"content":"<p>You are given an array <code>pairs</code>, where <code>pairs[i] = [x<sub>i</sub>, y<sub>i</sub>]</code>, and:</p>\n\n<ul>\n\t<li>There are no duplicates.</li>\n\t<li><code>x<sub>i</sub> < y<sub>i</sub></code></li>\n</ul>\n\n<p>Let <code>ways</code> be the number of rooted trees that satisfy the following conditions:</p>\n\n<ul>\n\t<li>The tree consists of nodes whose values appeared in <code>pairs</code>.</li>\n\t<li>A pair <code>[x<sub>i</sub>, y<sub>i</sub>]</code> exists in <code>pairs</code> <strong>if and only if</strong> <code>x<sub>i</sub></code> is an ancestor of <code>y<sub>i</sub></code> or <code>y<sub>i</sub></code> is an ancestor of <code>x<sub>i</sub></code>.</li>\n\t<li><strong>Note:</strong> the tree does not have to be a binary tree.</li>\n</ul>\n\n<p>Two ways are considered to be different if there is at least one node that has different parents in both ways.</p>\n\n<p>Return:</p>\n\n<ul>\n\t<li><code>0</code> if <code>ways == 0</code></li>\n\t<li><code>1</code> if <code>ways == 1</code></li>\n\t<li><code>2</code> if <code>ways > 1</code></li>\n</ul>\n\n<p>A <strong>rooted tree</strong> is a tree that has a single root node, and all edges are oriented to be outgoing from the root.</p>\n\n<p>An <strong>ancestor</strong> of a node is any node on the path from the root to that node (excluding the node itself). The root has no ancestors.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img src=\"https://assets.leetcode.com/uploads/2020/12/03/trees2.png\" style=\"width: 208px; height: 221px;\" />\n<pre>\n<strong>Input:</strong> pairs = [[1,2],[2,3]]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> There is exactly one valid rooted tree, which is shown in the above figure.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/12/03/tree.png\" style=\"width: 234px; height: 241px;\" />\n<pre>\n<strong>Input:</strong> pairs = [[1,2],[2,3],[1,3]]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> There are multiple valid rooted trees. Three of them are shown in the above figures.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> pairs = [[1,2],[2,3],[2,4],[1,5]]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> There are no valid rooted trees.</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= pairs.length <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= x<sub>i </sub>< y<sub>i</sub> <= 500</code></li>\n\t<li>The elements in <code>pairs</code> are unique.</li>\n</ul>\n",
"similarQuestions":"[{\"title\": \"Create Binary Tree From Descriptions\", \"titleSlug\": \"create-binary-tree-from-descriptions\", \"difficulty\": \"Medium\", \"translatedTitle\": null}, {\"title\": \"Maximum Star Sum of a Graph\", \"titleSlug\": \"maximum-star-sum-of-a-graph\", \"difficulty\": \"Medium\", \"translatedTitle\": null}]",
"Think inductively. The first step is to get the root. Obviously, the root should be in pairs with all the nodes. If there isn't exactly one such node, then there are 0 ways.",
"The number of pairs involving a node must be less than or equal to that number of its parent.",
"Actually, if it's equal, then there is not exactly 1 way, because they can be swapped.",
"Recursively, given a set of nodes, get the node with the most pairs, then this must be a root and have no parents in the current set of nodes."
"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
