BCA / B.Tech 11 min read

Full Binary Tree in Data Structures

Full Binary Tree in Data Structures:


What is a Full Binary Tree?
A Full Binary Tree is a special type of binary tree in which every node has either 0 or 2 children. This means every node is either a leaf node (with no children) or has exactly two children. The structure of this tree is very organized and easy to analyze mathematically.

Characteristics of a Full Binary Tree:
  • Number of Nodes: If the height of the tree is `h`, a full binary tree can have a maximum of `2^(h+1) - 1` nodes.
  • Child Nodes: Every node is either a leaf node or has two children. No node has only one child.
  • Number of Leaf Nodes: The number of leaf nodes is always `n + 1`, where `n` is the number of internal nodes.
  • Depth: The depth of nodes in a full binary tree is uniform, which helps maintain the balance of the tree.

Types related to Full Binary Tree:
Perfect Binary Tree, Complete Binary Tree, Balanced Binary Tree.

Advantages of a Full Binary Tree:
Efficient Searching, Fast Insertion and Deletion, Hierarchical Data Storage, and Space Efficiency.

Disadvantages of a Full Binary Tree:
Complexity, Not Suitable for Large Data (can consume a lot of memory), and Deletion issues that may require rebalancing.

Examples of Full Binary Trees:
Huffman Coding Tree, Merkle Tree (in cryptography), and Heaps.

Python Program to Check for a Full Binary Tree:
The provided Python code defines a `Node` class and a function `is_full_binary_tree(root)` that recursively checks if a given binary tree is a full binary tree. It returns `True` if every node has 0 or 2 children, and `False` otherwise.