Package g3501_3600.s3547_maximum_sum_of_edge_values_in_a_graph

Class Solution

  • All Implemented Interfaces:
    
public final class Solution

    3547 - Maximum Sum of Edge Values in a Graph.

    Hard

    You are given an und****irected graph of n nodes, numbered from 0 to n - 1. Each node is connected to at most 2 other nodes.

    The graph consists of m edges, represented by a 2D array edges, where <code>edgesi = a<sub>i</sub>, b<sub>i</sub></code> indicates that there is an edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code>.

    You have to assign a unique value from 1 to n to each node. The value of an edge will be the product of the values assigned to the two nodes it connects.

    Your score is the sum of the values of all edges in the graph.

    Return the maximum score you can achieve.

    Example 1:

    Input: n = 7, edges = [0,1,1,2,2,0,3,4,4,5,5,6]

    Output: 130

    Explanation:

    The diagram above illustrates an optimal assignment of values to nodes. The sum of the values of the edges is: (7 * 6) + (7 * 5) + (6 * 5) + (1 * 3) + (3 * 4) + (4 * 2) = 130.

    Example 2:

    Input: n = 6, edges = [0,3,4,5,2,0,1,3,2,4,1,5]

    Output: 82

    Explanation:

    The diagram above illustrates an optimal assignment of values to nodes. The sum of the values of the edges is: (1 * 2) + (2 * 4) + (4 * 6) + (6 * 5) + (5 * 3) + (3 * 1) = 82.

    Constraints:

    • <code>1 <= n <= 5 * 10<sup>4</sup></code>

    • m == edges.length

    • 1 &lt;= m &lt;= n

    • edges[i].length == 2

    • <code>0 <= a<sub>i</sub>, b<sub>i</sub>< n</code>

    • <code>a<sub>i</sub> != b<sub>i</sub></code>

    • There are no repeated edges.

    • Each node is connected to at most 2 other nodes.

    • 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 Long maxScore(Integer n, Array<IntArray> edges)

      • Methods inherited from class java.lang.Object

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