# Trees

Daniel Weibel
Created 1 Sep 2017
Last updated 9 Nov 2017

# First of All…

A tree is just a special type of graph, namely a connected acyclic graph.

# Terminology

## Height of a Node

• Number of edges on the longest path from this node to a leaf
• Leaves have height 0

## Height of a Tree

• Height of the root

## Depth of a Node

• Number of edges on the path from this node to the root
• Root has depth 0

## Levels of a Tree

• A tree has Height + 1 levels
• Root is at level 1

# Binary Trees

TODO: draw example binary tree with e.g. 10 nodes

• Height of a binary tree with $n$ nodes: $\lfloor\Log n\rfloor$
• Maximum number of nodes in a binary tree with $n$ levels: $2^n-1$