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        "question": {
            "questionId": "1986",
            "questionFrontendId": "1857",
            "boundTopicId": null,
            "title": "Largest Color Value in a Directed Graph",
            "titleSlug": "largest-color-value-in-a-directed-graph",
            "content": "<p>There is a <strong>directed graph</strong> of <code>n</code> colored nodes and <code>m</code> edges. The nodes are numbered from <code>0</code> to <code>n - 1</code>.</p>\r\n\r\n<p>You are given a string <code>colors</code> where <code>colors[i]</code> is a lowercase English letter representing the <strong>color</strong> of the <code>i<sup>th</sup></code> node in this graph (<strong>0-indexed</strong>). You are also given a 2D array <code>edges</code> where <code>edges[j] = [a<sub>j</sub>, b<sub>j</sub>]</code> indicates that there is a <strong>directed edge</strong> from node <code>a<sub>j</sub></code> to node <code>b<sub>j</sub></code>.</p>\r\n\r\n<p>A valid <strong>path</strong> in the graph is a sequence of nodes <code>x<sub>1</sub> -&gt; x<sub>2</sub> -&gt; x<sub>3</sub> -&gt; ... -&gt; x<sub>k</sub></code> such that there is a directed edge from <code>x<sub>i</sub></code> to <code>x<sub>i+1</sub></code> for every <code>1 &lt;= i &lt; k</code>. The <strong>color value</strong> of the path is the number of nodes that are colored the <strong>most frequently</strong> occurring color along that path.</p>\r\n\r\n<p>Return <em>the <strong>largest color value</strong> of any valid path in the given graph, or </em><code>-1</code><em> if the graph contains a cycle</em>.</p>\r\n\r\n<p>&nbsp;</p>\r\n<p><strong>Example 1:</strong></p>\r\n\r\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/04/21/leet1.png\" style=\"width: 400px; height: 182px;\" /></p>\r\n\r\n<pre>\r\n<strong>Input:</strong> colors = &quot;abaca&quot;, edges = [[0,1],[0,2],[2,3],[3,4]]\r\n<strong>Output:</strong> 3\r\n<strong>Explanation:</strong> The path 0 -&gt; 2 -&gt; 3 -&gt; 4 contains 3 nodes that are colored <code>&quot;a&quot; (red in the above image)</code>.\r\n</pre>\r\n\r\n<p><strong>Example 2:</strong></p>\r\n\r\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/04/21/leet2.png\" style=\"width: 85px; height: 85px;\" /></p>\r\n\r\n<pre>\r\n<strong>Input:</strong> colors = &quot;a&quot;, edges = [[0,0]]\r\n<strong>Output:</strong> -1\r\n<strong>Explanation:</strong> There is a cycle from 0 to 0.\r\n</pre>\r\n\r\n<p>&nbsp;</p>\r\n<p><strong>Constraints:</strong></p>\r\n\r\n<ul>\r\n\t<li><code>n == colors.length</code></li>\r\n\t<li><code>m == edges.length</code></li>\r\n\t<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>\r\n\t<li><code>0 &lt;= m &lt;= 10<sup>5</sup></code></li>\r\n\t<li><code>colors</code> consists of lowercase English letters.</li>\r\n\t<li><code>0 &lt;= a<sub>j</sub>, b<sub>j</sub>&nbsp;&lt; n</code></li>\r\n</ul>",
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            "exampleTestcases": "\"abaca\"\n[[0,1],[0,2],[2,3],[3,4]]\n\"a\"\n[[0,0]]",
            "categoryTitle": "Algorithms",
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                    "name": "Hash Table",
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                    "name": "Topological Sort",
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                    "lang": "C++",
                    "langSlug": "cpp",
                    "code": "class Solution {\r\npublic:\r\n    int largestPathValue(string colors, vector<vector<int>>& edges) {\r\n        \r\n    }\r\n};",
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                    "lang": "Java",
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                    "code": "class Solution {\r\n    public int largestPathValue(String colors, int[][] edges) {\r\n        \r\n    }\r\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Python",
                    "langSlug": "python",
                    "code": "class Solution(object):\r\n    def largestPathValue(self, colors, edges):\r\n        \"\"\"\r\n        :type colors: str\r\n        :type edges: List[List[int]]\r\n        :rtype: int\r\n        \"\"\"",
                    "__typename": "CodeSnippetNode"
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                    "lang": "Python3",
                    "langSlug": "python3",
                    "code": "class Solution:\r\n    def largestPathValue(self, colors: str, edges: List[List[int]]) -> int:",
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                {
                    "lang": "C",
                    "langSlug": "c",
                    "code": "int largestPathValue(char * colors, int** edges, int edgesSize, int* edgesColSize){\r\n\r\n}",
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                    "lang": "C#",
