##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
Balanced binary trees
A balanced binary tree with nodes has height . Why? Each level doubles the number of nodes.
Level has node (the root). Level has nodes. Level has nodes. Level has nodes. If the tree has total nodes, then , so .
This is why operations on balanced trees (like AVL trees or red-black trees) take time. You traverse from root to leaf, which is steps.
