DATA STRUCTURES INTRODUCTION

1. DATA STRUCTURESINTRODUCTION CSC 172 SPRING 2004

2. COURSE GOALS • Write (lots of) great code • Understand the use of abstraction in computer science • Design efficient data structures and algorithms • Understand the use of mathematical tools in analysis for computer science • Develop general problem solving skills

3. What this course is about • Abstraction • Specifically, abstraction in computer programming through the use of abstract data types (ADTs) • Abstraction is powerful • Complexity of detail is encapulated and hidden • Allowing operations at a higher level • Your ability to abstract directly effects your productivity (as a lot of things) • Analysis • What makes a good abstraction?

4. Abstraction “The The acts of the mind, wherein it exerts its power over simple ideas, are chiefly these three: 1. Combining several simple ideas into one compound one, and thus all complex ideas are made. 2. The second is bringing tow ideas, whether simple or complex, together, and setting them by one another so as to take a view of them at once, without uniting them into one, by which it gets all its ideas of relations. 3. The third is separating them from all other ideas that accompany them in their real existence: this is called abstraction, and thus all its general ideas are made” - John Lock, An Essay Concerning Human Understanding (1690)

5. Abstraction “Leaving out of consideration one or more qualities of a complex object so as to attend to others.” - Mirriam Webster’s 9th Collegiate

6. Computer Science • The Mechanization of Abstraction “Computer Science is a science of abstraction – creating the right model for thinking about a problem and devising the appropriate mechanizable techniques to solve it” - Alfred Aho, 1995

7. Creativity as Science “Every other science deals with the universe as it is. The physicist’s job, for example, is to understand how the world works, not to invent a world in which physical laws would be simpler or more pleasant to follow. Computer Scientists, on the other hand, must create abstractions of real-world problems that can be understood by computer users and, at the same time, that can be represented and manipulated inside a computer” - Jeffrey Ullman, 1995

8. Example: Dictionary ADT • A dictionary is an abstract model of a database • In dictionaries, we look up definitions using words • Words : “keys” • Definitions : “elements” • The main operation supported by a dictionary is searching by key

9. Dictionary ADT • Simple container methods • size() • isEmpty() • Querry methods • findElement(k) • Update methods • insertItem(k,e) • remove(k) • Special object • NO_SUCH_KEY, returned by an unsuccessful search

10. Example: Dictionary ADT • As “users”, we can think about dictionaries in terms of such functionality without worrying about how they are implemented • Abstraction, problem conceptualization • As “programmers” we can think about how dictionaries are implemented without worrying about how they are used • Analysis, what is fast & efficient

11. Which Abstractions/Implementations? • Lists • Stacks • Queues • Trees • Sets • Graphs

12. What analysis? • “Anyone” can write a computer program. • What is the difference between a good solution and a not-so-good solution? • Running time • Memory requirements • Mathematical tools • Proof by induction • Combinatorics • Probability • Asymptotic analysis (Big-Oh)

13. Example • One dimensional pattern recognition • Input: a vector x of n floating point numbers • Output: the maximum sum found in any contiguous subvector of the input. • X[2..6] or 187 • How would you solve this?

14. Obvious solution • Check all pairs int sum; int maxsofar = 0; for (int i = 0; i<x.length;i++) for (int j = i; j<x.length;j++){ sum = 0; for (int k = i;k<=j;k++) sum += x[k]; maxsofar = max(sum,maxsofar); }

15. How long does the obvious solution take? • We could “measure” it – benchmarking • What is a “good size” of input to measure? • What machine do we measure it on?

16. How long does the obvious solution take? • We could “analyse” it • Multiply the “cost” (time required) to do something by the number of times you have to do it. • If n is the length of the array • Outer loop runs exactly n times • Inner loop runs at most n times • Inner most loop runs no more than n times • Let’s say the “+=“ and “max” take unit time

17. How long does the obvious solution take? • Innermost cost = n * 1 //worst case • Innerloop cost = n * (Innermost cost) +1 • Outerloop cost = n * (Innerloop cost) Outerloop cost = n * ( n * (Innermost cost) +1) Outerloop cost = n * (n *(n + 1) +1) Outerloop cost = n * (n2 + n + 1) Outerloop cost = n3 + n2 +n

18. How long does the obvious solution take? • We call this an “n3” solution • Can you think of a better (faster) way? • Can you do an analysis that will prove it better? • That is what we do in CSC 172 • For some very common tasks

19. Instructor Prof. Ted Pawlicki, pawlicki@cs.rochester.edu CSB 722, ext. 54198 Office Hours: TR 2PM-3PM -lunch meetings also available Lecture: T,R 2:00PM-3:15PM AM Dewey 1-101

20. Text • Data Structures & Problem Solving using Java 2nd Ed. By Mark Allen Weiss • Class, Lab, & Workshops

21. Grad TAs (Mostly Projects)

22. Lead UG TA (Mostly grades)

23. Labs: Taylor 30 MW 4:50-6:05 MW 6:15-7:30 * MW 2:00-3:15 TR 3:25-4:40 * Register as a class

24. WORKSHOPS Sign up Tuesday

25. EXAMS

26. Workshops • Required - attendance • 10% of Grade • Positive effect on grades • Independent of extra credit • Group skills are valued by employers • Industrial & academic

27. Extra Credit Reports • 10% boost for 10-20 page analysis of the UG CS curriculum at a selected institution • Instructor assigns institution • Overview of curricular requirements • Syllabus of 1st year courses (CS1 & CS2) • Compare & contrast to UR CS curriculum • Revision expected

28. Is this a hard course? • Yes • One course has to be the hardest • All majors have hard courses • “No pain, no gain” • Start early

29. Q&A • Do you understand what is expected of you?