The Art of Data Structures Introduction. Richard E Sarkis CSC 162: The Art of Data Structures

Transcription

1 The Art of Data Structures Introduction Richard E Sarkis CSC 162: The Art of Data Structures

2 Class Administrivia

3 Agenda To review the ideas of computer science, programming, and problem-solving To understand abstraction and the role it plays in the problem-solving process To understand and implement the notion of an abstract data type

4 Class Overview

5 Just the Facts, Ma am Mr. Richard Sarkis Bausch & Lomb Hall, Room 470 Take elevators to the 4th floor of B&L Hall, make a left and all the way to the end of the hall

6 Class Organization Class content provided mostly through a class website, and the rest through Blackboard Course components are: Lectures Assignments Quizzes

7 Lectures See class website for schedule! Course will include Lecture slides (i.e. my lecture notes) Live, demonstrative coding Discussions from the class Class participation is vital We are a small class (v.s people)

8 Syllabus

9 What is Computer Science?

10 Why Computer Science? Everything is bits and computation! Astronomy - simulation and observation data Biology Protein folding Music Sound processing Mechanical Engineering Load bearing Literature Text analysis What are you studying?

11 Lies, damned lies Common misconceptions about Computer Science Computer science is the study of computers Computer science is the study of how to write computer programs Computer science is the study of the uses and applications of computers and software

12 What would we like our children- the general public of the future to learn about computer science in schools? We need to do away with the myth that computer science is about computers. Computer science is no more about computers than astronomy is about telescopes, biology is about microscopes or chemistry is about beakers and test tubes. Science is not about tools, it is about how we use them and what we find out when we do." Micheal R. Fellows, Ian Parberry (1993) "SIGACT trying to get children excited about CS". in: Computing Research News. January 1993.

13 Computer science is the study of computation. Feasibility, structure, expression, and mechanization of the methodical processes (or algorithms) that underlie the acquisition, representation, processing, storage, communication of, and access to information

14 What a tool The computer is just a tool, described and realized by the concepts computer science

15 Why Programming?

16 The art of programming is the art of organizing complexity, of mastering multitude and avoiding its bastard chaos as effectively as possible. Edsger W. Dijkstra (1970) "Notes On Structured Programming" (EWD249), Section 3 ("On The Reliability of Mechanisms"), p. 7.

17 Why Programming? Simply using off the shelf applications will get you a long way: Spreadsheets, Photo editors, word processors But if you are doing novel, creative work, sooner or later, you will need to solve a new problem Learning good principles of programming will make it possible with more fun and less frustration

18 Programming Take a computing problem and create an executable program Analyze and understand the problem Design a data model and an algorithm Data model: way to represent the information Algorithm: formal computation steps Implement the algorithm in a computer language

19 Programming Programming!= solving a problem Programming is teaching somebody else how to solve a problem Somebody else is a computer A computer is a device that can be programmed to carry out a finite set of operations on binary numbers Computers can t do anything that they are not programmed to do

20 Procedural Abstraction n sqrt( ) square root of n

21 Tic-Tac-Toe An almost universally known game To create a Tic-Tac-Toe program you have to teach a computer: The rules of the game A strategy to play the game (Plus other things, like input/output, etc)

22 Programming Example

23 Why Python?

24 Why Python? It's powerful, accessible and used in many fields

25 Why Python? Python is a language of choice for: Scientists (NASA) Web site builders (Reddit) Researchers in the humanities (Somebody ) Application developers (Dropbox)

26 Why Python? We'll be using Version 3.6 or later

27 Why Python? Python can be used in a variety of contexts, we'll be using Jupyter notebooks This class will use Jupyter notebooks exclusively!

28 Why Python? Python installations can be complex with the large number of third-party packages (Jupyter, NumPy, matplotlib, etc.) Anaconda is a great re-packaging of Python and a variety of packages: downloads

29 Why Data Structures and Algorithms?

30 Why Data Structures and Algorithms? Our goal is to write good programs

31 Why Data Structures and Algorithms? Write computer programs in some language (e.g. Python) Mathematical maturity to understand proof Abstraction

32 Why Data Structures and Algorithms? Imagine it's You're a law clerk, charged with organizing the records of a newly created law firm. How do you expect people to use the files? What sorts of questions will they want to answer -- what sorts of things will they want to look up?

