leetcode-problemset/leetcode/originData/maximum-score-of-a-node-sequence.json

{
    "data": {
        "question": {
            "questionId": "2353",
            "questionFrontendId": "2242",
            "boundTopicId": null,
            "title": "Maximum Score of a Node Sequence",
            "titleSlug": "maximum-score-of-a-node-sequence",
            "content": "<p>There is an <strong>undirected</strong> graph with <code>n</code> nodes, numbered from <code>0</code> to <code>n - 1</code>.</p>\n\n<p>You are given a <strong>0-indexed</strong> integer array <code>scores</code> of length <code>n</code> where <code>scores[i]</code> denotes the score of node <code>i</code>. You are also given a 2D integer array <code>edges</code> where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> denotes that there exists an <strong>undirected</strong> edge connecting nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code>.</p>\n\n<p>A node sequence is <b>valid</b> if it meets the following conditions:</p>\n\n<ul>\n\t<li>There is an edge connecting every pair of <strong>adjacent</strong> nodes in the sequence.</li>\n\t<li>No node appears more than once in the sequence.</li>\n</ul>\n\n<p>The score of a node sequence is defined as the <strong>sum</strong> of the scores of the nodes in the sequence.</p>\n\n<p>Return <em>the <strong>maximum score</strong> of a valid node sequence with a length of </em><code>4</code><em>. </em>If no such sequence exists, return<em> </em><code>-1</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/04/15/ex1new3.png\" style=\"width: 290px; height: 215px;\" />\n<pre>\n<strong>Input:</strong> scores = [5,2,9,8,4], edges = [[0,1],[1,2],[2,3],[0,2],[1,3],[2,4]]\n<strong>Output:</strong> 24\n<strong>Explanation:</strong> The figure above shows the graph and the chosen node sequence [0,1,2,3].\nThe score of the node sequence is 5 + 2 + 9 + 8 = 24.\nIt can be shown that no other node sequence has a score of more than 24.\nNote that the sequences [3,1,2,0] and [1,0,2,3] are also valid and have a score of 24.\nThe sequence [0,3,2,4] is not valid since no edge connects nodes 0 and 3.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/03/17/ex2.png\" style=\"width: 333px; height: 151px;\" />\n<pre>\n<strong>Input:</strong> scores = [9,20,6,4,11,12], edges = [[0,3],[5,3],[2,4],[1,3]]\n<strong>Output:</strong> -1\n<strong>Explanation:</strong> The figure above shows the graph.\nThere are no valid node sequences of length 4, so we return -1.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == scores.length</code></li>\n\t<li><code>4 &lt;= n &lt;= 5 * 10<sup>4</sup></code></li>\n\t<li><code>1 &lt;= scores[i] &lt;= 10<sup>8</sup></code></li>\n\t<li><code>0 &lt;= edges.length &lt;= 5 * 10<sup>4</sup></code></li>\n\t<li><code>edges[i].length == 2</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt;= n - 1</code></li>\n\t<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>\n\t<li>There are no duplicate edges.</li>\n</ul>\n",
            "translatedTitle": null,
            "translatedContent": null,
            "isPaidOnly": false,
            "difficulty": "Hard",
            "likes": 207,
            "dislikes": 2,
            "isLiked": null,
            "similarQuestions": "[{\"title\": \"Get the Maximum Score\", \"titleSlug\": \"get-the-maximum-score\", \"difficulty\": \"Hard\", \"translatedTitle\": null}]",
            "exampleTestcases": "[5,2,9,8,4]\n[[0,1],[1,2],[2,3],[0,2],[1,3],[2,4]]\n[9,20,6,4,11,12]\n[[0,3],[5,3],[2,4],[1,3]]",
            "categoryTitle": "Algorithms",
            "contributors": [],
            "topicTags": [
                {
                    "name": "Array",
                    "slug": "array",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                },
                {
                    "name": "Graph",
                    "slug": "graph",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                },
                {
                    "name": "Sorting",
                    "slug": "sorting",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                },
                {
                    "name": "Enumeration",
                    "slug": "enumeration",
                    "translatedName": null,
                    "__typename": "TopicTagNode"
                }
            ],
            "companyTagStats": null,
            "codeSnippets": [
                {
                    "lang": "C++",
                    "langSlug": "cpp",
                    "code": "class Solution {\npublic:\n    int maximumScore(vector<int>& scores, vector<vector<int>>& edges) {\n        \n    }\n};",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Java",
                    "langSlug": "java",
                    "code": "class Solution {\n    public int maximumScore(int[] scores, int[][] edges) {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Python",
                    "langSlug": "python",
                    "code": "class Solution(object):\n    def maximumScore(self, scores, edges):\n        \"\"\"\n        :type scores: List[int]\n        :type edges: List[List[int]]\n        :rtype: int\n        \"\"\"\n        ",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Python3",
                    "langSlug": "python3",
                    "code": "class Solution:\n    def maximumScore(self, scores: List[int], edges: List[List[int]]) -> int:\n        ",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "C",
                    "langSlug": "c",
                    "code": "\n\nint maximumScore(int* scores, int scoresSize, int** edges, int edgesSize, int* edgesColSize){\n\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "C#",
                    "langSlug": "csharp",
                    "code": "public class Solution {\n    public int MaximumScore(int[] scores, int[][] edges) {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "JavaScript",
