Remove Max Number of Edges to Keep Graph Fully Traversable
<p>Alice and Bob have an undirected graph of <code>n</code> nodes and three types of edges:</p>

<ul>
	<li>Type 1: Can be traversed by Alice only.</li>
	<li>Type 2: Can be traversed by Bob only.</li>
	<li>Type 3: Can be traversed by both Alice and Bob.</li>
</ul>

<p>Given an array <code>edges</code> where <code>edges[i] = [type<sub>i</sub>, u<sub>i</sub>, v<sub>i</sub>]</code> represents a bidirectional edge of type <code>type<sub>i</sub></code> between nodes <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code>, find the maximum number of edges you can remove so that after removing the edges, the graph can still be fully traversed by both Alice and Bob. The graph is fully traversed by Alice and Bob if starting from any node, they can reach all other nodes.</p>

<p>Return <em>the maximum number of edges you can remove, or return</em> <code>-1</code> <em>if Alice and Bob cannot fully traverse the graph.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2020/08/19/ex1.png" style="width: 179px; height: 191px;" /></strong></p>

<pre>
<strong>Input:</strong> n = 4, edges = [[3,1,2],[3,2,3],[1,1,3],[1,2,4],[1,1,2],[2,3,4]]
<strong>Output:</strong> 2
<strong>Explanation: </strong>If we remove the 2 edges [1,1,2] and [1,1,3]. The graph will still be fully traversable by Alice and Bob. Removing any additional edge will not make it so. So the maximum number of edges we can remove is 2.
</pre>

<p><strong class="example">Example 2:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2020/08/19/ex2.png" style="width: 178px; height: 190px;" /></strong></p>

<pre>
<strong>Input:</strong> n = 4, edges = [[3,1,2],[3,2,3],[1,1,4],[2,1,4]]
<strong>Output:</strong> 0
<strong>Explanation: </strong>Notice that removing any edge will not make the graph fully traversable by Alice and Bob.
</pre>

<p><strong class="example">Example 3:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2020/08/19/ex3.png" style="width: 178px; height: 190px;" /></strong></p>

<pre>
<strong>Input:</strong> n = 4, edges = [[3,2,3],[1,1,2],[2,3,4]]
<strong>Output:</strong> -1
<b>Explanation: </b>In the current graph, Alice cannot reach node 4 from the other nodes. Likewise, Bob cannot reach 1. Therefore it&#39;s impossible to make the graph fully traversable.</pre>

<p>&nbsp;</p>

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

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= edges.length &lt;= min(10<sup>5</sup>, 3 * n * (n - 1) / 2)</code></li>
	<li><code>edges[i].length == 3</code></li>
	<li><code>1 &lt;= type<sub>i</sub> &lt;= 3</code></li>
	<li><code>1 &lt;= u<sub>i</sub> &lt; v<sub>i</sub> &lt;= n</code></li>
	<li>All tuples <code>(type<sub>i</sub>, u<sub>i</sub>, v<sub>i</sub>)</code> are distinct.</li>
</ul>

[]
[]
[{"value": "cpp", "text": "C++", "defaultCode": "class Solution {\npublic:\n    int maxNumEdgesToRemove(int n, vector<vector<int>>& edges) {\n        \n    }\n};"}, {"value": "java", "text": "Java", "defaultCode": "class Solution {\n    public int maxNumEdgesToRemove(int n, int[][] edges) {\n        \n    }\n}"}, {"value": "python", "text": "Python", "defaultCode": "class Solution(object):\n    def maxNumEdgesToRemove(self, n, edges):\n        \"\"\"\n        :type n: int\n        :type edges: List[List[int]]\n        :rtype: int\n        \"\"\"\n        "}, {"value": "python3", "text": "Python3", "defaultCode": "class Solution:\n    def maxNumEdgesToRemove(self, n: int, edges: List[List[int]]) -> int:\n        "}, {"value": "c", "text": "C", "defaultCode": "int maxNumEdgesToRemove(int n, int** edges, int edgesSize, int* edgesColSize) {\n    \n}"}, {"value": "csharp", "text": "C#", "defaultCode": "public class Solution {\n    public int MaxNumEdgesToRemove(int n, int[][] edges) {\n        \n    }\n}"}, {"value": "javascript", "text": "JavaScript", "defaultCode": "/**\n * @param {number} n\n * @param {number[][]} edges\n * @return {number}\n */\nvar maxNumEdgesToRemove = function(n, edges) {\n    \n};"}, {"value": "typescript", "text": "TypeScript", "defaultCode": "function maxNumEdgesToRemove(n: number, edges: number[][]): number {\n    \n};"}, {"value": "php", "text": "PHP", "defaultCode": "class Solution {\n\n    /**\n     * @param Integer $n\n     * @param Integer[][] $edges\n     * @return Integer\n     */\n    function maxNumEdgesToRemove($n, $edges) {\n        \n    }\n}"}, {"value": "swift", "text": "Swift", "defaultCode": "class Solution {\n    func maxNumEdgesToRemove(_ n: Int, _ edges: [[Int]]) -> Int {\n        \n    }\n}"}, {"value": "kotlin", "text": "Kotlin", "defaultCode": "class Solution {\n    fun maxNumEdgesToRemove(n: Int, edges: Array<IntArray>): Int {\n        \n    }\n}"}, {"value": "dart", "text": "Dart", "defaultCode": "class Solution {\n  int maxNumEdgesToRemove(int n, List<List<int>> edges) {\n    \n  }\n}"}, {"value": "golang", "text": "Go", "defaultCode": "func maxNumEdgesToRemove(n int, edges [][]int) int {\n    \n}"}, {"value": "ruby", "text": "Ruby", "defaultCode": "# @param {Integer} n\n# @param {Integer[][]} edges\n# @return {Integer}\ndef max_num_edges_to_remove(n, edges)\n    \nend"}, {"value": "scala", "text": "Scala", "defaultCode": "object Solution {\n    def maxNumEdgesToRemove(n: Int, edges: Array[Array[Int]]): Int = {\n        \n    }\n}"}, {"value": "rust", "text": "Rust", "defaultCode": "impl Solution {\n    pub fn max_num_edges_to_remove(n: i32, edges: Vec<Vec<i32>>) -> i32 {\n        \n    }\n}"}, {"value": "racket", "text": "Racket", "defaultCode": "(define/contract (max-num-edges-to-remove n edges)\n  (-> exact-integer? (listof (listof exact-integer?)) exact-integer?)\n  )"}, {"value": "erlang", "text": "Erlang", "defaultCode": "-spec max_num_edges_to_remove(N :: integer(), Edges :: [[integer()]]) -> integer().\nmax_num_edges_to_remove(N, Edges) ->\n  ."}, {"value": "elixir", "text": "Elixir", "defaultCode": "defmodule Solution do\n  @spec max_num_edges_to_remove(n :: integer, edges :: [[integer]]) :: integer\n  def max_num_edges_to_remove(n, edges) do\n    \n  end\nend"}]
{
  "name": "maxNumEdgesToRemove",
  "params": [
    {
      "name": "n",
      "type": "integer"
    },
    {
      "type": "integer[][]",
      "name": "edges"
    }
  ],
  "return": {
    "type": "integer"
  }
}
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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>. 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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>"]}
['Union Find', 'Graph']