<p>Given the <code>root</code> of a binary tree, return <em>the length of the longest path, where each node in the path has the same value</em>. This path may or may not pass through the root.</p>

<p><strong>The length of the path</strong> between two nodes is represented by the number of edges between them.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/10/13/ex1.jpg" style="width: 450px; height: 238px;" />
<pre>
<strong>Input:</strong> root = [5,4,5,1,1,null,5]
<strong>Output:</strong> 2
<strong>Explanation:</strong> The shown image shows that the longest path of the same value (i.e. 5).
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/10/13/ex2.jpg" style="width: 450px; height: 238px;" />
<pre>
<strong>Input:</strong> root = [1,4,5,4,4,null,5]
<strong>Output:</strong> 2
<strong>Explanation:</strong> The shown image shows that the longest path of the same value (i.e. 4).
</pre>

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

<ul>
	<li>The number of nodes in the tree is in the range <code>[0, 10<sup>4</sup>]</code>.</li>
	<li><code>-1000 &lt;= Node.val &lt;= 1000</code></li>
	<li>The depth of the tree will not exceed <code>1000</code>.</li>
</ul>

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
 
class Solution {
public:
    void search_univalue_path(TreeNode* node, int target, int& matches) {
        if (node == nullptr || node->val != target)    return;
        
        int left_matches = 0;
        search_univalue_path(node->left, target, left_matches);
        int right_matches = 0;
        search_univalue_path(node->right, target, right_matches);
        
        matches = 1 + std::max(left_matches, right_matches);
    }

    void search_for_longest_univalue_path(TreeNode* node, int& longest_path) {
        if (node == nullptr || (node->left == nullptr && node->right == nullptr))    return;

        const int node_val = node->val;
        int left_matches = 0;
        if (node->left != nullptr && node->left->val == node->val) {
            search_univalue_path(node->left, node_val, left_matches);
        }

        int right_matches = 0;
        if (node->right != nullptr && node->right->val == node->val) {
            search_univalue_path(node->right, node_val, right_matches);
        }

        longest_path = std::max(longest_path, left_matches+right_matches);
        
        search_for_longest_univalue_path(node->left, longest_path);
        search_for_longest_univalue_path(node->right, longest_path);
    }

    int longestUnivaluePath(TreeNode* root) {
        int longest_path = 0;
        search_for_longest_univalue_path(root, longest_path);

        return longest_path;
    }
};
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