code>queries[i]</code>. If a such value does not exist, add <code>-1</code> instead.</li>
</ul>

<p>Return <em>the array</em> <code>answer</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/09/28/bstreeedrawioo.png" style="width: 261px; height: 281px;" />
<pre>
<strong>Input:</strong> root = [6,2,13,1,4,9,15,null,null,null,null,null,null,14], queries = [2,5,16]
<strong>Output:</strong> [[2,2],[4,6],[15,-1]]
<strong>Explanation:</strong> We answer the queries in the following way:
- The largest number that is smaller or equal than 2 in the tree is 2, and the smallest number that is greater or equal than 2 is still 2. So the answer for the first query is [2,2].
- The largest number that is smaller or equal than 5 in the tree is 4, and the smallest number that is greater or equal than 5 is 6. So the answer for the second query is [4,6].
- The largest number that is smaller or equal than 16 in the tree is 15, and the smallest number that is greater or equal than 16 does not exist. So the answer for the third query is [15,-1].
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/09/28/bstttreee.png" style="width: 101px; height: 121px;" />
<pre>
<strong>Input:</strong> root = [4,null,9], queries = [3]
<strong>Output:</strong> [[-1,4]]
<strong>Explanation:</strong> The largest number that is smaller or equal to 3 in the tree does not exist, and the smallest number that is greater or equal to 3 is 4. So the answer for the query is [-1,4].
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[2, 10<sup>5</sup>]</code>.</li>
	<li><code>1 &lt;= Node.val &lt;= 10<sup>6</sup></code></li>
	<li><code>n == queries.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= queries[i] &lt;= 10<sup>6</sup></code></li>
</ul>

['closest-binary-search-tree-value', 'closest-binary-search-tree-value-ii', 'search-in-a-binary-search-tree']
[]
[{"value": "cpp", "text": "C++", "defaultCode": "/**\n * Definition for a binary tree node.\n * struct TreeNode {\n *     int val;\n *     TreeNode *left;\n *     TreeNode *right;\n *     TreeNode() : val(0), left(nullptr), right(nullptr) {}\n *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}\n *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}\n * };\n */\nclass Solution {\npublic:\n    vector<vector<int>> closestNodes(TreeNode* root, vector<int>& queries) {\n        \n    }\n};"}, {"value": "java", "text": "Java", "defaultCode": "/**\n * Definition for a binary tree node.\n * public class TreeNode {\n *     int val;\n *     TreeNode left;\n *     TreeNode right;\n *     TreeNode() {}\n *     TreeNode(int val) { this.val = val; }\n *     TreeNode(int val, TreeNode left, TreeNode right) {\n *         this.val = val;\n *         this.left = left;\n *         this.right = right;\n *     }\n * }\n */\nclass Solution {\n    public List<List<Integer>> closestNodes(TreeNode root, List<Integer> queries) {\n        \n    }\n}"}, {"value": "python", "text": "Python", "defaultCode": "# Definition for a binary tree node.\n# class TreeNode(object):\n#     def __init__(self, val=0, left=None, right=None):\n#         self.val = val\n#         self.left = left\n#         self.right = right\nclass Solution(object):\n    def closestNodes(self, root, queries):\n        \"\"\"\n        :type root: Optional[TreeNode]\n        :type queries: List[int]\n        :rtype: List[List[int]]\n        \"\"\"\n        "}, {"value": "python3", "text": "Python3", "defaultCode": "# Definition for a binary tree node.\n# class TreeNode:\n#     def __init__(self, val=0, left=None, right=None):\n#         self.val = val\n#         self.left = left\n#         self.right = right\nclass Solution:\n    def closestNodes(self, root: Optional[TreeNode], queries: List[int]) -> List[List[int]]:\n        "}, {"value": "c", "text": "C", "defaultCode": "/**\n * Definition for a binary tree node.