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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.
1using System;
2using System.Collections.Generic;
3
4public class Solution {
5 public int LongestPath(int[] parent, string s) {
6 int n = parent.Length;
7 List<int>[] children = new List<int>[n];
8 for (int i = 0; i < n; i++) {
9 children[i] = new List<int>();
10 }
11 for (int i = 1; i < n; i++) {
12 children[parent[i]].Add(i);
13 }
14 int max_length = 0;
15 Dfs(0, s, children, ref max_length);
16 return max_length;
17 }
18
19 private int Dfs(int node, string s, List<int>[] children, ref int max_length) {
20 int firstLongest = 0, secondLongest = 0;
21 foreach (int child in children[node]) {
22 int pathLength = Dfs(child, s, children, ref max_length);
23 if (s[node] != s[child]) {
24 if (pathLength > firstLongest) {
25 secondLongest = firstLongest;
26 firstLongest = pathLength;
27 } else if (pathLength > secondLongest) {
28 secondLongest = pathLength;
29 }
30 }
31 }
32 max_length = Math.Max(max_length, firstLongest + secondLongest + 1);
33 return firstLongest + 1;
34 }
35}
In this C# version, the DFS algorithm leverages lists to represent child nodes, facilitating traversal and comparison of paths according to distinct character criteria for nodes. The result captures the longest available path.
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.