Package g2201_2300.s2285_maximum_total_importance_of_roads

Class Solution

java.lang.Object
g2201_2300.s2285_maximum_total_importance_of_roads.Solution
public class Solution extends java.lang.Object
2285 - Maximum Total Importance of Roads.

Medium

You are given an integer n denoting the number of cities in a country. The cities are numbered from 0 to n - 1.

You are also given a 2D integer array roads where roads[i] = [ai, bi] denotes that there exists a bidirectional road connecting cities ai and bi.

You need to assign each city with an integer value from 1 to n, where each value can only be used once. The importance of a road is then defined as the sum of the values of the two cities it connects.

Return the maximum total importance of all roads possible after assigning the values optimally.

Example 1:

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

Output: 43

Explanation: The figure above shows the country and the assigned values of [2,4,5,3,1].

  • The road (0,1) has an importance of 2 + 4 = 6.

  • The road (1,2) has an importance of 4 + 5 = 9.

  • The road (2,3) has an importance of 5 + 3 = 8.

  • The road (0,2) has an importance of 2 + 5 = 7.

  • The road (1,3) has an importance of 4 + 3 = 7.

  • The road (2,4) has an importance of 5 + 1 = 6.

The total importance of all roads is 6 + 9 + 8 + 7 + 7 + 6 = 43.

It can be shown that we cannot obtain a greater total importance than 43.

Example 2:

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

Output: 20

Explanation: The figure above shows the country and the assigned values of [4,3,2,5,1].

  • The road (0,3) has an importance of 4 + 5 = 9.

  • The road (2,4) has an importance of 2 + 1 = 3.

  • The road (1,3) has an importance of 3 + 5 = 8.

The total importance of all roads is 9 + 3 + 8 = 20.

It can be shown that we cannot obtain a greater total importance than 20.

Constraints:

  • 2 <= n <= 5 * 104
  • 1 <= roads.length <= 5 * 104
  • roads[i].length == 2
  • 0 <= ai, bi <= n - 1
  • ai != bi
  • There are no duplicate roads.

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    long
    maximumImportance(int n, int[][] roads)
     

    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

    • maximumImportance

      public long maximumImportance(int n, int[][] roads)