{ "data": { "question": { "questionId": "3179", "questionFrontendId": "2920", "boundTopicId": null, "title": "Maximum Points After Collecting Coins From All Nodes", "titleSlug": "maximum-points-after-collecting-coins-from-all-nodes", "content": "

There exists an undirected tree rooted at node 0 with n nodes labeled from 0 to n - 1. You are given a 2D integer array edges of length n - 1, where edges[i] = [ai, bi] indicates that there is an edge between nodes ai and bi in the tree. You are also given a 0-indexed array coins of size n where coins[i] indicates the number of coins in the vertex i, and an integer k.

\n\n

Starting from the root, you have to collect all the coins such that the coins at a node can only be collected if the coins of its ancestors have been already collected.

\n\n

Coins at nodei can be collected in one of the following ways:

\n\n\n\n

Return the maximum points you can get after collecting the coins from all the tree nodes.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: edges = [[0,1],[1,2],[2,3]], coins = [10,10,3,3], k = 5\nOutput: 11                        \nExplanation: \nCollect all the coins from node 0 using the first way. Total points = 10 - 5 = 5.\nCollect all the coins from node 1 using the first way. Total points = 5 + (10 - 5) = 10.\nCollect all the coins from node 2 using the second way so coins left at node 3 will be floor(3 / 2) = 1. Total points = 10 + floor(3 / 2) = 11.\nCollect all the coins from node 3 using the second way. Total points = 11 + floor(1 / 2) = 11.\nIt can be shown that the maximum points we can get after collecting coins from all the nodes is 11. \n
\n\n

Example 2:

