A complete binary tree is structurally constrained. This is important for efficiency!

  • Why? A complete binary tree with $n$ nodes has a height of $\lfloor \log_2 n \rfloor$.
  • This balanced shape prevents the tree from becoming skewed (like a linked list), which would degrade performance to $O(n)$.
  • The height being $O(\log n)$ is the key to our efficient operations.
Balanced (Efficient) h = O(log n) Skewed (Inefficient) h = O(n)