<p>You are given a <strong>tree</strong> (i.e. a connected, undirected graph that has no cycles) <strong>rooted</strong> at node <code>0</code> consisting of <code>n</code> nodes numbered from <code>0</code> to <code>n - 1</code>. The tree is represented by a <strong>0-indexed</strong> array <code>parent</code> of size <code>n</code>, where <code>parent[i]</code> is the parent of node <code>i</code>. Since node <code>0</code> is the root, <code>parent[0] == -1</code>.</p>

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

<p>Return <em>the length of the <strong>longest path</strong> in the tree such that no pair of <strong>adjacent</strong> nodes on the path have the same character assigned to them.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/03/25/testingdrawio.png" style="width: 201px; height: 241px;" />
<pre>
<strong>Input:</strong> parent = [-1,0,0,1,1,2], s = &quot;abacbe&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> The longest path where each two adjacent nodes have different characters in the tree is the path: 0 -&gt; 1 -&gt; 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. 
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/03/25/graph2drawio.png" style="width: 201px; height: 221px;" />
<pre>
<strong>Input:</strong> parent = [-1,0,0,0], s = &quot;aabc&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> The longest path where each two adjacent nodes have different characters is the path: 2 -&gt; 0 -&gt; 3. The length of this path is 3, so 3 is returned.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == parent.length == s.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= parent[i] &lt;= n - 1</code> for all <code>i &gt;= 1</code></li>
	<li><code>parent[0] == -1</code></li>
	<li><code>parent</code> represents a valid tree.</li>
	<li><code>s</code> consists of only lowercase English letters.</li>
</ul>

class Solution {
public:

int maxi;
    pair<int,char> solve(int index, vector<vector<int>>&adj, vector<int>&parent,string &s){
        if(index >= adj.size()){
            return {0,'$'};
        }


       vector<pair<int,char>>v;

       for(auto it:adj[index]){

            pair<int,char> temp = solve(it,adj,parent,s);

            if(temp.second != s[index] && temp.second!='$')
            v.push_back(temp);
       }    

       if(v.size()== 0){
         maxi = max(maxi,1);
        return {1,s[index]};
       }
       else if(v.size() == 1){
         maxi = max(maxi,v[0].first+1);
        return {v[0].first + 1,s[index]};
       }
       else{
        sort(v.begin(),v.end(),[](const auto &a, const auto &b){
        return a.first > b.first;
       });


       pair<int,char>left = v[0];
       pair<int,char>right = v[1];

       maxi = max(maxi,left.first + 1 + right.first);

       return {max(left.first,right.first) + 1, s[index]};

        

       }

    }
    int longestPath(vector<int>& parent, string s) {
        maxi = 0;
        int n = parent.size();
        vector<vector<int>>adj(n);

        for(int i=1;i<n;i++){
                adj[parent[i]].push_back(i);
        }

        solve(0,adj,parent,s);

        return maxi;
    }
};
215071