<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 {
    int totalLongesPath = 1;
    unordered_map<int, vector<int>> children;

    int longestPath_rec(int node, const string& s)
    {
        int lp = 1;

        for (int child : children[node])
        {
            int lp_child = longestPath_rec(child, s);

            if (s[child] != s[node])
            {
                totalLongesPath = max(totalLongesPath, lp + lp_child);
                lp = max(lp, lp_child + 1); 
            }
        }

        return lp;
    }

public:
    int longestPath(vector<int>& parent, string s) {
        for (int i=0; i<parent.size(); i++)
        {
            children[parent[i]].push_back(i);
        }

        longestPath_rec(0, s);
        return totalLongesPath;


        // int totalLongesPath = 1;
        // vector<int> longestPathEndignAtNode(parent.size(), 1);

        // for (int j=sorted_parents.size()-1; j>0; j--)
        // {
        //     int i = sorted_parents[j].second;
        //     int par = sorted_parents[j].first;

        //     if (s[i] != s[par])
        //     {
        //         totalLongesPath = max(totalLongesPath, longestPathEndignAtNode[par] + longestPathEndignAtNode[i]);
        //         longestPathEndignAtNode[par] = max(longestPathEndignAtNode[par], longestPathEndignAtNode[i] + 1);
        //     }
        // }

        // return totalLongesPath;
    }
};
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