Algorithms More than just solving the problem

1. INFO100 and CSE100 Fluency with Information Technology Algorithms More than just solving the problem Katherine Deibel Katherine Deibel, Fluency in Information Technology

2. What is an algorithm? • Algorithms are what computer scientists study • It's not just writing code! Katherine Deibel, Fluency in Information Technology

3. What Computer Scientists Do We solve problems EFFICIENTLY: • Define what the problem is • What inputs are given? What needs to be solved? What needs to be outputted? • Develop a solution process • Is it accurate? Is it efficient? Could we improve it? • Implementation • How do we organize the data? • Does the choice of software/hardware change the efficiency? Katherine Deibel, Fluency in Information Technology

4. Algorithms Everywhere • Theory • All about algorithms • Graphics • Even more algorithms • Architecture/Hardware • Branch prediction, memory schemes, etc. • Networks • Ensure transmission, data compression, etc. • Human-Computer Interaction • Efficiency of human input/output Katherine Deibel, Fluency in Information Technology

5. What is an algorithm? " [An] algorithm is a procedure and sequence of actions to accomplish some task. The concept of an algorithm is often illustrated by the example of a recipe, although many algorithms are much more complex; algorithms often have steps that repeat (iterate) or require decisions (such as logic or comparison). In most higher level programs, algorithms act in complex patterns, each using smaller and smaller sub-methods which are built up to the program as a whole." Source: Computer User's online dictionary Katherine Deibel, Fluency in Information Technology

6. What is an algorithm? • Simply put:An algorithm is a precise description of the steps and methods used to solve a problem or produce a specified result Katherine Deibel, Fluency in Information Technology

7. What is an algorithm? • Simply put:An algorithm is a precise description of the steps and methods used to solve a problem or produce a specified result Katherine Deibel, Fluency in Information Technology

8. Properties of Algorithms • For an algorithm to be well specified, it must have the following • Inputs specified • Outputs specified • Definiteness • Effectiveness • Finiteness Form of data to process Form of results to produce Agent always knows what to do next Agent able to do all commands Will stop with answer, or say ‘none’ Katherine Deibel, Fluency in Information Technology

9. Properties applied to a recipe • Title • Ingredients (inputs) • Steps • Exceptions • When to stop • Servings (outputs) Katherine Deibel, Fluency in Information Technology

10. Context Matters • Algorithms are abstract but how and where you execute them matters • Think about baking bread • In an electric oven • Brick oven • A bread machine • The recipes may need to differ depending on the machine in use Katherine Deibel, Fluency in Information Technology

11. Algorithms vs Programs • The recipe metaphor breaks down here • Algorithms are abstract: • Not specific to any hardware • Not specific to any programming language • Programs are instantiations of algorithms • Put into a specific language • Meant to work in specified contexts Katherine Deibel, Fluency in Information Technology

12. Previous Algorithms • We have already seen several algorithms (and programs) • Constructing a table of Fahrenheit to Celsius conversions (Ch. 20) • Computing the price of espresso drink (Ch. 18) • Computing weight in gold • Fingerspelling (parsing of input)

13. Sorting Algorithms Everyday application Katherine Deibel, Fluency in Information Technology

14. Elements of Sorting • Inputs specified:A list of items in any order • Outputs specified:The items in ascending order • Definiteness: • Effectiveness: • Finiteness:Clearly can be done in finite time Katherine Deibel, Fluency in Information Technology

15. Turn to your neighbor… With your neighbor(s), discuss how you would sort a deck of cards into numerical order (As, 2s, 3s,…, Qs, Ks) • How many different ways can you think of? • Is any better than theothers? • How do you know? Katherine Deibel, Fluency in Information Technology

16. Random Sort Algorithm: Check if deck is sorted If not sorted, shuffle the deck Repeat • Will it finish? • Will it be correct? • Is it efficient? Katherine Deibel, Fluency in Information Technology