\n * struct TreeNode {\n *     int val;\n *     struct TreeNode *left;\n *     struct TreeNode *right;\n * };\n */\n/**\n * Return an array of arrays of size *returnSize.\n * The sizes of the arrays are returned as *returnColumnSizes array.\n * Note: Both returned array and *columnSizes array must be malloced, assume caller calls free().\n */\nint** closestNodes(struct TreeNode* root, int* queries, int queriesSize, int* returnSize, int** returnColumnSizes) {\n    \n}"}, {"value": "csharp", "text": "C#", "defaultCode": "/**\n * Definition for a binary tree node.\n * public class TreeNode {\n *     public int val;\n *     public TreeNode left;\n *     public TreeNode right;\n *     public TreeNode(int val=0, TreeNode left=null, TreeNode right=null) {\n *         this.val = val;\n *         this.left = left;\n *         this.right = right;\n *     }\n * }\n */\npublic class Solution {\n    public IList<IList<int>> ClosestNodes(TreeNode root, IList<int> queries) {\n        \n    }\n}"}, {"value": "javascript", "text": "JavaScript", "defaultCode": "/**\n * Definition for a binary tree node.\n * function TreeNode(val, left, right) {\n *     this.val = (val===undefined ? 0 : val)\n *     this.left = (left===undefined ? null : left)\n *     this.right = (right===undefined ? null : right)\n * }\n */\n/**\n * @param {TreeNode} root\n * @param {number[]} queries\n * @return {number[][]}\n */\nvar closestNodes = function(root, queries) {\n    \n};"}, {"value": "typescript", "text": "TypeScript", "defaultCode": "/**\n * Definition for a binary tree node.\n * class TreeNode {\n *     val: number\n *     left: TreeNode | null\n *     right: TreeNode | null\n *     constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {\n *         this.val = (val===undefined ? 0 : val)\n *         this.left = (left===undefined ? null : left)\n *         this.right = (right===undefined ? null : right)\n *     }\n * }\n */\n\nfunction closestNodes(root: TreeNode | null, queries: number[]): number[][] {\n    \n};"}, {"value": "php", "text": "PHP", "defaultCode": "/**\n * Definition for a binary tree node.\n * class TreeNode {\n *     public $val = null;\n *     public $left = null;\n *     public $right = null;\n *     function __construct($val = 0, $left = null, $right = null) {\n *         $this->val = $val;\n *         $this->left = $left;\n *         $this->right = $right;\n *     }\n * }\n */\nclass Solution {\n\n    /**\n     * @param TreeNode $root\n     * @param Integer[] $queries\n     * @return Integer[][]\n     */\n    function closestNodes($root, $queries) {\n        \n    }\n}"}, {"value": "swift", "text": "Swift", "defaultCode": "/**\n * Definition for a binary tree node.\n * public class TreeNode {\n *     public var val: Int\n *     public var left: TreeNode?\n *     public var right: TreeNode?\n *     public init() { self.val = 0; self.left = nil; self.right = nil; }\n *     public init(_ val: Int) { self.val = val; self.left = nil; self.right = nil; }\n *     public init(_ val: Int, _ left: TreeNode?, _ right: TreeNode?) {\n *         self.val = val\n *         self.left = left\n *         self.right = right\n *     }\n * }\n */\nclass Solution {\n    func closestNodes(_ root: TreeNode?, _ queries: [Int]) -> [[Int]] {\n        \n    }\n}"}, {"value": "kotlin", "text": "Kotlin", "defaultCode": "/**\n * Example:\n * var ti = TreeNode(5)\n * var v = ti.`val`\n * Definition for a binary tree node.