# Is a balanced binary tree a complete binary tree?

Considering that the opposite is true it's not mentioned anything about this. I am assuming its not, but I need a very good distinction between these two types of binary trees.

All I know is this:

• A binary tree is balanced (or height balanced), if the height of any node’s right subtree and left subtree differ no more than $1$.
• A complete binary tree of height h is a binary tree that is full down to level $h-1$, with level $h$ filled in from left to right.
• Take it as an exercise to find a balanced binary tree which isn't complete, and on the other hand to prove that every complete binary tree is balanced. Try to use the definitions. – Yuval Filmus Mar 8 '16 at 22:33

A complete binary tree is a binary tree of length $$h$$ such that all the levels from $$1$$ to $$h-1$$ are completed and the last level gets completed from left to right. As in the image below. A balanced binary tree is a binary tree of height $$h$$ such that the height of any node’s right subtree and left subtree differ no more than $$1$$. So it doesn't say anything about it having to be completed from left to right. 