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CompSci 201, Analysis+Markov

CompSci 201, Analysis+Markov. Jeff Forbes February 9, 2018. H is for …. Hashing Distribute keys evenly and efficiently HTTP HyperText Transfer Protocol Hacking For the social good… Hexadecimal 0x001A57 is Duke Blue. Plan for the Day.

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CompSci 201, Analysis+Markov

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  1. CompSci 201, Analysis+Markov Jeff Forbes February 9, 2018 Compsci 201, Fall 2017, Analysis+Markov

  2. H is for … • Hashing • Distribute keys evenly and efficiently • HTTP • HyperText Transfer Protocol • Hacking • For the social good… • Hexadecimal • 0x001A57 is Duke Blue Compsci 201, Fall 2017, Analysis+Markov

  3. Plan for the Day • How do we comparing objects in Java, so they can be ordered? • What is object-oriented programming? • How does that impact Markov? • How can we make claims about the efficiency of algorithms/programs? • Motivating empirical and mathematical analysis CompSci 201, Spring 2018, Analysis+Markov

  4. Comparing and Sorting • Arrays.sort, Collections.sort • {“ant”, “bat”, “cat”, “dog”} • What algorithm is used in sorting? • How to change to sort-in-reverse or other order • Strings are Comparable • Lexicographic order • “zebra” > “aardvark” but “Zebra” < “aardvark” CompSci 201, Spring 2018, Analysis+Markov

  5. (x,y) < (z,w) • Can we compare Point objects? • http://stackoverflow.com/questions/5178092/sorting-a-list-of-points-with-java • https://stackoverflow.com/questions/6886836/can-i-use-the-operator-to-compare-point-objects-in-java • To be “comparable”, implement the Comparable interface, supply .compareTo(..) method CompSci 201, Spring 2018, Analysis+Markov

  6. compareTo • takes another Object (of the same class) as an argument • Returns • a negative value if the current object is less than the argument, • zero if the argument is equal, and • a positive value if the current object is greater than the argument x ≤ y is equivalent to x.compareTo(y) <= 0

  7. Build on What You Know • How does .equals work? • Make sure you have the correct type • Cast, compare public boolean equals(Object o) { if (o == null || ! (o instanceof Point)) { return false; } Point p = (Point) o; return p.x == x && p.y == y; } CompSci 201, Spring 2018, Analysis+Markov

  8. Extend what you know • This is method in Point class Point implements Comparable<Point> • How do we extend to WordGram? public intcompareTo(Point p) { if (this.x < p.x) return -1; if (this.x > p.x) return 1; if (this.y < p.y) return -1; if (this.y > p.y) return 1 return 0; } CompSci 201, Spring 2018, Analysis+Markov

  9. What is a Java Interface? • An enforceable abstraction: methods required • Set and Map interfaces • Comparable interface • If Set<String> is parameter then can pass … • HashSet<String> or TreeSet<String> • Can sort String or anything that’s Comparable • Call .compareTo(..) method CompSci 201, Spring 2018, Analysis+Markov

  10. What does Object-Oriented mean? • Very common method of organizing code • Design classes, which encapsulate state and behavior • Some classes can be similar to, but different from their parent class: inheritance • Super class, subclass • Inherit behavior, use as is or modify and use or both • Hard to design a hierarchy of classes, but important • More of this in CompSci 308 or on-the-job training • We solve simple problems, don't design re-usable libraries • Simple doesn't mean it's not hard/difficult • OO in Markov?

