Package g2001_2100.s2065_maximum_path_quality_of_a_graph

Class Solution

java.lang.Object
g2001_2100.s2065_maximum_path_quality_of_a_graph.Solution
public class Solution extends java.lang.Object
2065 - Maximum Path Quality of a Graph.

Hard

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.

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] <= 108
  • 0 <= edges.length <= 2000
  • edges[j].length == 3
  • 0 <= uj < vj <= n - 1
  • 10 <= timej, maxTime <= 100
  • All the pairs [uj, vj] are unique.
  • There are at most four edges connected to each node.
  • The graph may not be connected.

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    int
    maximalPathQuality(int[] values, int[][] edges, int maxTime)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • maximalPathQuality

      public int maximalPathQuality(int[] values, int[][] edges, int maxTime)