Notes on Introduction to Binary Trees

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Overview of Binary Trees

• Binary Tree: A hierarchical data structure with nodes having at most two children.
  • Comparison with linear data structures: arrays, stacks, queues, linked lists.
• Hierarchy: Visual representation similar to folders within folders in a computer.

Basic Terminology

• Root: The starting point of the tree.
• Children: Nodes that branch off from a parent (e.g., two children of a node).
• Leaf Nodes: Nodes that do not have children (end nodes).
• Subtree: A portion of the tree that can be itself a tree.
• Ancestors: Nodes that are predecessors of a given node (parent, grandparent, etc.).

Types of Binary Trees

1. Full Binary Tree:

   • Every node has either 0 or 2 children.
   • Example: Nodes with 2 children or no children.

2. Complete Binary Tree:

   • All levels are fully filled except possibly for the last level, which is filled from left to right.
   • Example: Full nodes on levels except the last one which has nodes on the left.

3. Perfect Binary Tree:

   • All leaf nodes are at the same level.
   • Example: All leaves aligned horizontally at the same depth.

4. Balanced Binary Tree:

   • The height should be at most log(n) where n is the number of nodes.
   • Example: For n=8, height should not exceed 3.
   • Ensures efficient search and operations.

5. Degenerate Trees (Skew Trees):

   • Every node has only one child, resembling a linked list.
   • Example: Linear structure where each node points to just one child.

Conclusion

• Understanding binary trees is crucial as they frequently appear in coding interviews.
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