public class Solution
extends 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.