programming-for-dummies

Taking Action on Trees 385
Traversing a tree
When you store data in an array or a collection, that data is stored in a line
so you can search the entire data structure by starting at one end and examining
each data chunk one by one until you get to the end. However, trees
are different because they offer multiple branches.
To search a tree, the computer must examine multiple nodes exactly once,
which is known as traversing a tree. Four popular ways to search a tree, as
shown in Figure 5-11, include
Figure 5-11:
The four
different
ways to
traverse
a tree.
4
8
9
10
11
12
19
Preorder: 10, 8, 4, 9, 12, 11, 19
In-order: 4, 8, 9, 10, 11, 12, 19
Postorder: 4, 9, 8, 11, 19, 12, 10
Level order: 10, 8, 12, 4, 9, 11, 19
✦ Preorder
✦ In-order
✦ Postorder
✦ Level order
Preorder traversal
Preorder traversal starts at the top of a tree (the root node) and then traverses
the left nodes. When it reaches a leaf node, it backtracks and goes
down the right nodes, as follows:
Book III
Chapter 5
Graphs and Trees
1. Visit the root node.
2. Traverse the left sub-tree in preorder.
3. Traverse the right sub-tree in preorder.
In-order traversal
When traversing an ordered binary tree, the in-order traversal retrieves data
in order by following these steps: