<p>Given a binary tree <code>root</code>, a node <em>X</em> in the tree is named&nbsp;<strong>good</strong> if in the path from root to <em>X</em> there are no nodes with a value <em>greater than</em> X.</p>

<p>Return the number of <strong>good</strong> nodes in the binary tree.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2020/04/02/test_sample_1.png" style="width: 263px; height: 156px;" /></strong></p>

<pre>
<strong>Input:</strong> root = [3,1,4,3,null,1,5]
<strong>Output:</strong> 4
<strong>Explanation:</strong> Nodes in blue are <strong>good</strong>.
Root Node (3) is always a good node.
Node 4 -&gt; (3,4) is the maximum value in the path starting from the root.
Node 5 -&gt; (3,4,5) is the maximum value in the path
Node 3 -&gt; (3,1,3) is the maximum value in the path.</pre>

<p><strong class="example">Example 2:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2020/04/02/test_sample_2.png" style="width: 157px; height: 161px;" /></strong></p>

<pre>
<strong>Input:</strong> root = [3,3,null,4,2]
<strong>Output:</strong> 3
<strong>Explanation:</strong> Node 2 -&gt; (3, 3, 2) is not good, because &quot;3&quot; is higher than it.</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> root = [1]
<strong>Output:</strong> 1
<strong>Explanation:</strong> Root is considered as <strong>good</strong>.</pre>

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

<ul>
	<li>The number of nodes in the binary tree is in the range&nbsp;<code>[1, 10^5]</code>.</li>
	<li>Each node&#39;s value is between <code>[-10^4, 10^4]</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:
    int dfs(TreeNode* root, int maxOnPath) {
        if(root == NULL) return 0;
        int count = root->val >= maxOnPath ? 1 : 0;
        maxOnPath = max(maxOnPath, root->val);
        int val =  count + dfs(root->left, maxOnPath) + dfs(root->right, maxOnPath);
        root->left = NULL;
        root->right = NULL;
        return val;
    }
    
    int goodNodes(TreeNode* root) {
        return dfs(root, root->val);
    }
};
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