33 Why Data Structures and Algorithms? Records of a particular case, by: date plaintiff, defendant, client name court docket # All cases with given: plaintiff defendant judge point of law size of award

34 Why Data Structures and Algorithms? What other indices would you keep? How hard would it be to find things for which you don't have an index? What shortcuts might be possible?

35 Why Data Structures and Algorithms? The list of operations you want the files to support is analogous to an Abstract Data Type (ADT). The physical organization is analogous to a Data Structure (DS).

36 Why Data Structures and Algorithms? It's very important to distinguish between these two concepts We will look at three main things this semester: ADTs, DSes, and algorithms

37 Why Data Structures and Algorithms? An Abstract Data Type (ADT) represents a particular set of behaviors You can formally define, perhaps using mathematical logic) what an ADT is/does

38 Why Data Structures and Algorithms? For example, a Stack is a list implements a LIFO policy on additions/deletions

39 Why Data Structures and Algorithms? A data structure is more concrete Typically, it is a technique or strategy for implementing an ADT

40 Why Data Structures and Algorithms? Use a linked list or an array to implement a stack class

41 Why Data Structures and Algorithms? stack queue Some common ADTs that all trained programmers know about: priority queue dictionary sequence, set

42 Why Data Structures and Algorithms? Some common data structures used to implement those ADTS: array linked list hash table (open, closed, circular trees (binary search trees, heaps, AVL trees, 2-3 trees, tries, red/black trees, B-trees)

43 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. - A. Aho

44 Why Data Structures and Algorithms? Abstract data types has similarity to procedural abstraction A logical description of how we view the data A set of operations allowed No care about implementation underneath

45 Why Data Structures and Algorithms? User Encapsulation provides information hiding Hides the details of the implementation Interface Implementation Operations

46 Case in Point: Factoring

47 Case in Point: Factoring Computers are fast, but some problems still take a long time Example : 7 x 13 = 91 7 x 13 =? (multiplication),? x? = 91 (factoring) Giant numbers : 100 digits RSA factoring challenge (google) Rsa, cryptography, factoring

48 Case in Point: Factoring RSA Challenge RSA-704 Status: Factored in 2012 Decimal Digits: Decimal Digit Sum: 1009

49 Case in Point: Factoring RSA Challenge RSA-220 Status : Not Factored Decimal Digits : 220 (729 bits)

50 Case in Point: Factoring What's so hard about factoring?

51 Case in Point: Factoring What's so hard about factoring? Divide by 2, 3, 5, 7... until you find a factor Brute Force Search is very slow when the search space is huge Is searching necessary? (so far, it seems so)

52 Case in Point: Factoring Needle in a haystack problem Searching may not be necessary if you have a magnet (closed form) Figuring triangle sum

53 Big-O

54 Big-O Given an algorithm can you estimate how much time and memory it will take to process a given amount of data?

55 Big-O I have two programs They both do the same thing I measure their run time

56 Big-O prog1 takes 1 sec to process a 1GB array and 2.25 sec to process a 1.5GB array. prog2 takes 3 sec to process a 1GB array and sec to process a 1.5GB array. Which should I use on my 100GB array?

57 Big-O

58 Big-O How many people have heard of this? It captures the notion of asymptotic complexity how much time (and sometimes space) it takes to solve a problem of a given input size If you keep taking CS, you'll learn a lot more about this in 173, 280, or 282

59 Big-O Sorting is a canonical example For lists of length N, we'll look at sorts that take time proportional to 2 N, N 2, Nlog(N), and N (in special cases) Note that if N is big enough, Nlog(N) is still less than N 2 (Does everybody know what log is?)

60 Conclusion This course will cover a variety of intermediate topics: Analytical Process Standard Techniques Data Structures Lists, Stacks, Queues, Trees, Heaps, Hashes, Graphs, Sets

61 Conclusion Algorithms Sorting, Greedy, Backtracking, Randomized, Dynamic Programming Mathematics Proof by Induction Recurrence Relations

62 Questions?