3241 - Time Taken to Mark All Nodes.

Hard

There exists an undirected tree with n nodes numbered 0 to n - 1. You are given a 2D integer array edges of length n - 1, where <code>edgesi = u_i, v_i</code> indicates that there is an edge between nodes <code>u_i</code> and <code>v_i</code> in the tree.

Initially, all nodes are unmarked. For each node i:

• If i is odd, the node will get marked at time x if there is at least one node adjacent to it which was marked at time x - 1.

• If i is even, the node will get marked at time x if there is at least one node adjacent to it which was marked at time x - 2.

Return an array times where times[i] is the time when all nodes get marked in the tree, if you mark node i at time t = 0.

Note that the answer for each times[i] is independent , i.e. when you mark node i all other nodes are unmarked.

Example 1:

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

Output: 2,4,3

Explanation:

• For i = 0:

• For i = 1:

• For i = 2:

Example 2:

Input: edges = [0,1]

Output: 1,2

Explanation:

• For i = 0:

• For i = 1:

Example 3:

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

Output: 4,6,3,5,5

Explanation:

Constraints:

• <code>2 <= n <= 10⁵</code>

• edges.length == n - 1

• edges[i].length == 2

• 0 <= edges[i][0], edges[i][1] <= n - 1

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