Package g2001_2100.s2065_maximum_path_quality_of_a_graph

Class Solution

  • All Implemented Interfaces:
    
public final class Solution

    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 <code>i<sup>th</sup></code> node. You are also given a 0-indexed 2D integer array edges, where each <code>edgesj = 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>, and it takes <code>time<sub>j</sub></code> 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 &lt;= n &lt;= 1000

    • <code>0 <= valuesi<= 10<sup>8</sup></code>

    • 0 &lt;= edges.length &lt;= 2000

    • edges[j].length == 3

    • <code>0 <= u<sub>j</sub>< v<sub>j</sub><= n - 1</code>

    • <code>10 <= time<sub>j</sub>, maxTime <= 100</code>

    • All the pairs <code>u<sub>j</sub>, v<sub>j</sub></code> are unique.

    • There are at most four edges connected to each node.

    • The graph may not be connected.

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final Integer maximalPathQuality(IntArray values, Array<IntArray> edges, Integer maxTime)

      • Methods inherited from class java.lang.Object

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