1448. 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

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].

Approach

Solution

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def goodNodes(self, root: TreeNode) -> int:
        def dfs(node, max_val):
            if not node:
                return 0

            is_good = 1 if node.val >= max_val else 0
            new_max = max(max_val, node.val)

            return is_good + dfs(node.left, new_max) + dfs(node.right, new_max)

        return dfs(root, root.val)

Explanation