\n \"\"\n\n
\nInput: edges = [[0,1],[0,2]], coins = [8,4,4], k = 0\nOutput: 16\nExplanation: \nCoins will be collected from all the nodes using the first way. Therefore, total points = (8 - 0) + (4 - 0) + (4 - 0) = 16.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": null, "translatedContent": null, "isPaidOnly": false, "difficulty": "Hard", "likes": 163, "dislikes": 11, "isLiked": null, "similarQuestions": "[]", "exampleTestcases": "[[0,1],[1,2],[2,3]]\n[10,10,3,3]\n5\n[[0,1],[0,2]]\n[8,4,4]\n0", "categoryTitle": "Algorithms", "contributors": [], "topicTags": [ { "name": "Array", "slug": "array", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Dynamic Programming", "slug": "dynamic-programming", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Bit Manipulation", "slug": "bit-manipulation", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Tree", "slug": "tree", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Depth-First Search", "slug": "depth-first-search", "translatedName": null, "__typename": "TopicTagNode" } ], "companyTagStats": null, "codeSnippets": [ { "lang": "C++", "langSlug": "cpp", "code": "class Solution {\npublic:\n int maximumPoints(vector>& edges, vector& coins, int k) {\n \n }\n};", "__typename": "CodeSnippetNode" }, { "lang": "Java", "langSlug": "java", "code": "class Solution {\n public int maximumPoints(int[][] edges, int[] coins, int k) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Python", "langSlug": "python", "code": "class Solution(object):\n def maximumPoints(self, edges, coins, k):\n \"\"\"\n :type edges: List[List[int]]\n :type coins: List[int]\n :type k: int\n :rtype: int\n \"\"\"\n ", "__typename": "CodeSnippetNode" }, { "lang": "Python3", "langSlug": "python3", "code": "class Solution:\n def maximumPoints(self, edges: List[List[int]], coins: List[int], k: int) -> int:\n ", "__typename": "CodeSnippetNode" }, { "lang": "C", "langSlug": "c", "code": "int maximumPoints(int** edges, int edgesSize, int* edgesColSize, int* coins, int coinsSize, int k) {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "C#", "langSlug": "csharp", "code": "public class Solution {\n public int MaximumPoints(int[][] edges, int[] coins, int k) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "JavaScript", "langSlug": "javascript", "code": "/**\n * @param {number[][]} edges\n * @param {number[]} coins\n * @param {number} k\n * @return {number}\n */\nvar maximumPoints = function(edges, coins, k) {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "TypeScript", "langSlug": "typescript", "code": "function maximumPoints(edges: number[][], coins: number[], k: number): number {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "PHP", "langSlug": "php", "code": "class Solution {\n\n /**\n * @param Integer[][] $edges\n * @param Integer[] $coins\n * @param Integer $k\n * @return Integer\n */\n function maximumPoints($edges, $coins, $k) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Swift", "langSlug": "swift", "code": "class Solution {\n func maximumPoints(_ edges: [[Int]], _ coins: [Int], _ k: Int) -> Int {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Kotlin", "langSlug": "kotlin", "code": "class Solution {\n fun maximumPoints(edges: Array, coins: IntArray, k: Int): Int {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Dart", "langSlug": "dart", "code": "class Solution {\n int maximumPoints(List> edges, List coins, int k) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Go", "langSlug": "golang", "code": "func maximumPoints(edges [][]int, coins []int, k int) int {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "Ruby", "langSlug": "ruby", "code": "# @param {Integer[][]} edges\n# @param {Integer[]} coins\n# @param {Integer} k\n# @return {Integer}\ndef maximum_points(edges, coins, k)\n \nend", "__typename": "CodeSnippetNode" }, { "lang": "Scala", "langSlug": "scala", "code": "object Solution {\n def maximumPoints(edges: Array[Array[Int]], coins: Array[Int], k: Int): Int = {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Rust", "langSlug": "rust", "code": "impl Solution {\n pub fn maximum_points(edges: Vec>, coins: Vec, k: i32) -> i32 {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Racket", "langSlug": "racket", "code": "(define/contract (maximum-points edges coins k)\n (-> (listof (listof exact-integer?)) (listof exact-integer?) exact-integer? exact-integer?)\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec maximum_points(Edges :: [[integer()]], Coins :: [integer()], K :: integer()) -> integer().\nmaximum_points(Edges, Coins, K) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec maximum_points(edges :: [[integer]], coins :: [integer], k :: integer) :: integer\n def maximum_points(edges, coins, k) do\n \n end\nend", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"5.8K\", \"totalSubmission\": \"15.5K\", \"totalAcceptedRaw\": 5751, \"totalSubmissionRaw\": 15534, \"acRate\": \"37.0%\"}", "hints": [ "Let dp[x][t] be the maximum points we can get from the subtree rooted at node x and the second operation has been used t times in its ancestors.", "Note that the value of each node <= 104, so when t >= 14 dp[x][t] is always 0.", "General equation will be: dp[x][t] = max((coins[x] >> t) - k + sigma(dp[y][t]), (coins[x] >> (t + 1)) + sigma(dp[y][t + 1])) where nodes denoted by y in the sigma, are the direct children of node x." ], "solution": null, "status": null, "sampleTestCase": "[[0,1],[1,2],[2,3]]\n[10,10,3,3]\n5", "metaData": "{\n \"name\": \"maximumPoints\",\n \"params\": [\n {\n \"name\": \"edges\",\n \"type\": \"integer[][]\"\n },\n {\n \"type\": \"integer[]\",\n \"name\": \"coins\"\n },\n {\n \"type\": \"integer\",\n \"name\": \"k\"\n }\n ],\n \"return\": {\n \"type\": \"integer\"\n }\n}", "judgerAvailable": true, "judgeType": "large", "mysqlSchemas": [], "enableRunCode": true, "enableTestMode": false, "enableDebugger": true, "envInfo": "{\"cpp\": [\"C++\", \"

Compiled with clang 11 using the latest C++ 20 standard.

\\r\\n\\r\\n

Your code is compiled with level two optimization (-O2). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.

\\r\\n\\r\\n

Most standard library headers are already included automatically for your convenience.

