2246. Longest Path With Different Adjacent Characters
You are given a tree (i.e. a connected, undirected graph that has no cycles) rooted at node
0 consisting of
n nodes numbered from
n - 1. The tree is represented by a 0-indexed array
parent of size
parent[i] is the parent of node
i. Since node
0 is the root,
parent == -1.
You are also given a string
s of length
s[i] is the character assigned to node
Return the length of the longest path in the tree such that no pair of adjacent nodes on the path have the same character assigned to them.
Input: parent = [-1,0,0,1,1,2], s = “abacbe” Output: 3 Explanation: The longest path where each two adjacent nodes have different characters in the tree is the path: 0 -> 1 -> 3. The length of this path is 3, so 3 is returned. It can be proven that there is no longer path that satisfies the conditions.
Input: parent = [-1,0,0,0], s = “aabc” Output: 3 Explanation: The longest path where each two adjacent nodes have different characters is the path: 2 -> 0 -> 3. The length of this path is 3, so 3 is returned.
After reading the problem, the first idea in my mind is DFS, since that’s the common way to solve Tree problems.
Given a node, we can determine the longest path that starts at from it by its children. There are some cases we might consider:
# Without any children
This is the simplest case, and the longest path is
# At least one child
If the current node label and its child are the same, so the longest path if we follow that path is
0. But we still have to continue DFS for that child, since might be the case when the longest path is started by that child. For example:
If there are more than two children, we have to find out the top 2 longest path, and the longest path is
sum of that two path + 1. Look at the Example 2 above to find out why.