\n * class TreeNode(var `val`: Int) {\n *     var left: TreeNode? = null\n *     var right: TreeNode? = null\n * }\n */\nclass Solution {\n    fun closestNodes(root: TreeNode?, queries: List<Int>): List<List<Int>> {\n        \n    }\n}"}, {"value": "dart", "text": "Dart", "defaultCode": "/**\n * Definition for a binary tree node.\n * class TreeNode {\n *   int val;\n *   TreeNode? left;\n *   TreeNode? right;\n *   TreeNode([this.val = 0, this.left, this.right]);\n * }\n */\nclass Solution {\n  List<List<int>> closestNodes(TreeNode? root, List<int> queries) {\n    \n  }\n}"}, {"value": "golang", "text": "Go", "defaultCode": "/**\n * Definition for a binary tree node.\n * type TreeNode struct {\n *     Val int\n *     Left *TreeNode\n *     Right *TreeNode\n * }\n */\nfunc closestNodes(root *TreeNode, queries []int) [][]int {\n    \n}"}, {"value": "ruby", "text": "Ruby", "defaultCode": "# Definition for a binary tree node.\n# class TreeNode\n#     attr_accessor :val, :left, :right\n#     def initialize(val = 0, left = nil, right = nil)\n#         @val = val\n#         @left = left\n#         @right = right\n#     end\n# end\n# @param {TreeNode} root\n# @param {Integer[]} queries\n# @return {Integer[][]}\ndef closest_nodes(root, queries)\n    \nend"}, {"value": "scala", "text": "Scala", "defaultCode": "/**\n * Definition for a binary tree node.\n * class TreeNode(_value: Int = 0, _left: TreeNode = null, _right: TreeNode = null) {\n *   var value: Int = _value\n *   var left: TreeNode = _left\n *   var right: TreeNode = _right\n * }\n */\nobject Solution {\n    def closestNodes(root: TreeNode, queries: List[Int]): List[List[Int]] = {\n        \n    }\n}"}, {"value": "rust", "text": "Rust", "defaultCode": "// Definition for a binary tree node.\n// #[derive(Debug, PartialEq, Eq)]\n// pub struct TreeNode {\n//   pub val: i32,\n//   pub left: Option<Rc<RefCell<TreeNode>>>,\n//   pub right: Option<Rc<RefCell<TreeNode>>>,\n// }\n// \n// impl TreeNode {\n//   #[inline]\n//   pub fn new(val: i32) -> Self {\n//     TreeNode {\n//       val,\n//       left: None,\n//       right: None\n//     }\n//   }\n// }\nuse std::rc::Rc;\nuse std::cell::RefCell;\nimpl Solution {\n    pub fn closest_nodes(root: Option<Rc<RefCell<TreeNode>>>, queries: Vec<i32>) -> Vec<Vec<i32>> {\n        \n    }\n}"}, {"value": "racket", "text": "Racket", "defaultCode": "; Definition for a binary tree node.\n#|\n\n; val : integer?\n; left : (or/c tree-node? #f)\n; right : (or/c tree-node? #f)\n(struct tree-node\n  (val left right) #:mutable #:transparent)\n\n; constructor\n(define (make-tree-node [val 0])\n  (tree-node val #f #f))\n\n|#\n\n(define/contract (closest-nodes root queries)\n  (-> (or/c tree-node? #f) (listof exact-integer?) (listof (listof exact-integer?)))\n  )"}, {"value": "erlang", "text": "Erlang", "defaultCode": "%% Definition for a binary tree node.\n%%\n%% -record(tree_node, {val = 0 :: integer(),\n%%                     left = null  :: 'null' | #tree_node{},\n%%                     right = null :: 'null' | #tree_node{}}).\n\n-spec closest_nodes(Root :: #tree_node{} | null, Queries :: [integer()]) -> [[integer()]].\nclosest_nodes(Root, Queries) ->\n  ."}, {"value": "elixir", "text": "Elixir", "defaultCode": "# Definition for a binary tree node.\n#\n# defmodule TreeNode do\n#   @type t :: %__MODULE__{\n#           val: integer,\n#           left: TreeNode.t() | nil,\n#           right: TreeNode.t() | nil\n#         }\n#   defstruct val: 0, left: nil, right: nil\n# end\n\ndefmodule Solution do\n  @spec closest_nodes(root :: TreeNode.t | nil, queries :: [integer]) :: [[integer]]\n  def closest_nodes(root, queries) do\n    \n  end\nend"}]
{
  "name": "closestNodes",
  "params": [
    {
      "name": "root",
