2065. Maximum Path Quality of a Graph
Description
There is an undirected graph with n
nodes numbered from 0
to n  1
(inclusive). You are given a 0indexed integer array values
where values[i]
is the value of the i^{th}
node. You are also given a 0indexed 2D integer array edges
, where each edges[j] = [u_{j}, v_{j}, time_{j}]
indicates that there is an undirected edge between the nodes u_{j}
and v_{j}
,_{ }and it takes time_{j}
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.
Note: There are at most four edges connected to each node.
Example 1:
Input: values = [0,32,10,43], edges = [[0,1,10],[1,2,15],[0,3,10]], maxTime = 49 Output: 75 Explanation: One possible path is 0 > 1 > 0 > 3 > 0. The total time taken is 10 + 10 + 10 + 10 = 40 <= 49. The nodes visited are 0, 1, and 3, giving a maximal path quality of 0 + 32 + 43 = 75.
Example 2:
Input: values = [5,10,15,20], edges = [[0,1,10],[1,2,10],[0,3,10]], maxTime = 30 Output: 25 Explanation: One possible path is 0 > 3 > 0. The total time taken is 10 + 10 = 20 <= 30. The nodes visited are 0 and 3, giving a maximal path quality of 5 + 20 = 25.
Example 3:
Input: values = [1,2,3,4], edges = [[0,1,10],[1,2,11],[2,3,12],[1,3,13]], maxTime = 50 Output: 7 Explanation: One possible path is 0 > 1 > 3 > 1 > 0. The total time taken is 10 + 13 + 13 + 10 = 46 <= 50. The nodes visited are 0, 1, and 3, giving a maximal path quality of 1 + 2 + 4 = 7.
Constraints:
n == values.length
1 <= n <= 1000
0 <= values[i] <= 10^{8}
0 <= edges.length <= 2000
edges[j].length == 3
0 <= u_{j }< v_{j} <= n  1
10 <= time_{j}, maxTime <= 100
 All the pairs
[u_{j}, v_{j}]
are unique.  There are at most four edges connected to each node.
 The graph may not be connected.
Solutions
Solution 1

