<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 max(int v1, int v2) {
        if(v1 > v2) return v1;
        
        return v2;
    }

    struct s_backtrack {
        int parent;
        int child; // node index
        int longest_len;
        int secondlongest;
        int current_len;
    };

    int traverse(int curnode, 
            vector<vector<int>> &nodes,
            int nodecount,
            int &longest,
            string &s) {

        int curchild = 0;
        int longest1 = 0; // max
        int longest2 = 0; // second
        while(curchild < nodes[curnode].size()) {
            // try a child
            char curchar = s[curnode];
            char childchar = s[nodes[curnode][curchild]];
            int len = traverse(nodes[curnode][curchild], nodes, nodecount, longest, s);
            if(curchar != childchar) {
                if(len > longest1) {
                    longest2 = longest1;
                    longest1 = len;
                } else if(len > longest2) {
                    longest2 = len;
                }
            }
            curchild++;
        }

        longest = max(longest, longest1 + longest2 + 1);
        return longest1 + 1;
    }

    int longestPath(vector<int>& parent, string s) {
        vector<vector<int>> nodes; // nodes[parent] = { children }
        int nodecount = parent.size();
        vector<int> empty;
        for(int i = 0 ; i < nodecount ; i++) {
            nodes.emplace_back(empty);
        }
        for(int i = 1 ; i < nodecount ; i++) {
            nodes[parent[i]].emplace_back(i);
        }
        int longest = 0;
        traverse(0, nodes, nodecount, longest, s);
        return longest;
    }

};
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