# 687. Longest Univalue Path

Given a binary tree, find the length of the longest path where each node in the path has the same value. This path may or may not pass through the root.

The length of path between two nodes is represented by the number of edges between them.

**Example 1:**

**Input:**

```
              5
             / \
            4   5
           / \   \
          1   1   5
```

**Output:** 2

**Example 2:**

**Input:**

```
              1
             / \
            4   5
           / \   \
          4   4   5
```

**Output:** 2

**Note:** The given binary tree has not more than 10000 nodes. The height of the tree is not more than 1000.

```cpp
int helper(TreeNode* node, int& res) { // time: O(n); space: O(n)
    if (!node) return 0;
    int left = helper(node->left, res); // the longest univalue path starting from left child
    left = (node->left && node->left->val == node->val) ? left + 1 : 0;
    int right = helper(node->right, res); // the longest univalue path starting from right child
    right = (node->right && node->right->val == node->val) ? right + 1 : 0;
    res = max(res, left + right);
    return max(left, right);
}
int longestUnivaluePath(TreeNode* root) {
    int res = 0;
    helper(root, res);
    return res;
}
```

```cpp
int helper(TreeNode* node, int parent, int& res) {
    if (!node) return 0;
    int left = helper(node->left, node->val, res);
    int right = helper(node->right, node->val, res);
    res = max(res, left + right);
    if (node->val == parent) return max(left, right) + 1;
    else return 0;
}
int longestUnivaluePath(TreeNode* root) {
    int res = 0;
    if (root) helper(root, root->val, res);
    return res;
}
```


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