                    "langSlug": "javascript",
                    "code": "/**\n * @param {number[]} scores\n * @param {number[][]} edges\n * @return {number}\n */\nvar maximumScore = function(scores, edges) {\n    \n};",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Ruby",
                    "langSlug": "ruby",
                    "code": "# @param {Integer[]} scores\n# @param {Integer[][]} edges\n# @return {Integer}\ndef maximum_score(scores, edges)\n    \nend",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Swift",
                    "langSlug": "swift",
                    "code": "class Solution {\n    func maximumScore(_ scores: [Int], _ edges: [[Int]]) -> Int {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Go",
                    "langSlug": "golang",
                    "code": "func maximumScore(scores []int, edges [][]int) int {\n    \n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Scala",
                    "langSlug": "scala",
                    "code": "object Solution {\n    def maximumScore(scores: Array[Int], edges: Array[Array[Int]]): Int = {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Kotlin",
                    "langSlug": "kotlin",
                    "code": "class Solution {\n    fun maximumScore(scores: IntArray, edges: Array<IntArray>): Int {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Rust",
                    "langSlug": "rust",
                    "code": "impl Solution {\n    pub fn maximum_score(scores: Vec<i32>, edges: Vec<Vec<i32>>) -> i32 {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "PHP",
                    "langSlug": "php",
                    "code": "class Solution {\n\n    /**\n     * @param Integer[] $scores\n     * @param Integer[][] $edges\n     * @return Integer\n     */\n    function maximumScore($scores, $edges) {\n        \n    }\n}",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "TypeScript",
                    "langSlug": "typescript",
                    "code": "function maximumScore(scores: number[], edges: number[][]): number {\n\n};",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Racket",
                    "langSlug": "racket",
                    "code": "(define/contract (maximum-score scores edges)\n  (-> (listof exact-integer?) (listof (listof exact-integer?)) exact-integer?)\n\n  )",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Erlang",
                    "langSlug": "erlang",
                    "code": "-spec maximum_score(Scores :: [integer()], Edges :: [[integer()]]) -> integer().\nmaximum_score(Scores, Edges) ->\n  .",
                    "__typename": "CodeSnippetNode"
                },
                {
                    "lang": "Elixir",
                    "langSlug": "elixir",
                    "code": "defmodule Solution do\n  @spec maximum_score(scores :: [integer], edges :: [[integer]]) :: integer\n  def maximum_score(scores, edges) do\n\n  end\nend",
                    "__typename": "CodeSnippetNode"
                }
            ],
            "stats": "{\"totalAccepted\": \"3.1K\", \"totalSubmission\": \"10.4K\", \"totalAcceptedRaw\": 3103, \"totalSubmissionRaw\": 10426, \"acRate\": \"29.8%\"}",
            "hints": [
                "For every node sequence of length 4, there are 3 relevant edges. How can we consider valid triplets of edges?",
                "Fix the middle 2 nodes connected by an edge in the node sequence. Can you determine the other 2 nodes that will give the highest possible score?",
                "The other 2 nodes must each be connected to one of the middle nodes. If we only consider nodes with the highest scores, how many should we store to ensure we don’t choose duplicate nodes?",
                "For each node, we should store the 3 adjacent nodes with the highest scores to ensure we can find a sequence with no duplicate nodes via the method above."
            ],
            "solution": null,
            "status": null,
            "sampleTestCase": "[5,2,9,8,4]\n[[0,1],[1,2],[2,3],[0,2],[1,3],[2,4]]",
            "metaData": "{\n  \"name\": \"maximumScore\",\n  \"params\": [\n    {\n      \"type\": \"integer[]\",\n      \"name\": \"scores\"\n    },\n    {\n      \"type\": \"integer[][]\",\n      \"name\": \"edges\"\n    }\n  ],\n  \"return\": {\n    \"type\": \"integer\"\n  }\n}",
            "judgerAvailable": true,
            "judgeType": "large",
            "mysqlSchemas": [],
            "enableRunCode": true,
            "enableTestMode": false,
            "enableDebugger": true,
            "envInfo": "{\"cpp\": [\"C++\", \"<p>Compiled with <code> clang 11 </code> using the latest C++ 17 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 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>. 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 2.13.7</code>.</p>\"], \"kotlin\": [\"Kotlin\", \"<p><code>Kotlin 1.3.10</code>.</p>\"], \"rust\": [\"Rust\", \"<p><code>Rust 1.58.1</code></p>\\r\\n\\r\\n<p>Supports <a href=\\\"https://crates.io/crates/rand\\\" target=\\\"_blank\\\">rand </a> v0.6\\u00a0from crates.io</p>\"], \"php\": [\"PHP\", \"<p><code>PHP 8.1</code>.</p>\\r\\n<p>With bcmath module</p>\"], \"typescript\": [\"Typescript\", \"<p><code>TypeScript 4.5.4, 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 ES2020 features</a>.</p>\\r\\n\\r\\n<p><a href=\\\"https://lodash.com\\\" target=\\\"_blank\\\">lodash.js</a> library is included by default.</p>\"], \"racket\": [\"Racket\", \"<p>Run with <code>Racket 8.3</code>.</p>\"], \"erlang\": [\"Erlang\", \"Erlang/OTP 24.2\"], \"elixir\": [\"Elixir\", \"Elixir 1.13.0 with Erlang/OTP 24.2\"]}",
            "libraryUrl": null,
            "adminUrl": null,
            "challengeQuestion": null,
            "__typename": "QuestionNode"
        }
    }
}