Summary of "L21. Vertical Order Traversal of Binary Tree | C++ | Java"

Summary of “L21. Vertical Order Traversal of Binary Tree | C++ | Java”

This video tutorial explains the problem of Vertical Order Traversal of a Binary Tree and provides a detailed approach to solving it using C++ and Java. The explanation covers problem understanding, data structures used, traversal methodology, and a code walkthrough.

Main Ideas and Concepts

Problem Definition Vertical order traversal of a binary tree means grouping the nodes vertically from left to right. Within each vertical line, nodes are ordered from top to bottom. If nodes overlap vertically and horizontally, smaller values come first.
Key Observations
- Each vertical line corresponds to an integer coordinate on the x-axis.
- Each node has a level (y-axis) representing its depth in the tree.
- Nodes are grouped by vertical coordinate, then sorted by level, and if nodes share the same vertical and level, they are sorted by node value.
- The output is a list of lists (or vector of vectors), where each inner list represents one vertical line.

Methodology / Step-by-Step Instructions

Assign Coordinates to Nodes
- Vertical coordinate (x):
  - Move to left child → x - 1
  - Move to right child → x + 1
- Level (y):
  - Increase by 1 as you move down each level in the tree.
Data Structures
- Use a map to store nodes by vertical → level → sorted nodes:
  - C++: map<int, map<int, multiset<int>>>
  - Java: TreeMap<Integer, TreeMap<Integer, PriorityQueue<Integer>>>
- Use a queue for level order traversal, where each element stores (node, vertical, level).
Traversal
- Perform a level order traversal (BFS) starting with the root node at (vertical=0, level=0).
- For each node:
  - Insert the node’s value into the map at [vertical][level].
  - Enqueue the left child with (vertical - 1, level + 1) if it exists.
  - Enqueue the right child with (vertical + 1, level + 1) if it exists.
Building the Result
- After traversal, iterate over the map in ascending order of verticals.
- For each vertical, iterate over levels in ascending order.
- For each level, retrieve the sorted nodes and append them to a temporary list.
- Append this list to the final answer list.
Handling Overlapping Nodes
- Use a multiset (C++) or priority queue (Java) to automatically sort nodes with the same vertical and level.
- This accounts for duplicate values and ensures nodes are output in sorted order.
Code Implementation Details
- C++ uses pairs and multisets; Java uses tuples (or custom classes), TreeMaps, and priority queues.
- The queue stores (node, vertical, level) tuples.
- Insertions and retrievals are done carefully to maintain order.

Complexity

Time Complexity Approximately O(N log N) due to sorting nodes at each vertical and level (multiset/priority queue insertions).
Space Complexity O(N) for storing all nodes in the map and queue.

Additional Notes

The presenter encourages viewers to try solving the problem using other traversal methods like inorder or preorder as homework.
The tutorial is part of a three-video series sponsored by a platform called “Reliable”.
Both C++ and Java code are presented side-by-side for clarity.
The presenter emphasizes the importance of understanding the data structures used (maps, multisets, priority queues) and the traversal logic.

Speakers / Sources

Main Speaker / Presenter: The video narrator (unnamed) who explains the concept, approach, and code.
Sponsor Mentioned: Reliable by an academy (briefly mentioned at the beginning).

This summary captures the key ideas, methodology, and implementation details for vertical order traversal of a binary tree as explained in the video.