COMP 202: Principles of Object-Oriented Programming II← Tree Traversal Algorithms → |
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The Mutable Binary Tree Framework stores data in a hierarchical fashion, where mutation is allowed:
When we process a list, we basically have two ways to traverse it and move data along: forward (as in forward accumulation) or reverse (as in reverse accumulation). In contrast, due to its non-linear structure, a binary tree can be traversed in many more different ways. However, we can categorize data movement in two "directions": top-down and bottom-up. In this lecture, we will study four tree traversal algorithms that are most common in tree processing.
For the sake of definiteness, we consider the following trees as examples throughout:
mtTree: an empty tree
biTree: the non-empty tree
1
/ \
2 3
/ \ \
4 5 6
/
7
Here is what it means to process a tree by traversing it in in order.
Here is a concrete example of an in-order traversal of the above biTree.
Write a visitor that prints the contents of a binary in in-order traversal. What should the output be for the above biTree?
As you can see, there is so much similarity between the code for exercise 1 and InOrderAdd. The question is whether or not we can separate the variants from the invariant and capture the abstraction of in-order traversal as the invariant.
Clearly, tree traversal is a visitor. What does it mean to "process the root"? How can we enforce the order of processing?
Processing the root and each of the subtrees: use an abstract function ILambda; the concrete ILambdas are the variants.
Enforcing the order of processing: use the order in which the arguments of of a function are evaluated; this is the invariant.
So here is the invariant code for in-order tree traversal.
Here is what it means to process a tree by traversing it in in order.
Write an invariant post order traversal visitor analogous to the above in order traversal visitor.
Here is what it means to process a tree by traversing it in in order.
Write an invariant pre order traversal visitor analogous to the above in order traversal visitor.
URL: http://www.cs.rice.edu/teaching/202/08-fall/lectures/tree/index.shtml
Copyright © 2008-2010 Mathias Ricken and Stephen Wong