[LeetCode] 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 0 to n - 1. The tree is represented by a 0-indexed array parent of size n, where parent[i] is the parent of node i. Since node 0 is the root, parent[0] == -1.

You are also given a string s of length n, where s[i] is the character assigned to node i.

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.

Example 1:

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. 

Example 2:

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.

Constraints:

• n == parent.length == s.length
• 1 <= n <= 105
• 0 <= parent[i] <= n - 1 for all i >= 1
• parent[0] == -1
• parent represents a valid tree.
• s consists of only lowercase English letters.

相邻字符不同的最长路径。

给你一棵 树（即一个连通、无向、无环图），根节点是节点 0 ，这棵树由编号从 0 到 n - 1 的 n 个节点组成。用下标从 0 开始、长度为 n 的数组 parent 来表示这棵树，其中 parent[i] 是节点 i 的父节点，由于节点 0 是根节点，所以 parent[0] == -1 。

另给你一个字符串 s ，长度也是 n ，其中 s[i] 表示分配给节点 i 的字符。

请你找出路径上任意一对相邻节点都没有分配到相同字符的 最长路径 ，并返回该路径的长度。

来源：力扣（LeetCode）
链接：https://leetcode.cn/problems/longest-path-with-different-adjacent-characters
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思路是 DFS 后序遍历，因为路径不一定穿过根节点。这个思路类似543题和1245题。可以先做一下这两题。

因为题目给的是无向无环图，所以我们需要先把图用一个邻接表建立起来。图建立好之后，我们从节点 0 开始做 DFS 遍历，对于当前节点 root 的所有孩子节点 child，如果 root 指向的 s 中的字母跟 child 指向的一样，则跳过。否则我们就去计算一下每个 child 节点的深度。对于当前节点而言，穿过当前节点的最长路径 = 两个深度最大的子树 + 1。但是我们往当前节点的父节点返回的值是深度最大的子树 + 1。

时间O(n)

空间O(n)

Java实现

 1 class Solution {
 2     List<Integer>[] g;
 3     String s;
 4     int res;
 5     
 6     public int longestPath(int[] parent, String s) {
 7         this.s = s;
 8         int n = parent.length;
 9         g = new ArrayList[n];
10         for (int i = 0; i < n; i++) {
11             g[i] = new ArrayList<>();
12         }
13         for (int i = 1; i < n; i++) {
14             g[parent[i]].add(i);
15         }
16         dfs(0);
17         return res;
18     }
19     
20     private int dfs(int root) {
21         int max1 = 0;
22         int max2 = 0;
23         for (int child : g[root]) {
24             int depth = dfs(child);
25             if (s.charAt(root) == s.charAt(child)) {
26                 continue;
27             }
28             if (depth > max1) {
29                 max2 = max1;
30                 max1 = depth;
31             } else if (depth > max2) {
32                 max2 = depth;
33             }
34         }
35         res = Math.max(res, max1 + max2 + 1);
36         return max1 + 1;
37     }
38 }

相关题目

543. Diameter of Binary Tree

1245. Tree Diameter

2246. Longest Path With Different Adjacent Characters

LeetCode 题目总结