CS302: Fundamental Algorithms (and Data Structures)

Transcription

1 CS302: Fundamental Algorithms (and Data Structures) Fall 2006 Instructor: Dr. Lynne Parker

2 CS302: Fundamental Algorithms (and Data Structures) Dr. Lynne Parker, Associate Professor, Dept. of Computer Science C220 TA: Charles Phillips C110g TA (1/2-time): Michael Bailey C125d TA (1/2-time): Yuanyuan Li C125c Mon. 1 2:30 PM: Bailey office hrs. Tues. 12:30 2:00 PM: Phillips office hrs. 2:10 3:25: Class 3:30 4:30 PM Parker office hrs. Our Office Hours: Wed. 1 2:30 PM: Bailey office hrs. 2:30 5:30 PM: Lab 1 (Bailey) Thurs. 12:30 2:00 PM: Phillips office hrs. 2:10 3:25: Class 3:30 4:30 Parker office hrs. Fri. 9:05 12:05 AM: Lab 2 (Phillips)

3 Today s Topics Administrivia (syllabus, labs, ) Overview of Data Structures and Algorithms Bookstore example Abstraction Interface Implementation Reminder of C stuff Homework!!

4 The bookstore example How do you find the book you re looking for? You need to use some kind of algorithm and

5 The bookstore example How do you find the book you re looking for? You need to use some kind of algorithm and of course, we want the best algorithm possible, but

6 The bookstore example How do you find the book you re looking for? You need to use some kind of algorithm and of course, we want the best algorithm possible, but what best means will depend on how the books are organized (stored)

7 MessyBookPile, Inc. This bookstore keeps its books all it one big pile, with no organization of any kind Your algorithm is then: For each book: If it is not the book I want, continue searching If the bookstore has 1,000,000 books, and if it takes 10 seconds for you to check each book, it make take you as long as 4 months (!) to find the book you want Not very good, is it? NOTE: Search time is directly proportional to the number of books: O(n).

8 LongBookShelf, Inc. This competitor bookstore keeps its books all in one very long array sorted by ISBN One possible algorithm is then (linear search): For each book If it is not the book I want, continue searching (Obviously, this is the same algorithm used with MessyBookPile, Inc.) Again search time is directly proportional to the number of books: O(n). Hmmm we didn t make use of the fact that the books are sorted

9 LongBookShelf, Inc. Another possible algorithm is then (binary search): Look at the middle book If it is the book I want, stop. If the book I want comes before the middle book, search the first half of the books using this same algorithm If the book I want comes after the middle book, search the second half of the books using this same algorithm This now makes use of the fact that the books are sorted. And, it s recursive! Now search time is proportional to the logarithm of the number of books: O(log 2 n) 1,000,000 books, 10 seconds/book =???

10 LongBookShelf, Inc. Another possible algorithm is then (binary search): Look at the middle book If it is the book I want, stop. If the book I want comes before the middle book, search the first half of the books using this same algorithm If the book I want comes after the middle book, search the second half of the books using this same algorithm This now makes use of the fact that the books are sorted. And, it s recursive! Now search time is proportional to the logarithm of the number of books: O(log 2 n) 1,000,000 books, 10 seconds/book = 200s < 4 min!!! [ 2 20 = 1,048,576; so, log 2 (1,000,000) 20 ]

11 BinaryBooks, Inc. This bookstore keeps its books organized in a binary search tree It s suing LongBookShelf, Inc., because they stole the idea of a binary search from BinaryBooks, Inc. The algorithm is binary search: Look at a node of the tree If it contains the book I want, stop if the book I want comes before the book in this node, search this node s left child, using the same algorithm If the book I want comes after the book in this node, search this node s right child, using this same algorithm

12 CategoriesRUs, Inc. This other competitor bookstore keeps its books all organized by sections The search algorithm is now: For each section If it is the section of the book I want Search each book in that section using one of the previous algorithms This is a little faster than the previous algorithms

13 Bottom line The choice and efficiency of an algorithm depends on how the data is organized Likewise, how you re going to store your data depends on what you want to do with it. If you don t care about searching, you might not care if the algorithm is linear search or binary search. In addition, a data structure depends on the properties of the data it stores Pile of books: equality Sorted books: less than

14 Interface vs. Implementation Consider an int variable int is a data type It could be that the computer you re using stores int in 1 s complement or 2 s complement format When you use it, you don t care how it s really implemented inside the computer All you care about is that the following operations are defined for that particular data type: +, -, *, /, <, >,,, ==,!=, ++, -- A data type like that is called an Abstract Data Type (or ADT)

15 Interface vs. Implementation So, what you really care about is the interface of an ADT, not its implementation The interface of an ADT is the set of operations defined for it So, in the bookstore example, you could create a general interface for your bookstore, and then have as many individual implementations as you wanted This sounds like Object-Oriented Programming (or OOP)

16 Interface vs. Implementation BookSet void add(book b) void remove(book b) bool has(book b) SortedArrayBookSet Attributes Operations BinaryTreeBookSet Attributes Operations HashBookSet Attributes Operations

17 Now Refresher on C Stuff 3 readings for today: 1. Fundamentals 2. General C Stuff 3. Coding Clearly See Schedule/Readings/Notes link for these handouts:

18 That s all, folks Your homework: Lab 1 assigned today!! Due Monday, Sept. 11. See Lab Assignments link: Read 3 assignments for today, and work examples contained in them: See Schedule/Readings/Notes link for today: