DSA & Algorithms
Part 11 of 21 · DSA Interview PatternsBinary Trees — BFS / Level Order — Layers, Width & Zigzag
Level-order BFS for layers, width, zigzag, and closest-value-by-depth.
- 1Gist
- 2Maps
- 3Q&A
- 4Sandbox
Voice readout needs Web Speech Synthesis in this browser.
The answer depends on the depth layer
Prefer
BFS with a level snapshot
The queue holds the next frontier. The length you captured is exactly one layer.
- Min depth is the first leaf the queue reaches.
- Right-side view is the last value in each level.
- Space tracks the widest level, not the height.
Alternative
DFS that records depth, for a shortest-leaf question
It works if you track the minimum. BFS finds that leaf first and can stop.
- Forgetting to snapshot len(queue) before the inner loop.
- Enqueueing null children.
- Assuming the queue stays O(height) on a wide tree.
One layer at a time
Snapshot, drain, enqueue children. That is the whole pattern.
- 1
Queue the root
An empty tree returns immediately. - 2
Drain the current length
That many pops are one level. - 3
Enqueue the real children
The queue you left behind is the next level.
Overview
Level-order BFS for layers, width, zigzag, and closest-value-by-depth.
Below is the full pattern: when to reach for it, a top-down picture, runnable Python and TypeScript templates, complexity, traps, LeetCode drills, and Q&A.
When to use / recognition cues
Use BFS/level-order when answers depend on depth layers, width, or closest nodes by distance in a tree.
Recognition cues
- level order traversal / zigzag
- right side view
- average of levels
- min depth (BFS finds shallowest leaf first)
Mental model
Flow
- 1
1. Queue the root
- next2. Snapshot this level size
- 2
2. Snapshot this level size
- next3. Visit the node, enqueue kids
- 3
3. Visit the node, enqueue kids
- next4. Queue holds the next level
- 4
4. Queue holds the next level
Lesson map
Binary Trees — BFS / Level Order — Layers, Width & Zigzag
Level-order BFS for layers, width, zigzag, and closest-value-by-depth.
Architecture. Architecture
Select a node to see why it exists, or an edge to see the protocol, direction, effect, and consequence.
Mermaid export
flowchart TB q["1. Queue the root"] l["2. Snapshot this level size"] kids["3. Visit the node, enqueue kids"] next["4. Queue holds the next level"] q -->|1. Queue the root| l l -->|2. Snapshot this level size| kids kids -->|3. Visit the node, enqueue kids| next
Read the chart from top to bottom. Two-way decisions keep the card narrow on a phone.
Core template (Python)
Press Run. Snippets must be self-contained — no network, files, or native modules.
Core template (TypeScript)
Press Run. Snippets must be self-contained — no network, files, or native modules.
Complexity analysis
- O(n) time, O(w) queue space (w = max width).
Common pitfalls & interview traps
LeetCode drill (real problems)
- Binary Tree Level Order Traversal
- Binary Tree Zigzag Level Order Traversal
- Binary Tree Right Side View
- Average of Levels in Binary Tree
- Minimum Depth of Binary Tree
- Populating Next Right Pointers in Each Node
Go deeper
- Back to the pattern map.
- NeetCode roadmap
- CP-Algorithms
Interview Q&A
Why BFS for min depth?
Answer
First leaf reached is shallowest.
Level size trick?
Answer
for _ in range(len(q)) processes exactly one layer.
Right side view?
Answer
Last node in each level, or DFS preferring right.
Zigzag?
Answer
Alternate reverse, or push/pop opposite ends.
Space concern?
Answer
Wide bushy trees hold O(n/2) on last level.
Next pointers?
Answer
BFS connect neighbors; perfect tree can use constant space tricks.