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

Definition (Postorder Traversal): Let T be an ordered rooted tree with root r. If T
consists only of r, then r is the postorder traversal of T. Otherwise, suppose T 1 ,
T 2 , …, T n are subtrees at r from left to right in T. Then the postorder traversal
begins by traversing T 1 in postorder, T 2 in postorder, …, T n in postorder, and r.
Example: In the tree example at the top of page 199, the postorder traversal
order is 1.1, 1, 2.1, 2.2.1, 2.2, 2.3, 2, and 0.
Notation: Let add_to_list(v) be a global function to append a vertex v to a list.
The list must be initialized to / at some point before use.
Note: The tree traversal algorithms are all easily defined recursively using a
global list that must be initialized first.
201
procedure preorder_traversal( T: ordered rooted tree )
r := root(T)
add_to_list(r)
for each child c of r from left to right
T(c) := subtree with c as its root
preorder_traversal( T(c) )
procedure inorder_traversal( T: ordered rooted tree )
r := root(T)
if r = leaf then add_to_list(r)
else
q := first child of r from left to right
T(q) := subtree with q as its root
inorder( T(q) )
add_to_list(r)
for each remaining child c of r from left to right
T(c) := subtree with c as its root
inorder_traversal( T(c) )
202