3486 - Longest Special Path II.

Hard

You are given an undirected tree rooted at node 0, with n nodes numbered from 0 to n - 1. This is 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 in which all node values are distinct , except for at most one value that may appear twice.

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 = [0,1,1,1,2,3,1,3,1,2,4,6,4,7,2,3,5,2,3,6,5,6,8,3], nums = 1,1,0,3,1,2,1,1,0

Output: 9,3

Explanation:

In the image below, nodes are colored by their corresponding values in nums.

The longest special paths are 1 -> 2 -> 4 and 1 -> 3 -> 6 -> 8, both having a length of 9. The minimum number of nodes across all longest special paths is 3.

Example 2:

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

Output: 5,2

Explanation:

The longest path is 0 -> 3 consisting of 2 nodes with a length of 5.

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.