{ "data": { "question": { "questionId": "2189", "questionFrontendId": "2065", "boundTopicId": null, "title": "Maximum Path Quality of a Graph", "titleSlug": "maximum-path-quality-of-a-graph", "content": "<p>There is an <strong>undirected</strong> graph with <code>n</code> nodes numbered from <code>0</code> to <code>n - 1</code> (<strong>inclusive</strong>). You are given a <strong>0-indexed</strong> integer array <code>values</code> where <code>values[i]</code> is the <strong>value </strong>of the <code>i<sup>th</sup></code> node. You are also given a <strong>0-indexed</strong> 2D integer array <code>edges</code>, where each <code>edges[j] = [u<sub>j</sub>, v<sub>j</sub>, time<sub>j</sub>]</code> indicates that there is an undirected edge between the nodes <code>u<sub>j</sub></code> and <code>v<sub>j</sub></code>,<sub> </sub>and it takes <code>time<sub>j</sub></code> seconds to travel between the two nodes. Finally, you are given an integer <code>maxTime</code>.</p>\n\n<p>A <strong>valid</strong> <strong>path</strong> in the graph is any path that starts at node <code>0</code>, ends at node <code>0</code>, and takes <strong>at most</strong> <code>maxTime</code> seconds to complete. You may visit the same node multiple times. The <strong>quality</strong> of a valid path is the <strong>sum</strong> of the values of the <strong>unique nodes</strong> visited in the path (each node's value is added <strong>at most once</strong> to the sum).</p>\n\n<p>Return <em>the <strong>maximum</strong> quality of a valid path</em>.</p>\n\n<p><strong>Note:</strong> There are <strong>at most four</strong> edges connected to each node.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/19/ex1drawio.png\" style=\"width: 269px; height: 170px;\" />\n<pre>\n<strong>Input:</strong> values = [0,32,10,43], edges = [[0,1,10],[1,2,15],[0,3,10]], maxTime = 49\n<strong>Output:</strong> 75\n<strong>Explanation:</strong>\nOne possible path is 0 -> 1 -> 0 -> 3 -> 0. The total time taken is 10 + 10 + 10 + 10 = 40 <= 49.\nThe nodes visited are 0, 1, and 3, giving a maximal path quality of 0 + 32 + 43 = 75.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/19/ex2drawio.png\" style=\"width: 269px; height: 170px;\" />\n<pre>\n<strong>Input:</strong> values = [5,10,15,20], edges = [[0,1,10],[1,2,10],[0,3,10]], maxTime = 30\n<strong>Output:</strong> 25\n<strong>Explanation:</strong>\nOne possible path is 0 -> 3 -> 0. The total time taken is 10 + 10 = 20 <= 30.\nThe nodes visited are 0 and 3, giving a maximal path quality of 5 + 20 = 25.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/10/19/ex31drawio.png\" style=\"width: 236px; height: 170px;\" />\n<pre>\n<strong>Input:</strong> values = [1,2,3,4], edges = [[0,1,10],[1,2,11],[2,3,12],[1,3,13]], maxTime = 50\n<strong>Output:</strong> 7\n<strong>Explanation:</strong>\nOne possible path is 0 -> 1 -> 3 -> 1 -> 0. The total time taken is 10 + 13 + 13 + 10 = 46 <= 50.\nThe nodes visited are 0, 1, and 3, giving a maximal path quality of 1 + 2 + 4 = 7.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == values.length</code></li>\n\t<li><code>1 <= n <= 1000</code></li>\n\t<li><code>0 <= values[i] <= 10<sup>8</sup></code></li>\n\t<li><code>0 <= edges.length <= 2000</code></li>\n\t<li><code>edges[j].length == 3 </code></li>\n\t<li><code>0 <= u<sub>j </sub>< v<sub>j</sub> <= n - 1</code></li>\n\t<li><code>10 <= time<sub>j</sub>, maxTime <= 100</code></li>\n\t<li>All the pairs <code>[u<sub>j</sub>, v<sub>j</sub>]</code> are <strong>unique</strong>.</li>\n\t<li>There are <strong>at most four</strong> edges connected to each node.</li>\n\t<li>The graph may not be connected.</li>\n</ul>\n", "translatedTitle": null, "translatedContent": null, "isPaidOnly": false, "difficulty": "Hard", "likes": 247, "dislikes": 24, "isLiked": null, "similarQuestions": "[{\"title\": \"Cherry Pickup\", \"titleSlug\": \"cherry-pickup\", \"difficulty\": \"Hard\", \"translatedTitle\": null}, {\"title\": \"Minimum Cost to Reach Destination in Time\", \"titleSlug\": \"minimum-cost-to-reach-destination-in-time\", \"difficulty\": \"Hard\", \"translatedTitle\": null}]", "exampleTestcases": "[0,32,10,43]\n[[0,1,10],[1,2,15],[0,3,10]]\n49\n[5,10,15,20]\n[[0,1,10],[1,2,10],[0,3,10]]\n30\n[1,2,3,4]\n[[0,1,10],[1,2,11],[2,3,12],[1,3,13]]\n50", "categoryTitle": "Algorithms", "contributors": [], "topicTags": [ { "name": "Array", "slug": "array", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Backtracking", "slug": "backtracking", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Graph", "slug": "graph", "translatedName": null, "__typename": "TopicTagNode" } ], "companyTagStats": null, "codeSnippets": [ { "lang": "C++", "langSlug": "cpp", "code": "class Solution {\npublic:\n int maximalPathQuality(vector<int>& values, vector<vector<int>>& edges, int maxTime) {\n \n }\n};", "__typename": "CodeSnippetNode" }, { "lang": "Java", "langSlug": "java", "code": "class Solution {\n public int maximalPathQuality(int[] values, int[][] edges, int maxTime) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Python", "langSlug": "python", "code": "class Solution(object):\n def maximalPathQuality(self, values, edges, maxTime):\n \"\"\"\n :type values: List[int]\n :type edges: List[List[int]]\n :type maxTime: int\n :rtype: int\n \"\"\"\n ", "__typename": "CodeSnippetNode" }, { "lang": "Python3", "langSlug": "python3", "code": "class Solution:\n def maximalPathQuality(self, values: List[int], edges: List[List[int]], maxTime: int) -> int:\n ", "__typename": "CodeSnippetNode" }, { "lang": "C", "langSlug": "c", "code": "\n\nint maximalPathQuality(int* values, int valuesSize, int** edges, int edgesSize, int* edgesColSize, int maxTime){\n\n}", "__typename": "CodeSnippetNode" }, { "lang": "C#", "langSlug": "csharp", "code": "public class Solution {\n public int MaximalPathQuality(int[] values, int[][] edges, int maxTime) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "JavaScript", "langSlug": "javascript", "code": "/**\n * @param {number[]} values\n * @param {number[][]} edges\n * @param {number} maxTime\n * @return {number}\n */\nvar maximalPathQuality = function(values, edges, maxTime) {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "Ruby", "langSlug": "ruby", "code": "# @param {Integer[]} values\n# @param {Integer[][]} edges\n# @param {Integer} max_time\n# @return {Integer}\ndef maximal_path_quality(values, edges, max_time)\n \nend", "__typename": "CodeSnippetNode" }, { "lang": "Swift", "langSlug": "swift", "code": "class Solution {\n func maximalPathQuality(_ values: [Int], _ edges: [[Int]], _ maxTime: Int) -> Int {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Go", "langSlug": "golang", "code": "func maximalPathQuality(values []int, edges [][]int, maxTime int) int {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "Scala", "langSlug": "scala", "code": "object Solution {\n def maximalPathQuality(values: Array[Int], edges: Array[Array[Int]], maxTime: Int): Int = {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Kotlin", "langSlug": "kotlin", "code": "class Solution {\n fun maximalPathQuality(values: IntArray, edges: Array<IntArray>, maxTime: Int): Int {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Rust", "langSlug": "rust", "code": "impl Solution {\n pub fn maximal_path_quality(values: Vec<i32>, edges: Vec<Vec<i32>>, max_time: i32) -> i32 {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "PHP", "langSlug": "php", "code": "class Solution {\n\n /**\n * @param Integer[] $values\n * @param Integer[][] $edges\n * @param Integer $maxTime\n * @return Integer\n */\n function maximalPathQuality($values, $edges, $maxTime) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "TypeScript", "langSlug": "typescript", "code": "function maximalPathQuality(values: number[], edges: number[][], maxTime: number): number {\n\n};", "__typename": "CodeSnippetNode" }, { "lang": "Racket", "langSlug": "racket", "code": "(define/contract (maximal-path-quality values edges maxTime)\n (-> (listof exact-integer?) (listof (listof exact-integer?)) exact-integer? exact-integer?)\n\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec maximal_path_quality(Values :: [integer()], Edges :: [[integer()]], MaxTime :: integer()) -> integer().\nmaximal_path_quality(Values, Edges, MaxTime) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec maximal_path_quality(values :: [integer], edges :: [[integer]], max_time :: integer) :: integer\n def maximal_path_quality(values, edges, max_time) do\n\n end\nend", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"7.7K\", \"totalSubmission\": \"13.4K\", \"totalAcceptedRaw\": 7703, \"totalSubmissionRaw\": 13398, \"acRate\": \"57.5%\"}", "hints": [ "How many nodes can you visit within maxTime seconds?", "Can you try every valid path?" ], "solution": null, "status": null, "sampleTestCase": "[0,32,10,43]\n[[0,1,10],[1,2,15],[0,3,10]]\n49", "metaData": "{\n \"name\": \"maximalPathQuality\",\n \"params\": [\n {\n \"name\": \"values\",\n \"type\": \"integer[]\"\n },\n {\n \"type\": \"integer[][]\",\n \"name\": \"edges\"\n },\n {\n \"type\": \"integer\",\n \"name\": \"maxTime\"\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>. 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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. 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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 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" } } }