Trees (chapter 17)

With arrays:

The size of the data set cannot be changed once the array is created

It is costly to move elements around (add, delete, rearrange)

Linear search is inefficient, but works

Binary search is more efficient

With linked lists:

The size of the data set can change

Moving elements around is efficient (add, delete, sort, etc.)

Linear search is still relatively inefficent, but works

Binary search is very inefficient

Like linked lists, trees are implemented with pointers.

In a linked list, each node has a pointer to the element that comes after it in the list

In a tree, each node has pointers to all of the nodes that come below it, called its children.

Nodes that have no children are called the leaves of the tree.

Examples:

Family tree

Animal taxonomies

File system directory structure

Binary trees

In some trees, all nodes have the same number of children.

In other trees, the number of children may vary

Binary trees are trees in which all non-leaf nodes have either one of two children

Binary trees are useful for storing information that will be accessed via a set of binary decisions

Examples:

Greater-than/Less-than decisions (Binary search)

Anything else with two choices (Morse code example)

Morse code

Morse code is a system for representing the alphabet in which each letter of the alphabet is represented by a short sequence of dots and dashes.

In Morse code

A = dot-dash

B = dash-dot-dot-dot

C = dash-dot-dash-dot

D = dash-dot-dot

E = dot

etc.

To find out what letter is represented by a particular sequence of dots and dashes, you just start at the top of the tree and follow the links indicated by the sequence. Wherever you stop, that's the letter.

Binary search trees

Binary trees can also be used to hold dynamic lists of numbers.

Adding to a binary tree

Deleting from a binary tree

Searching for an element in a binary tree

Recursion in binary trees

Subtrees

Binary tree code

Tree search algorithms