17. Count Good Nodes in Binary Tree.cpp

/*
Count Good Nodes in Binary Tree
===============================

Given a binary tree root, a node X in the tree is named good if in the path from root to X there are no nodes with a value greater than X.

Return the number of good nodes in the binary tree.

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

Example 2:
Input: root = [3,3,null,4,2]
Output: 3
Explanation: Node 2 -> (3, 3, 2) is not good, because "3" is higher than it.

Example 3:
Input: root = [1]
Output: 1
Explanation: Root is considered as good.

Constraints:
The number of nodes in the binary tree is in the range [1, 10^5].
Each node's value is between [-10^4, 10^4].
*/

/**
 * 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 dfs(TreeNode *root, int Max, int &ans)
    {
        if (!root)
            return;

        if (Max <= root->val)
            ans++;

        Max = max(Max, root->val);
        dfs(root->left, Max, ans);
        dfs(root->right, Max, ans);
    }

    int goodNodes(TreeNode *root)
    {
        int ans = 0;
        dfs(root, root->val, ans);
        return ans;
    }
};