Topics for Exam 2
CS 241: Data Structures, Fall 2007

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Exam will include exercises from chapters 6-10 and 11.3 in the text, vocabulary, questions on material covered in class, and questions on labs (perhaps writing very short snippets of code).

Chapter 6: Linked Structures

• What is a linked list?
• Iterative implementation of a list operations, e.g. add, remove, contains
• Compare to ArrayList implementation. When is one better than the other?
• How do you maintain a sorted linked list (see Card lab).

Chapter 7: Complexity Analysis of Algorithms

• How do you compare algorithms?
• Costs: space and time.
• Asymptotic notation. big-theta (Θ), big-Oh (&Omicron), and big-Omega (Ω)
• Know relative behavior of common functions such as aⁿ, n^a, log(n), n!, etc
• Know how to calculate the complexity of simple algorithms (e.g. loops, nested loops)
• Know the simple series: arithmetic (sum_k k), geometric (sum_k x^k), harmonic (sum_k 1/k)
• Know basic log identities, i.e. expand log(ab), log(a/b), log(a^b)

Chapter 8: Searching and Sorting

• Binary search
• Comparable Interface
• Sorting algorithms: bubble, stooge, insertion, selection, merge, quick
• Compare sorts based on: complexity, stability, in-place, comparison, divide and conquer, swapping adjacent items, special cases.

Chapter 9: Recursion

• What is the structure of an inductive proof?
• Induction problems - see examples from homework and class.
• Know how to calculate the complexity of a simple recursive program (e.g. using telescoping)
• Recursive implementation of a linked list, e.g. add, remove
• Compare and contrast dynamic programming to recursion. Recall fibonacci example.

Chapters 10 and 11: Trees: General and Binary

• Terminology: root, children, leaf node, internal node, level, depth, degenerate tree, (proper) descendants, (proper) ancestors, siblings,height, full tree, perfect tree, binary tree, binary search tree, subtree.
• Characteristics of perfect binary tree - what is relationship between height and the number of nodes?
• Traversing: pre-order, post-order, in-order, level-order
• Examples: decision trees, game trees (minimax), binary search trees, mazes
• Other functions on binary trees:
  • Inserting a value into the tree.
  • Searching a tree to see if an item is in it.
  • Finding the height of a tree.
  • Printing the tree structure - using parenthesis or as a tree on its side.

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