\"], \"java\": [\"Java\", \"

OpenJDK 17. Java 8 features such as lambda expressions and stream API can be used.

\\r\\n\\r\\n

Most standard library headers are already included automatically for your convenience.

\\r\\n

Includes Pair class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.

\"], \"python\": [\"Python\", \"

Python 2.7.12.

\\r\\n\\r\\n

Most libraries are already imported automatically for your convenience, such as array, bisect, collections. If you need more libraries, you can import it yourself.

\\r\\n\\r\\n

For Map/TreeMap data structure, you may use sortedcontainers library.

\\r\\n\\r\\n

Note that Python 2.7 will not be maintained past 2020. For the latest Python, please choose Python3 instead.

\"], \"c\": [\"C\", \"

Compiled with gcc 8.2 using the gnu11 standard.

\\r\\n\\r\\n

Your code is compiled with level one optimization (-O1). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.

\\r\\n\\r\\n

Most standard library headers are already included automatically for your convenience.

\\r\\n\\r\\n

For hash table operations, you may use uthash. \\\"uthash.h\\\" is included by default. Below are some examples:

\\r\\n\\r\\n

1. Adding an item to a hash.\\r\\n

\\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
\\r\\n

\\r\\n\\r\\n

2. Looking up an item in a hash:\\r\\n

\\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
\\r\\n

\\r\\n\\r\\n

3. Deleting an item in a hash:\\r\\n

\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n    HASH_DEL(users, user);  \\r\\n}\\r\\n
\\r\\n

\"], \"csharp\": [\"C#\", \"

C# 10 with .NET 6 runtime

\"], \"javascript\": [\"JavaScript\", \"

Node.js 16.13.2.

\\r\\n\\r\\n

Your code is run with --harmony flag, enabling new ES6 features.

\\r\\n\\r\\n

lodash.js library is included by default.

\\r\\n\\r\\n

For Priority Queue / Queue data structures, you may use 5.3.0 version of datastructures-js/priority-queue and 4.2.1 version of datastructures-js/queue.

\"], \"ruby\": [\"Ruby\", \"

Ruby 3.1

\\r\\n\\r\\n

Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms

\"], \"swift\": [\"Swift\", \"

Swift 5.5.2.

\"], \"golang\": [\"Go\", \"

Go 1.21

\\r\\n

Support https://godoc.org/github.com/emirpasic/gods@v1.18.1 library.

\"], \"python3\": [\"Python3\", \"

Python 3.10.

\\r\\n\\r\\n

Most libraries are already imported automatically for your convenience, such as array, bisect, collections. If you need more libraries, you can import it yourself.

\\r\\n\\r\\n

For Map/TreeMap data structure, you may use sortedcontainers library.

\"], \"scala\": [\"Scala\", \"

Scala 2.13.7.

\"], \"kotlin\": [\"Kotlin\", \"

Kotlin 1.9.0.

\"], \"rust\": [\"Rust\", \"

Rust 1.58.1

\\r\\n\\r\\n

Supports rand v0.6\\u00a0from crates.io

\"], \"php\": [\"PHP\", \"

PHP 8.1.

\\r\\n

With bcmath module

\"], \"typescript\": [\"Typescript\", \"

TypeScript 5.1.6, Node.js 16.13.2.

\\r\\n\\r\\n

Your code is run with --harmony flag, enabling new ES2022 features.

\\r\\n\\r\\n

lodash.js library is included by default.

\"], \"racket\": [\"Racket\", \"

Run with Racket 8.3.

\"], \"erlang\": [\"Erlang\", \"Erlang/OTP 25.0\"], \"elixir\": [\"Elixir\", \"Elixir 1.13.4 with Erlang/OTP 25.0\"], \"dart\": [\"Dart\", \"

Dart 2.17.3

\\r\\n\\r\\n

Your code will be run directly without compiling

\"]}", "libraryUrl": null, "adminUrl": null, "challengeQuestion": null, "__typename": "QuestionNode" } } }