What is the brute force approach and complexity for Binary Tree Level Order Traversal II?

Find the height, then for depth d from H − 1 down to 0, walk the whole tree and keep depth d with time complexity O(N · H) and space complexity O(H).

What is the optimal approach and complexity for Binary Tree Level Order Traversal II?

Run the normal BFS unchanged, then reverse the outer list once with optimal time complexity O(N) and space complexity O(N).

How do you identify the pattern for Binary Tree Level Order Traversal II?

Look for key signals in the prompt: "bottom-up level order" indicates The same rows as LC 102, only in the opposite order.; "from leaf to root" indicates The deepest row must come first in the answer.; "left to right within each level" indicates Inside a row, the order does not change, so the rows are flipped but the values are not..

Binary Tree Level Order Traversal II

Medium·LeetCode #107 Pro OnlyBasic Reinforcement

LeetCode

Problem Statement

You are given the root of a binary tree. Return the node values one row at a time, like a normal level order traversal, but from the bottom row up: the deepest row comes first, then the row above it, and the root's row comes last.

Inside each row, keep the usual order: left to right. Only the order of the rows is flipped.

Input

The root of a binary tree. It can be empty (null).

In the examples, a tree is written in level order: the root first, then each row left to right. A null marks a missing child.

Output

A list of rows, with the deepest row first and the root's row last. Each row is read left to right.

Example 1

Input: root = [3, 9, 20, null, null, 15, 7]

Output: [[15, 7], [9, 20], [3]]

The top-down rows are [3], [9, 20] and [15, 7]. Reading them from the bottom up gives [15, 7], [9, 20] and [3]. Inside [15, 7] the order is still left to right.

Example 2

Input: root = [1]

Output: [[1]]

A single node is one row.

Example 3

Input: root = []

Output: []

No nodes, so no rows.

Constraints

• The number of nodes in the tree is in the range [0, 2000].
• −1000 ≤ Node.val ≤ 1000

Pattern Recognition Clues

Recognising these key signals in the problem description immediately identifies the pattern:

“bottom-up level order”

→ The same rows as LC 102, only in the opposite order.

“from leaf to root”

→ The deepest row must come first in the answer.

“left to right within each level”

→ Inside a row, the order does not change, so the rows are flipped but the values are not.

Approach Complexity Ladder

Brute Force — walk the tree from the deepest row upO(N · H)O(H)

Find the height, then for depth d from H − 1 down to 0, walk the whole tree and keep depth d

Optimal — level order, then reverse the list of rowsO(N)O(N)

Run the normal BFS unchanged, then reverse the outer list once

Brute Force Intuition

Find the height H. Then, for depth d from H − 1 down to 0, walk the whole tree and collect the nodes at depth d. The rows come out bottom-up directly, so nothing needs reversing.

Recognition rule for this sub-pattern:

Pop exactly `size` nodes per round; that round is one level.

Remember this · Tree BFS

Trigger

Level order, per-level max/average, right side view, minimum depth, nodes at distance k.

Think

Does the question care about depth / rows rather than paths?

Key question

How many nodes are in the current level (queue size at the start of the level)?

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