                    "langSlug": "csharp",
                    "code": "public class Solution {\r\n    public int LargestPathValue(string colors, int[][] edges) {\r\n        \r\n    }\r\n}",
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                    "lang": "JavaScript",
                    "langSlug": "javascript",
                    "code": "/**\r\n * @param {string} colors\r\n * @param {number[][]} edges\r\n * @return {number}\r\n */\r\nvar largestPathValue = function(colors, edges) {\r\n    \r\n};",
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                    "lang": "Ruby",
                    "langSlug": "ruby",
                    "code": "# @param {String} colors\r\n# @param {Integer[][]} edges\r\n# @return {Integer}\r\ndef largest_path_value(colors, edges)\r\n    \r\nend",
                    "__typename": "CodeSnippetNode"
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                    "lang": "Swift",
                    "langSlug": "swift",
                    "code": "class Solution {\r\n    func largestPathValue(_ colors: String, _ edges: [[Int]]) -> Int {\r\n        \r\n    }\r\n}",
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                    "lang": "Go",
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                    "code": "func largestPathValue(colors string, edges [][]int) int {\r\n    \r\n}",
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                    "lang": "Scala",
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                    "code": "object Solution {\r\n    def largestPathValue(colors: String, edges: Array[Array[Int]]): Int = {\r\n        \r\n    }\r\n}",
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                    "lang": "Kotlin",
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                    "code": "class Solution {\r\n    fun largestPathValue(colors: String, edges: Array<IntArray>): Int {\r\n        \r\n    }\r\n}",
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                {
                    "lang": "Rust",
                    "langSlug": "rust",
                    "code": "impl Solution {\r\n    pub fn largest_path_value(colors: String, edges: Vec<Vec<i32>>) -> i32 {\r\n        \r\n    }\r\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "PHP",
                    "langSlug": "php",
                    "code": "class Solution {\r\n\r\n    /**\r\n     * @param String $colors\r\n     * @param Integer[][] $edges\r\n     * @return Integer\r\n     */\r\n    function largestPathValue($colors, $edges) {\r\n        \r\n    }\r\n}",
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                    "lang": "TypeScript",
                    "langSlug": "typescript",
                    "code": "function largestPathValue(colors: string, edges: number[][]): number {\r\n\r\n};",
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                    "lang": "Racket",
                    "langSlug": "racket",
                    "code": "(define/contract (largest-path-value colors edges)\r\n  (-> string? (listof (listof exact-integer?)) exact-integer?)\r\n\r\n  )",
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            "hints": [
                "Use topological sort.",
                "let dp[u][c] := the maximum count of vertices with color c of any path starting from vertex u. (by JerryJin2905)"
            ],
            "solution": null,
            "status": null,
            "sampleTestCase": "\"abaca\"\n[[0,1],[0,2],[2,3],[3,4]]",
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For the latest Python, please choose Python3 instead.</p>\"], \"c\": [\"C\", \"<p>Compiled with <code>gcc 8.2</code> using the gnu99 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://docs.microsoft.com/en-us/dotnet/csharp/whats-new/csharp-9\\\" target=\\\"_blank\\\">C# 10 with .NET 6 runtime</a></p>\\r\\n\\r\\n<p>Your code is compiled with debug flag enabled (<code>/debug</code>).</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 <a href=\\\"https://github.com/datastructures-js/priority-queue\\\" target=\\\"_blank\\\">datastructures-js/priority-queue</a> and <a href=\\\"https://github.com/datastructures-js/queue\\\" target=\\\"_blank\\\">datastructures-js/queue</a>.</p>\"], \"ruby\": [\"Ruby\", \"<p><code>Ruby 3.1</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 5.5.2</code>.</p>\"], \"golang\": [\"Go\", \"<p><code>Go 1.17.6</code>.</p>\\r\\n\\r\\n<p>Support <a href=\\\"https://godoc.org/github.com/emirpasic/gods\\\" target=\\\"_blank\\\">https://godoc.org/github.com/emirpasic/gods</a> library.</p>\"], \"python3\": [\"Python3\", \"<p><code>Python 3.10</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>. 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