3425 - Longest Special Path.

Hard

You are given an undirected tree rooted at node 0 with n nodes numbered from 0 to n - 1, represented by a 2D array edges of length n - 1, where <code>edgesi = u_i, v_i, length_i</code> indicates an edge between nodes <code>u_i</code> and <code>v_i</code> with length <code>length_i</code>. You are also given an integer array nums, where nums[i] represents the value at node i.

A special path is defined as a downward path from an ancestor node to a descendant node such that all the values of the nodes in that path are unique.

Note that a path may start and end at the same node.

Return an array result of size 2, where result[0] is the length of the longest special path, and result[1] is the minimum number of nodes in all possible longest special paths.

Example 1:

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

Output: 6,2

Explanation:

The longest special paths are 2 -> 5 and 0 -> 1 -> 4, both having a length of 6. The minimum number of nodes across all longest special paths is 2.

Example 2:

Input: edges = [1,0,8], nums = 2,2

Output: 0,1

Explanation:

The longest special paths are 0 and 1, both having a length of 0. The minimum number of nodes across all longest special paths is 1.

Constraints:

• <code>2 <= n <= 5 * 10⁴</code>

• edges.length == n - 1

• edges[i].length == 3

• <code>0 <= u_i, v_i< n</code>

• <code>1 <= length_i<= 10³</code>

• nums.length == n

• <code>0 <= numsi<= 5 * 10⁴</code>

• The input is generated such that edges represents a valid tree.