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This approach uses Depth First Search (DFS) to explore the tree and find the longest path with different adjacent characters. The idea is to recursively explore each node, keeping track of the longest path encountered. As you traverse, ensure that any subsequent node is only considered in the path if it has a different character from its parent.
Time Complexity: O(n).
Space Complexity: O(n) due to the storage of the children array.
1from collections import defaultdict
2
3class Solution:
4 def longestPath(self, parent: List[int], s: str) -> int:
5 n = len(parent)
6 children = defaultdict(list)
7
8 for i in range(1, n):
9 children[parent[i]].append(i)
10
11 self.max_length = 0
12
13 def dfs(node):
14 first_longest, second_longest = 0, 0
15 for child in children[node]:
16 path_length = dfs(child)
17 if s[node] != s[child]:
18 if path_length > first_longest:
19 second_longest = first_longest
20 first_longest = path_length
21 elif path_length > second_longest:
22 second_longest = path_length
23 self.max_length = max(self.max_length, first_longest + second_longest + 1)
24 return first_longest + 1
25
26 dfs(0)
27 return self.max_lengthThis Python solution utilizes a DFS method where a dictionary stores children associated with each node. The maximum path is identified during the recursive search of each node's children, focusing on paths with unique characters.
Instead of using recursion, consider using an iterative Breadth First Search (BFS) approach. In this scenario, you explore each node level by level, maintaining a similar mechanism for avoiding paths with identical adjacent characters.
This approach generally requires additional bookkeeping to manage the nodes and their path lengths, but it can be beneficial in scenarios where recursion depth potential is problematic or not desired.
Time Complexity: O(n^2) in this version due to lack of adjacency list optimization.
Space Complexity: O(n) related to queue usage.
Utilizing a deque for BFS traversal, this Python solution avoids potential recursive depth issues. Paths are explored iteratively, updating the maximum path length encountered for nodes with alternating characters.