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Medium

Count Good Nodes in Binary Tree

A medium Binary Trees problem included in Love Babbar 450. Below: the roles whose interviews prioritise this topic, and how to practise it.

Topic
Binary Trees
Sheets
1
Core for
4 roles
Platform
LeetCode
Practice in the compilerWatch this solved step by step

The problem

Given the root of a binary tree, return the number of good nodes. A node X 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
Why
Good nodes: 3 (root), 4 (path: 3->4), 3 (path: 3->1->3), 5 (path: 3->4->5). Node 1 on path 3->1 is not good because 3 > 1.

Example 2

Input
root=[3,3,null,4,2]
Output
3
Why
Good nodes: 3 (root), 3 (path: 3->3), 4 (path: 3->3->4). Node 2 is not good because 3 > 2.

Example 3

Input
[1]
Output
1
Why
The root is always a good node.

Constraints

  • The number of nodes in the tree is in the range [1, 105].
  • -104 <= Node.val <= 104

How to think about it

Updated 2026-09-09

A node has no memory of the whole ancestry; it only cares about the single largest value encountered along the path from the root. Carry that running maximum downward. If the current value meets or exceeds that ceiling, count it and raise the ceiling for its descendants.

Approaches, worst first

  1. BFS queue with path maximums

    time O(n) · space O(w)

    Queue tuples of `(node, maxSoFar)`. Dequeue, increment total if `node.val >= maxSoFar`, and enqueue children paired with `max(maxSoFar, node.val)`. Avoids recursion limits on deep trees.

  2. DFS top-down accumulatorWrite this one

    time O(n) · space O(h)

    Recurse with the current node and `maxSoFar`. If node value is at least `maxSoFar`, contribute 1 and update `maxSoFar = max(maxSoFar, node.val)`. Sum results from left and right child calls.

Where people lose marks · 3
  • Initial max set to 0 breaks trees with strictly negative values; seed `maxSoFar` with `root.val` or negative infinity.
  • Using strict inequality `>` instead of `>=`; equal values along a path are good nodes by definition since no ancestor is strictly greater.
  • Mutating a shared global maximum instead of scoping `maxSoFar` to the specific branch path leads to cross-branch contamination.

The theory behind it

Binary Trees — the ground this problem stands on. All Binary Trees problems

What Binary Trees is

A binary tree is a branching data structure that starts at a single top node called the root, like an upside-down family tree. Every node holds a piece of data and can branch out to at most two children below it, known as the left child and the right child. Because there is no ordering rule about which values go left or right, finding a specific item can require checking every single node in the entire tree.

When to reach for it

Reach for binary trees when problems present hierarchical data with left and right child pointers. Questions asking for tree height, maximum depth, path sums from root to leaf, diameter, lowest common ancestor, or checking whether two trees are mirror reflections of each other all signal binary tree traversals. Any problem asking to inspect or reconstruct a tree layer by layer or path by path belongs here.

How the pattern works

Think recursively by focusing on what a single node must do. If the current node is null, return the base answer immediately. Otherwise, ask the left child for its result, ask the right child for its result, and combine both answers with the current node value before returning up to the parent. For horizontal scans, use a queue to read nodes layer by layer, measuring the queue length at the start of each layer to group nodes by depth.

What each operation costs

OperationTime
traverse all nodes using recursion or queueO(n)
search for an arbitrary value in an unordered treeO(n)
call stack memory on balanced treeO(log n)
call stack memory on skewed treeO(n)
What usually goes wrong with Binary Trees
  • Dereferencing left or right child pointers without checking if the current node is null, throwing null pointer errors on empty trees or leaf nodes.
  • Defining a leaf node incorrectly by stopping when either child is null instead of checking that both left and right children are simultaneously null.
  • Computing tree diameter by taking left height plus right height inside a recursive helper without updating a global maximum across every visited node.

Which roles need this problem

Binary Trees is a core topic for these 4 roles — if you're targeting one of them, this problem is early in your path, not optional.

SDE / Backend EngineerGraphics EngineerCompiler / PL EngineerBlockchain / Web3 Engineer

Secondary for 5 more roles, including Full-Stack Developer, Android Developer, iOS Developer.

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More Binary Trees problems

Problem set and role mapping as of .