Types of Binary Trees

Not all binary trees are the same. There are several types of binary trees, each with different properties.

Full Binary Tree

A full binary tree is a tree where every node has either 0 or 2 children, no node has only one child.

        [1]
       /   \
     [2]   [3]
    /   \
  [4]   [5]

✓ Full, every node has 0 or 2 children


        [1]
       /   \
     [2]   [3]
    /
  [4]

✗ Not full, [2] has only one child

Complete Binary Tree

A complete binary tree is a tree where every level is fully filled except possibly the last, and the last level is filled from left to right.

        [1]
       /   \
     [2]   [3]
    /   \  /
  [4]  [5][6]

✓ Complete, last level filled from the left


        [1]
       /   \
     [2]   [3]
    /   \     \
  [4]   [5]   [6]

✗ Not complete, last level not filled from the left

Perfect Binary Tree

A perfect binary tree is a tree where every level is completely filled. All leaf nodes are at the same depth.

        [1]
       /   \
     [2]   [3]
    /   \ /   \
  [4] [5][6]  [7]

✓ Perfect, all levels completely filled

A perfect binary tree is both full and complete!

Balanced Binary Tree

A balanced binary tree is a tree where the height of the left and right subtrees of every node differ by at most 1.

        [1]
       /   \
     [2]   [3]
    /   \
  [4]   [5]

✓ Balanced, height difference is at most 1


        [1]
       /
     [2]
    /
  [3]

✗ Not balanced, left subtree is much taller

Balanced trees are important because they keep operations like search, insert, and delete at O(log n) instead of degrading to O(n) in the worst case.

Summary

Type	Property
Full	Every node has 0 or 2 children
Complete	All levels filled except last, filled left to right
Perfect	All levels completely filled
Balanced	Height difference between subtrees is at most 1