"content":"<p>Alice has an undirected tree with <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>. The tree is represented as a 2D integer array <code>edges</code> of length <code>n - 1</code> where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is an edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> in the tree.</p>\n\n<p>Alice wants Bob to find the root of the tree. She allows Bob to make several <strong>guesses</strong> about her tree. In one guess, he does the following:</p>\n\n<ul>\n\t<li>Chooses two <strong>distinct</strong> integers <code>u</code> and <code>v</code> such that there exists an edge <code>[u, v]</code> in the tree.</li>\n\t<li>He tells Alice that <code>u</code> is the <strong>parent</strong> of <code>v</code> in the tree.</li>\n</ul>\n\n<p>Bob's guesses are represented by a 2D integer array <code>guesses</code> where <code>guesses[j] = [u<sub>j</sub>, v<sub>j</sub>]</code> indicates Bob guessed <code>u<sub>j</sub></code> to be the parent of <code>v<sub>j</sub></code>.</p>\n\n<p>Alice being lazy, does not reply to each of Bob's guesses, but just says that <strong>at least</strong> <code>k</code> of his guesses are <code>true</code>.</p>\n\n<p>Given the 2D integer arrays <code>edges</code>, <code>guesses</code> and the integer <code>k</code>, return <em>the <strong>number of possible nodes</strong> that can be the root of Alice's tree</em>. If there is no such tree, return <code>0</code>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/12/19/ex-1.png\" style=\"width: 727px; height: 250px;\" /></p>\n\n<pre>\n<strong>Input:</strong> edges = [[0,1],[1,2],[1,3],[4,2]], guesses = [[1,3],[0,1],[1,0],[2,4]], k = 3\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> \nRoot = 0, correct guesses = [1,3], [0,1], [2,4]\nRoot = 1, correct guesses = [1,3], [1,0], [2,4]\nRoot = 2, correct guesses = [1,3], [1,0], [2,4]\nRoot = 3, correct guesses = [1,0], [2,4]\nRoot = 4, correct guesses = [1,3], [1,0]\nConsidering 0, 1, or 2 as root node leads to 3 correct guesses.\n\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/12/19/ex-2.png\" style=\"width: 600px; height: 303px;\" /></p>\n\n<pre>\n<strong>Input:</strong> edges = [[0,1],[1,2],[2,3],[3,4]], guesses = [[1,0],[3,4],[2,1],[3,2]], k = 1\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> \nRoot = 0, correct guesses = [3,4]\nRoot = 1, correct guesses = [1,0], [3,4]\nRoot = 2, correct guesses = [1,0], [2,1], [3,4]\nRoot = 3, correct guesses = [1,0], [2,1], [3,2], [3,4]\nRoot = 4, correct guesses = [1,0], [2,1], [3,2]\nConsidering any node as root will give at least 1 correct guess. \n\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>edges.length == n - 1</code></li>\n\t<li><code>2 <= n <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= guesses.length <= 10<sup>5</sup></code></li>\n\t<li><code>0 <= a<sub>i</sub>, b<sub>i</sub>, u<sub>j</sub>, v<sub>j</sub> <= n - 1</code></li>\n\t<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>\n\t<li><code>u<sub>j</sub> != v<sub>j</sub></code></li>\n\t<li><code>edges</code> represents a valid tree.</li>\n\t<li><code>guesses[j]</code> is an edge of the tree.</li>\n\t<li><code>guesses</code> is unique.</li>\n\t<li><code>0 <= k <= guesses.length</code></li>\n</ul>\n",
"envInfo":"{\"cpp\": [\"C++\", \"<p>Compiled with <code> clang 11 </code> using the latest C++ 20 standard.</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 17</code>. Java 8 features such as lambda expressions and stream API can be used. </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 2.7.12</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\\\">will not be maintained past 2020</a>. For the latest Python, please choose Python3 instead.</p>\"], \"c\": [\"C\", \"<p>Compiled with <code>gcc 8.2</code> using the gnu11 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level one optimization (<code>-O1</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-10\\\" target=\\\"_blank\\\">C# 10 with .NET 6 runtime</a></p>\"], \"javascript\": [\"JavaScript\", \"<p><code>Node.js 16.13.2</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 5.3.0 version of <a href=\\\"https://github.com/datastructures-js/priority-queue/tree/fb4fdb984834421279aeb081df7af624d17c2a03\\\" target=\\\"_blank\\\">datastructures-js/priority-queue</a> and 4.2.1 version of <a href=\\\"https://githu
