What is the Maximum Width of Binary Tree pattern?

The Maximum Width of Binary Tree is a common coding interview pattern in Breadth First Search problems. It provides a structured approach to solving related algorithm challenges efficiently.

When should I use Maximum Width of Binary Tree?

Use the Maximum Width of Binary Tree pattern when you encounter problems matching its characteristics. Check the "When to Use" and "Clues" sections in the lesson for specific indicators.

Is Maximum Width of Binary Tree asked in FAANG interviews?

Yes, Maximum Width of Binary Tree is an essential pattern commonly tested in FAANG and top tech company technical interviews.

Breadth-First Search

Medium

Maximum Width of Binary Tree

Find the widest level of the tree (including nulls between end nodes).

15 min

Solve on LeetCode

Problem Understanding

Given the root of a binary tree, return the maximum width of the given tree.

Width: The number of nodes between the leftmost and rightmost non-null nodes in a level, including the null nodes between them.
Imagine filling the tree into a complete binary tree structure. We count the distance from Start to End index.

Algorithm Strategy

Since we need to count nulls between nodes without actually storing null objects (which would waste memory), we use Indexing Strategy (Heap Indexing).

Assign Indices:
- Root is index 1 (or 0).
- If node is i, Left Child is 2*i.
- Right Child is 2*i + 1.
BFS: Traverse level by level. Store (Node, Index) pairs in the Queue.
Compute Width: For each level, Width = (Last_Index - First_Index) + 1.

Interactive Visualization

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Empty Heap

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