<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 longestPath(vector<int>& parent, string s) {
        int N = s.size();
        vector<vector<int>> tree (N, vector<int>());
        for (int i = 1; i < N; i++) {
            tree[parent[i]].push_back(i);
        }

        int ans = 1;
        vector<int> dp(N, 1);  // dp[i] contain maximum path start from i to child node
        std::function<void(const vector<vector<int>>&, int)> DFS = 
            [&](const vector<vector<int>>& tree, int p) -> void {
            //printf("visist %d --------- %c\n", p, s[p]);
            int longest_1 = 0;  
            int longest_2 = 0;
            for (auto c: tree[p]) {
                 DFS(tree, c);
                if (s[p] != s[c]) {
                    if (longest_1 <= dp[c]) {
                        longest_2 = longest_1;
                        longest_1 = dp[c];
                    } else if (longest_2 <= dp[c]) {
                        longest_2 = dp[c];  // need to save 2 longest
                    }
                }
            }
            //printf("dp[%d] = %d\n", p, dp[p]);
            dp[p] = longest_1 + 1;
            ans = max(ans, longest_1 + longest_2 + 1);           
        };

        DFS(tree, 0);

        return ans;

    }
};
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