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3241. Time Taken to Mark All Nodes

Description

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 edges[i] = [ui, vi] indicates that there is an edge between nodes ui and vi 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:
    • Node 1 is marked at t = 1, and Node 2 at t = 2.
  • For i = 1:
    • Node 0 is marked at t = 2, and Node 2 at t = 4.
  • For i = 2:
    • Node 0 is marked at t = 2, and Node 1 at t = 3.

Example 2:

Input: edges = [[0,1]]

Output: [1,2]

Explanation:

  • For i = 0:
    • Node 1 is marked at t = 1.
  • For i = 1:
    • Node 0 is marked at t = 2.

Example 3:

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

Output: [4,6,3,5,5]

Explanation:

 

Constraints:

  • 2 <= n <= 105
  • 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.

Solutions

Solution 1

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