17. Insertion Sort Algorithm: Take first card and start a sorted pile For each remaining card Find the position where it belongs in the sorted pile Place card in correct spot Katherine Deibel, Fluency in Information Technology

18. Insertion Sort Deck: 4, 7, 2, 5, J, 8, … • Deck: 4 |7, 2, 5, J, 8, … • Deck: 4, 7 |2, 5, J, 8, … • Deck: 2, 4, 7 |5, J, 8, … • Deck: 2, 4, 5, 7 | J, 8, … • Deck: 2, 4, 5, 7, J |8, … • Deck: 2, 4, 5, 7, 8, J |… Katherine Deibel, Fluency in Information Technology

19. Insertion Sort • Does it end? Yes • Will it be correct? Yes • Is it efficient? • Fairly efficient in real world • Programming has varying performance: • Best: Linear O(n) • Worst: Quadratic O(n2) Katherine Deibel, Fluency in Information Technology

20. Merge Sort Algorithm: Split deck into two piles Merge sort first pile Merge sort second pile Merge the two sorted piles • This is a recursive function in that it is continually applied to itself Katherine Deibel, Fluency in Information Technology

21. Merge Sort Example Deck: 3, 6, 7, 2, 1, 8, 4, 5, • 3, 6, 7, 2 | 1, 8, 4, 5 (split) • 3, 6 | 7, 2 | 1, 8, 4, 5 (split) • 3, 6 |7, 2| 1, 8, 4, 5 (sort left) • 3, 6 |2, 7 | 1, 8, 4, 5 (sort right) • 2, 3, 6, 7 | 1, 8, 4, 5 (merge) • 2, 3, 6, 7 | 1, 8 | 4, 5 (split) • 2, 3, 6, 7 | 1, 8 | 4, 5 (sort left) • 2, 3, 6, 7 | 1, 8 | 4, 5 (sort right) • 2, 3, 6, 7 | 1, 4, 5, 8 (merge) • 1, 2, 3, 4, 5, 6, 7, 8 (merge) Katherine Deibel, Fluency in Information Technology

22. Merge Sort • Does it end? Yes • Will it be correct? Yes • Is it efficient? • Fairly efficient in real world • Programming has constantperformance: • Best: O(n log2 n) • Worst: O(n log2 n) • Worse than linear, better than quadratic Katherine Deibel, Fluency in Information Technology

23. Many Sorting Algorithms • Multiple approaches for sorting • Some more efficient in time in general • Some more efficient depending on nature of input • Examples of sorting performance:http://www.sorting-algorithms.com/ Katherine Deibel, Fluency in Information Technology

24. Encryption Keeping Secrets via Algorithms Katherine Deibel, Fluency in Information Technology

25. Encryption / Decryption • Encrypt: Transform data so that it is no longer understandable • Decrypt: Transform encrypted data to be understandable again Encryption and decryptionare algorithms Katherine Deibel, Fluency in Information Technology

26. Caesar Ciper • Supposedly used by Julius Caesar • Algorithm: • To encrypt:Move each letter n letters ahead • To decrypt:Move each letter n letters back • The movement wraps around the alphabet Y + 3  B Katherine Deibel, Fluency in Information Technology

27. Caesar Ciper • Example when n = 5 • A  F • B  G • … • M  R • … • Y  D • Z  E I LIKE CATS N QNPJ HFYX Katherine Deibel, Fluency in Information Technology

28. Caesar Cipher • Simple algorithm • Easy to implement • Easy to crack • Every play a cryptogram • The twelve most common letters in English (descending): ETAOIN SHRDLU Katherine Deibel, Fluency in Information Technology

29. RSA • Public key cryptography system invented in 1978 by Ron Rivest, AdiShamir, and Leonard Adleman • Before we get into the details… • Are any of you international students? • Is it before 1999? Katherine Deibel, Fluency in Information Technology

30. Encryption is a Munition • After WWII, encryption algorithms were deemed as military equipment • Actually listed as munitions • Export to foreign countries tightly controlled • Debates about teaching to international students • Richard White had the RSA algorithm tattooed on his arm and was theoretically unable to travel internationally • Printing and discussing of encryption algorithms is now recognized as free speech • Bernstein (Pretty Good Privacy) v. United States Katherine Deibel, Fluency in Information Technology

31. Back to RSA The basics of RSA: • Pick two large prime numbers p and q • Compute n = pq, m = (p-1)(q-1) • Choose a number e such that 1 < e < m and e and m's only common divisor is 1 • Calculate d = e-1 mod m • Publish n and e; d and m are kept private Encryption of integer i: c = ie mod n Decryption of integer c: i = cd mod m Katherine Deibel, Fluency in Information Technology

32. Makes sense, right? • RSA involves some fairly complex number theory • What you need to know • Based on prime numbers • Factoring numbers into prime components is computationally difficult • Larger prime numbers make RSA really secure (but only 99.9999999% secure) Katherine Deibel, Fluency in Information Technology

33. Public key systems • RSA is an example of a public key system • The encryption involves a numerical computation with several parameters • Some parameters are shared (public keys) • Some parameters are not (private keys) • Dominant form of encryption today • Scales by increasing the length of parameters Katherine Deibel, Fluency in Information Technology

34. Building your own algorithms Some tools Katherine Deibel, Fluency in Information Technology

35. Solving a Large Problem • Large problems share many properties: • They are daunting—there’s so much to do! • We don’t know were to begin • Not sure we know all of the tasks that must be done to produce a solution • Not sure we know how to do all of the parts— new knowledge may be required • Not sure it is within our capability—maybe an expert is needed Katherine Deibel, Fluency in Information Technology

36. Problem Decomposition • “Divide and conquer” is a political strategy, military strategy and IT strategy • Top-level Plan for Algorithm Building • Describe (in any language) a series of steps that produce a solution • For each step, solve it or decompose further • For steps needing decomposition, repeat 2 • Assemble solutions and test correctness • When solution fully assembled, evaluate Katherine Deibel, Fluency in Information Technology

37. 1. Give Steps to a Solution • Specify (in any language) a series of steps that produce a solution • For a huge problem the steps may at first be vague, but they can be (and must be) made more precise as the whole picture emerges • The goal is an algorithm(s), so • List and describe the inputs • List and describe the outputs • Be guided by figuring out how to transform the inputs into the outputs Katherine Deibel, Fluency in Information Technology

38. 2 and 3. Solve or Decompose • For each step, solve it or decompose it further, i.e. apply same technique • Most “top level” steps can’t be brained out, and need further decomposition • “Top level” steps often seem huge, too • The technique allows one to concentrate on only one problem at a time • As before, focus on transforming inputs to intermediary outputs to final outputs Katherine Deibel, Fluency in Information Technology

39. 4. Assemble and Test • Putting solutions together can be tough because of different assumptions made while solving the parts • A common practice is to combine parts along the way and to test continuously • Because of the need to test, pick a good order to solve the problems • Mistakes and backtracking are inevitable Katherine Deibel, Fluency in Information Technology

40. Example: Lab 8 • Lab 8 showed some of the basic ideas of writing an algorithm / program • Breaking down parts of the problem • Testing along the way • Continual effort to just progress forward Katherine Deibel, Fluency in Information Technology

41. Example: Chapter 22 • Implements Smooth Motion page:http://preview.tinyurl.com/fit-smooth • Fairly big application • 125 lines • 2500 nonspace characters • 6 functions • Chapter details the processof divide-and-conquer Katherine Deibel, Fluency in Information Technology

42. Summary • Algorithms describe the precise steps to solve a problem • Fundamental concept in computer science • Concerned with correctness, efficiency, and finiteness • Building algorithms is about abstracting and breaking down a problem • We do this all the time • The challenge of programming is telling a computer how to do the algorithm Katherine Deibel, Fluency in Information Technology