Compsci 201 Hashing. Jeff Forbes February 7, /7/18 CompSci 201, Spring 2018, Hashiing

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1 Compsci 201 Hashing Jeff Forbes February 7,

2 G is for Garbage Collection Nice to call new and not call delete! Git Version control that's so au courant GPL First open source license Google How to find Stack Overflow 2

3 Policy Reminder Discussion and classwork Generous allowance for missed work Don t STINF Assignments Late penalty. Submit extension form for excused absence Not accepted after 1 week APTs Do extra and you can do fewer in the future 3

4 Hashing: Log ( ) is big Comparison-based searches are too slow for lots of data How many comparisons needed for a billion elements? What if one billion web-pages indexed? Hashing is a search method: average case O(1) search Worst case is very bad, but in practice hashing is good Associate a number with every key, use the number to store the key Like catalog in library, given book title, find the book A hash function generates the number from the key Goal: Efficient to calculate Goal: Distributes keys evenly in hash table

5 Hashing Hash table array of fixed size with a key to each location each key is mapped to an index in the table 0 1 joe mary 43 4 sam

6 Hashing hashcode Every object has a hashcode integer value In our made-up example Object joe hashcode 31 Could two different objects have the same hashcode? 0 1 joe mary 43 4 sam

7 Hash function simple to compute Hashing example hashcode % (mod) 10 ali 73 Use hash function to calculate key to hash table Add key ali with hashcode 73 What happens? 0 1 joe mary 43 4 sam

8 Hashing details There will be collisions, two keys will hash to the same value We must handle collisions, still have efficient search What about birthday paradox : using birthday as hash function, will there be collisions in a room of 25 people? Several ways to handle collisions, in general array/vector used Linear probing, look in next spot if not found Hash to index hashcode(key) = h, try h+1, h+2,, wrap at end Clustering problems, deletion problems, growing problems Quadratic probing Hash to index h, try h+1 2, h+2 2, h+3 2,, wrap at end Fewer clustering problems Double hashing Hash to index h, with another hash function to j Try h, h+j, h+2j, n-1

9 Chaining with hashing With n buckets each bucket stores a structure (e.g.,list) Compute hash value h, look up key in table[h] How to store? Low-level linked lists (up until Java 8) Low-level binary search trees (Java 8+) Hopefully linked data structure are short, searching is fast Unsuccessful searches often faster than successful Empty linked lists searched more quickly than non-empty Potential problems? Hash table details Size of hash table should be a prime number Keep load factor small: # keys/size of table On average, with reasonable load factor, search is O(1) What if load factor gets too high? Rehash or other method

10 Hashing Two equal objects should hash to the same place (have the same hash code and key) mary joe mary 43 4 sam jill sarah 58 2/7/

11 String and Object.hashCode Every object has a.hashcode method Default version? Why does it work for Objects? x.equals(y) x.hashcode() == y.hashcode() Why do most classes override both.equals and.hashcode? Correctness and Performance 11

12 What are instance variables? Initialized? Index used so hash of cat!= act public int hashcode() { int h = hash; if (h == 0 && value.length > 0) { char val[] = value; } for (int i = 0; i < value.length; i++) { h = 31 * h + val[i]; } hash = h; } return h; 12

13 WordGram equals WordGram equals method What should it do? When should it return true or false? What to do next? public boolean equals(object other) { if (this == other) // point to the same Object return true; if (other == null // Nothing is equal to null! (other instanceof WordGram)) // Different return false; kinds of objects WordGram wg = (Wordgram) o; // Check if all the words are equal 13

14 WordGram hashcode The given hashcode works? Why store myhash? EfficientWordMarkov performs very poorly. Why? public WordGram(String[] words,int index,int size) { // complete this constructor myhash = 17; } public int hashcode() { // TODO return a better hash value return myhash;; } 14

15 WordGram hashcode v2 Compute hash by adding the individual values of the Strings in mywords Why not ideal? Consider hashcode values for the 4-gram "jump big dog jump" and "jump jump big dog" public WordGram(String[] words,int index,int size) { //.. Code omitted to set up mywords myhash = 0; for (String word: mywords) myhash += word.hashcode(); 15

16 How do we tell if two strings are equal? What about a String and an Object? Examine characters at index k in s1 and s2 If not equals, done, return false How many chars to examine? How do we make code easier to read than what s given in String.java? 16

17 Is this code the same? See while loop in public boolean equals(object o) { if (this == o) return true; if (! (o instanceof String)) return false; if (value.length!= o.value.length) return false; for(int k=0; k < value.length; k++){ if (value[k]!= o.value[k]) return false; } return true; } 17

18 When Strings Collide Generate strings that will collide Find such strings in the wild String hashcode String hashcode ayay aybz bzay bzbz buzzards righto snitz unprecludible

19 WOTO 19

20 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 20

21 Not Everything is Comparable 9/20/17 Compsci 201, Fall 2017, Compare+Analysis 21

22 (x,y) < (z,w) Can we compare Point objects? orting-a-list-of-points-with-java can-i-use-the-operator-to-compare-pointobjects-in-java To be comparable, implement the Comparable interface, supply.compareto(..) method 22

23 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

24 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; } 24

25 Extend what you know This is method in Point class Point implements Comparable<Point> public int compareto(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; } How do we extend to WordGram? 25

26 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 26

27 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?

28 Shafi Goldwasser 2012 Turing Award Winner RCS professor of computer science at MIT Twice Godel 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 28

29 Why use an interface? 29

30 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() Collection.html 30