      "type": "TreeNode"
    },
    {
      "type": "list<integer>",
      "name": "queries"
    }
  ],
  "return": {
    "type": "list<list<integer>>"
  }
}
{"cpp": ["C++", "<p>Compiled with <code> clang 19 </code> using the latest C++ 23 standard, and <code>libstdc++</code> provided by GCC 14.</p>\r\n\r\n<p>Your code is compiled with level two optimization (<code>-O2</code>). <a href=\"https://github.com/google/sanitizers/wiki/AddressSanitizer\" target=\"_blank\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\r\n\r\n<p>Most standard library headers are already included automatically for your convenience.</p>"], "java": ["Java", "<p><code>OpenJDK 21</code>. Using compile arguments: <code>--enable-preview --release 21</code></p>\r\n\r\n<p>Most standard library headers are already included automatically for your convenience.</p>\r\n<p>Includes <code>Pair</code> class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.</p>"], "python": ["Python", "<p><code>Python 2.7.18</code>.</p>\r\n\r\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\"https://docs.python.org/2/library/array.html\" target=\"_blank\">array</a>, <a href=\"https://docs.python.org/2/library/bisect.html\" target=\"_blank\">bisect</a>, <a href=\"https://docs.python.org/2/library/collections.html\" target=\"_blank\">collections</a>. If you need more libraries, you can import it yourself.</p>\r\n\r\n<p>For Map/TreeMap data structure, you may use <a href=\"http://www.grantjenks.com/docs/sortedcontainers/\" target=\"_blank\">sortedcontainers</a> library.</p>\r\n\r\n<p>Note that Python 2.7 <a href=\"https://www.python.org/dev/peps/pep-0373/\" target=\"_blank\">is not maintained anymore</a>. For the latest Python, please choose Python3 instead.</p>"], "c": ["C", "<p>Compiled with <code>gcc 14</code> using the gnu11 standard.</p>\r\n\r\n<p>Your code is compiled with level one optimization (<code>-O2</code>). <a href=\"https://github.com/google/sanitizers/wiki/AddressSanitizer\" target=\"_blank\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\r\n\r\n<p>Most standard library headers are already included automatically for your convenience.</p>\r\n\r\n<p>For hash table operations, you may use <a href=\"https://troydhanson.github.io/uthash/\" target=\"_blank\">uthash</a>. \"uthash.h\" is included by default. Below are some examples:</p>\r\n\r\n<p><b>1. Adding an item to a hash.</b>\r\n<pre>\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<p><b>2. Looking up an item in a hash:</b>\r\n<pre>\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<p><b>3. Deleting an item in a hash:</b>\r\n<pre>\r\nvoid delete_user(struct hash_entry *user) {\r\n    HASH_DEL(users, user);  \r\n}\r\n</pre>\r\n</p>"], "csharp": ["C#", "<p><a href=\"https://learn.microsoft.com/en-us/dotnet/csharp/whats-new/csharp-13\" target=\"_blank\">C# 13</a> with .NET 9 runtime</p>"], "javascript": ["JavaScript", "<p><code>Node.js 22.14.0</code>.</p>\r\n\r\n<p>Your code is run with <code>--harmony</code> flag, enabling <a href=\"http://node.green/\" target=\"_blank\">new ES6 features</a>.</p>\r\n\r\n<p><a href=\"https://lodash.com\" target=\"_blank\">lodash.js</a> library is included by default.</p>\r\n\r\n<p>For Priority Queue / Queue data structures, you may use 6.3.2 version of <a href=\"https://github.com/datastructures-js/priority-queue/tree/v6.3.2\" target=\"_blank\">datastructures-js/priority-queue</a> and 4.2.3 version of <a href=\"https://github.com/datastructures-js/queue/tree/v4.2.3\" target=\"_blank\">datastructures-js/queue</a> and 1.0.4 version of <a href=\"https://github.com/datastructures-js/deque/tree/v1.0.4\" target=\"_blank\">datastructures-js/deque</a>.