Longest Path With Different Adjacent Characters

Description

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.

Code

Time Complexity: $O(V+E)$, Space Complexity: $(V+E)$

遞迴的 return 和 global max 取的值不一樣，一個只考慮單邊，一個兩邊都可以。

小結：不要想只用遞迴就解決，global variable 有時候是必要的。

class Solution {
public:
    int g_res = 1;
    int longestPath(vector<int>& parent, string s) {
 
       unordered_map<int, vector<int>> child;
       for(int i = 0; i < parent.size(); i++) {
            child[parent[i]].push_back(i);
       }
 
        dfs(s, child, 0);
        return g_res;
    }
 
 
    int dfs(string& s, unordered_map<int,vector<int>>& child, int idx) {
        
        char curr_char = s[idx];
        int child_max = 0;
        int child_second = 0;
        int logest_path = 0;
        for(auto c: child[idx]) {
            int child_len = dfs(s, child, c);
            if(s[c] != curr_char) {
                if(child_len > child_max) {
                    child_second = child_max;
                    child_max = child_len;
                } else if (child_len > child_second) {
                    child_second = child_len;
                }
            }
            logest_path = max(logest_path, child_len);
        }
 
        g_res = max(g_res, child_max + child_second + 1);
        return max(child_max, child_second) + 1;
    }
};

Source

• Longest Path With Different Adjacent Characters - LeetCode