{ "data": { "question": { "questionId": "2189", "questionFrontendId": "2065", "categoryTitle": "Algorithms", "boundTopicId": 1082991, "title": "Maximum Path Quality of a Graph", "titleSlug": "maximum-path-quality-of-a-graph", "content": "
There is an undirected graph with n
nodes numbered from 0
to n - 1
(inclusive). You are given a 0-indexed integer array values
where values[i]
is the value of the ith
node. You are also given a 0-indexed 2D integer array edges
, where each edges[j] = [uj, vj, timej]
indicates that there is an undirected edge between the nodes uj
and vj
, and it takes timej
seconds to travel between the two nodes. Finally, you are given an integer maxTime
.
A valid path in the graph is any path that starts at node 0
, ends at node 0
, and takes at most maxTime
seconds to complete. You may visit the same node multiple times. The quality of a valid path is the sum of the values of the unique nodes visited in the path (each node's value is added at most once to the sum).
Return the maximum quality of a valid path.
\n\nNote: There are at most four edges connected to each node.
\n\n\n
Example 1:
\n\n\nInput: values = [0,32,10,43], edges = [[0,1,10],[1,2,15],[0,3,10]], maxTime = 49\nOutput: 75\nExplanation:\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\n\n
Example 2:
\n\n\nInput: values = [5,10,15,20], edges = [[0,1,10],[1,2,10],[0,3,10]], maxTime = 30\nOutput: 25\nExplanation:\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\n\n
Example 3:
\n\n\nInput: values = [1,2,3,4], edges = [[0,1,10],[1,2,11],[2,3,12],[1,3,13]], maxTime = 50\nOutput: 7\nExplanation:\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\n\n
\n
Constraints:
\n\nn == values.length
1 <= n <= 1000
0 <= values[i] <= 108
0 <= edges.length <= 2000
edges[j].length == 3
0 <= uj < vj <= n - 1
10 <= timej, maxTime <= 100
[uj, vj]
are unique.给你一张 无向 图,图中有 n
个节点,节点编号从 0
到 n - 1
(都包括)。同时给你一个下标从 0 开始的整数数组 values
,其中 values[i]
是第 i
个节点的 价值 。同时给你一个下标从 0 开始的二维整数数组 edges
,其中 edges[j] = [uj, vj, timej]
表示节点 uj
和 vj
之间有一条需要 timej
秒才能通过的无向边。最后,给你一个整数 maxTime
。
合法路径 指的是图中任意一条从节点 0
开始,最终回到节点 0
,且花费的总时间 不超过 maxTime
秒的一条路径。你可以访问一个节点任意次。一条合法路径的 价值 定义为路径中 不同节点 的价值 之和 (每个节点的价值 至多 算入价值总和中一次)。
请你返回一条合法路径的 最大 价值。
\n\n注意:每个节点 至多 有 四条 边与之相连。
\n\n\n\n
示例 1:
\n\n\n\n\n输入:values = [0,32,10,43], edges = [[0,1,10],[1,2,15],[0,3,10]], maxTime = 49\n输出:75\n解释:\n一条可能的路径为:0 -> 1 -> 0 -> 3 -> 0 。总花费时间为 10 + 10 + 10 + 10 = 40 <= 49 。\n访问过的节点为 0 ,1 和 3 ,最大路径价值为 0 + 32 + 43 = 75 。\n\n\n
示例 2:
\n\n\n\n\n输入:values = [5,10,15,20], edges = [[0,1,10],[1,2,10],[0,3,10]], maxTime = 30\n输出:25\n解释:\n一条可能的路径为:0 -> 3 -> 0 。总花费时间为 10 + 10 = 20 <= 30 。\n访问过的节点为 0 和 3 ,最大路径价值为 5 + 20 = 25 。\n\n\n
示例 3:
\n\n\n\n\n输入:values = [1,2,3,4], edges = [[0,1,10],[1,2,11],[2,3,12],[1,3,13]], maxTime = 50\n输出:7\n解释:\n一条可能的路径为:0 -> 1 -> 3 -> 1 -> 0 。总花费时间为 10 + 13 + 13 + 10 = 46 <= 50 。\n访问过的节点为 0 ,1 和 3 ,最大路径价值为 1 + 2 + 4 = 7 。\n\n
示例 4:
\n\n\n\n
\n输入:values = [0,1,2], edges = [[1,2,10]], maxTime = 10\n输出:0\n解释:\n唯一一条路径为 0 。总花费时间为 0 。\n唯一访问过的节点为 0 ,最大路径价值为 0 。\n\n\n
\n\n
提示:
\n\nn == values.length
1 <= n <= 1000
0 <= values[i] <= 108
0 <= edges.length <= 2000
edges[j].length == 3
0 <= uj < vj <= n - 1
10 <= timej, maxTime <= 100
[uj, vj]
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