</p>"], "ruby": ["Ruby", "<p><code>Ruby 3.2</code></p>\r\n\r\n<p>Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms</p>"], "swift": ["Swift", "<p><code>Swift 6.0</code>.</p>\r\n\r\n<p>You may use the following packages:<br/>\r\n<a href=\"https://github.com/apple/swift-algorithms/tree/1.2.0\" target=\"_blank\">swift-algorithms 1.2.0</a><br/>\r\n<a href=\"https://github.com/apple/swift-collections/tree/1.1.4\" target=\"_blank\">swift-collections 1.1.4</a><br/>\r\n<a href=\"https://github.com/apple/swift-numerics/tree/1.0.2\" target=\"_blank\">swift-numerics 1.0.2</a></p>"], "golang": ["Go", "<p><code>Go 1.23</code></p>\r\n<p>Support <a href=\"https://pkg.go.dev/github.com/emirpasic/gods@v1.18.1\" target=\"_blank\">https://pkg.go.dev/github.com/emirpasic/gods@v1.18.1</a> and <a href=\"https://pkg.go.dev/github.com/emirpasic/gods/v2@v2.0.0-alpha\" target=\"_blank\">https://pkg.go.dev/github.com/emirpasic/gods/v2@v2.0.0-alpha</a> library.</p>"], "python3": ["Python3", "<p><code>Python 3.11</code>.</p>\r\n\r\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\"https://docs.python.org/3/library/array.html\" target=\"_blank\">array</a>, <a href=\"https://docs.python.org/3/library/bisect.html\" target=\"_blank\">bisect</a>, <a href=\"https://docs.python.org/3/library/collections.html\" target=\"_blank\">collections</a>. If you need more libraries, you can import it yourself.</p>\r\n\r\n<p>For Map/TreeMap data structure, you may use <a href=\"http://www.grantjenks.com/docs/sortedcontainers/\" target=\"_blank\">sortedcontainers</a> library.</p>"], "scala": ["Scala", "<p><code>Scala 3.3.1</code>.</p>"], "kotlin": ["Kotlin", "<p><code>Kotlin 2.1.10</code>.</p>"], "rust": ["Rust", "<p><code>Rust 1.85.0</code>. Your code will be compiled with <code>opt-level</code> 2.</p>\r\n\r\n<p>Supports <a href=\"https://crates.io/crates/rand\" target=\"_blank\">rand v0.8</a> and <a href=\"https://crates.io/crates/regex\" target=\"_blank\">regex\u00a0v1</a> and <a href=\"https://crates.io/crates/itertools\" target=\"_blank\">itertools\u00a0v0.14</a> from crates.io</p>"], "php": ["PHP", "<p><code>PHP 8.2</code>.</p>\r\n<p>With bcmath module</p>"], "typescript": ["Typescript", "<p><code>TypeScript 5.7.3, Node.js 22.14.0</code>.</p>\r\n\r\n<p>Compile Options: <code>--alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2024</code></p>\r\n\r\n<p><a href=\"https://lodash.com\" target=\"_blank\">lodash.js</a> library is included by default.</p>\r\n\r\n<p>For Priority Queue / Queue data structures, you may use 6.3.2 version of <a href=\"https://github.com/datastructures-js/priority-queue/tree/v6.3.2\" target=\"_blank\">datastructures-js/priority-queue</a> and 4.2.3 version of <a href=\"https://github.com/datastructures-js/queue/tree/v4.2.3\" target=\"_blank\">datastructures-js/queue</a> and 1.0.4 version of <a href=\"https://github.com/datastructures-js/deque/tree/v1.0.4\" target=\"_blank\">datastructures-js/deque</a>.</p>"], "racket": ["Racket", "<p><a href=\"https://docs.racket-lang.org/guide/performance.html#%28tech._c%29\" target=\"_blank\">Racket CS</a> v8.15</p>\r\n\r\n<p>Using <code>#lang racket</code></p>\r\n\r\n<p>Required <code>data/gvector data/queue data/order data/heap</code> automatically for your convenience</p>"], "erlang": ["Erlang", "Erlang/OTP 26"], "elixir": ["Elixir", "Elixir 1.17 with Erlang/OTP 26"], "dart": ["Dart", "<p>Dart 3.2. You may use package <a href=\"https://pub.dev/packages/collection/versions/1.18.0\" target=\"_blank\">collection</a></p>\r\n\r\n<p>Your code will be run directly without compiling</p>"]}
['Array', 'Binary Search', 'Tree', 'Depth-First Search', 'Binary Search Tree', 'Binary Tree']