Discrete Mathematics University of Kentucky CS 275 Spring ... - MGNet

Example: Given a tree T = (V,E) with keys ordered 0 < 1 < 1.1 < 2 < 2.1 < 2.2 <
2.2.1 < 2.3, we represent it as
• 0
• 1 • 2
• 1.1 • 2.1 • 2.2 • 2.3
• 2.2.1
We will use this example for quite some time.
199
Definition (Preorder Traversal): Let T be an ordered rooted tree with root r. If T
consists only of r, then r is the preorder traversal of T. Otherwise, suppose T 1 ,
T 2 , …, T n are subtrees at r from left to right in T. Then the preorder traversal
begins at r and continues by traversing T 1 in preorder, T 2 in preorder, …, and T n
in preorder.
Example: In the tree example at the top of page 199, the preorder traversal order
is 0, 1, 1.1, 2, 2.1, 2.2, 2.2.1, and 2.3.
Definition (Inorder Traversal): Let T be an ordered rooted tree with root r. If T
consists only of r, then r is the inorder traversal of T. Otherwise, suppose T 1 , T 2 ,
…, T n are subtrees at r from left to right in T. Then the inorder traversal begins
by traversing T 1 in inorder, then r, and continues with T 2 in inorder, …, and T n
in inorder.
Example: In the tree example at the top of page 199, the inorder traversal order
is 1.1, 1, 0, 2.1, 2, 2.2.1, 2.2, and 2.3.
200