  11. ShafiGoldwasser • 2012 Turing Award Winner • RCS professor of computer science at MIT • Twice Gödel Prize winner • Grace Murray Hopper Award • National Academy • Co-inventor of zero-knowledge proof protocols Work on what you like, what feels right, I now of no other way to end up doing creative work CompSci 201, Spring 2018, Analysis+Markov

  12. Why use an interface? CompSci 201, Spring 2018, Analysis+Markov

  13. Why use an Interface? • Work with frameworks, e.g., java.util.Collection • Iterable, Serializable, and more – use with Java • ArrayList, LinkedList, TreeSet, HashSet all … • .clear(), .contains(o), .addAll(..), .size(), ….toArray() https://docs.oracle.com/javase/9/docs/api/java/util/Collection.html CompSci 201, Spring 2018, Analysis+Markov

  14. Concept: Inheritance • In Java, every class extends Object • Gets methods by default: .toString, .hashCode, .equals, and more • Subclass can overridebaseclassmethods • Make .equals work for String • Use @Override when changing a method from parent class • Helps compiler and developers CompSci 201, Spring 2018, Analysis+Markov

  15. Computer Science • Scientific Method • Observe some feature of the natural world. • Hypothesize a model that is consistent with the observations. • Predict events using the hypothesis. • Verify the predictions by making further observations. • Validate by repeating until the hypothesis and observations agree. • Principles • Experiments we design must be reproducible;hypothesis must be falsifiable. • In CompSci 201: • Empirical & mathematicalanalysis CompSci 201, Spring 2018, Analysis+Markov

  16. Dropping Glass Balls • Tower with 100 Floors • Given 2 glass balls • Want to determine the lowest floor from which a ball can be dropped and will break • How? • Is your algorithm the most efficient one? • Generalize to n floors CompSci 201, Spring 2018, Analysis+Markov

  17. In the worst case, how many balls will I have to drop? Glass balls continued http://bit.ly/201-s18-0209-1 • Assume the number of floors is 100 • In the best case how many balls will I have to drop to determine the lowest floor where a ball will break? If there are n floors, how many balls will you have to drop? (roughly)

  18. What is big-Oh about? (preview) • Intuition: avoid details when they don’t matter, and they don’t matter when input size (N) is big enough • For polynomials, use only leading term, ignore coefficients y = 3x y = 6x - 2 y = 15x + 44 y = x2 y = x2 - 6x+ 9 y = 3x2 + 4x • The first family is O(n), the second is O(n2) • Intuition: family of curves, generally the same shape • More formally: O(f(n)) is an upper-bound, when n is large enough the expression cf(n) is larger • Intuition: linear function: double input, double time, quadratic function: double input, quadruplethe time

  19. cf(N) g(N) x =n0 More on O-notation, big-Oh • Big-Oh hides/obscures some empirical analysis, but is good for general description of algorithm • Allows us to compare algorithms in the limit • 20N hours vs N2 microseconds: which is better? • O-notation is an upper-bound, this means that N is O(N), but it is also O(N2); we try to provide tight bounds. Formally: • g(N) ∈ O(f(N)) iff there exist constants c and n0 such that for all g(N) < cf(N), N > n

  20. Rank orders of growth • n4grows faster than n2 • n4 ∉ O(n2) • 0.001n4 is in the same growth class as 1E6n4 • 0.001n4, 1E6n4 ∈ O(n4) • Discussion Warmup • Rank orders of growth • 1 < log2n = log10n < n0.5 < n = 0.1n + 1E9 < 2n

  21. Reasoning about growth • Consider a 3-tower • How tall is a 5-tower? • How tall is a 10 tower? • How many blocks in a 5-tower? • Which best captures the height of an n-tower? http://bit.ly/201-s18-0209-2 CompSci 201, Spring 2018, Analysis+Markov

  22. Array vs. ArrayList • Run the code ArrayVsArrayList.java • https://coursework.cs.duke.edu/201spring18/classwork/blob/master/src/ArrayVsArrayList.java • Change the value of argument • Submit your data here: • Submit as many times as you want http://bit.ly/201-s18-0209-3

  23. Summary • You should be able to: • Write a compareTo method for a Comparable object • Create a subclass and override some behavior • Reflect – • What’s clear? What’s still muddy? • http://bit.ly/201-s18-reflect • Discussion warmup: • Rank orders of growth • Read Big-Oh notes CompSci 201, Spring 2018, Analysis+Markov

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