1. CIS 280 Hashing and Hash Tables

2. Calendar Today: Hashing and Hash Tables Wednesday: Calculus due, work Friday: Cuckoo hashing and linear hashing Monday: Hashing wrapup Wednesday: Work Friday: Review, final project due Wednesday, December 16, 8am: Final exam

3. Calculus Questions? Work an example: x^2 + 3*x - 4

4. Hashing Basic idea: create an integer “digest” that identifies a complex value. Speeds up equality check (check hash codes first) – example: MD5 Use as a psuedo array index to create a hash table An array maps well organized data (integer ranges) to values A hash table maps irregular data to value

5. Two Different Problems Hash functions: mapping data to integers Hash tables: mapping hash keys to values in a sparse way (similar to sparse arrays). http://en.wikipedia.org/wiki/Hash_function A hash is a sort of finger print for a complex object.

6. Hash Functions Goals: Quick to compute (linear time in the size of the object) Random behavior: closely related objects should map to non-related keys We’ll simplify by only hashing strings – any structure can be hashed though.

7. String Hashing Input: a string of characters (bytes), str Output: a number between 0 and n-1 Use a local variable, state, to hold a “state” that condenses the string, and F, a combining function state = 0; for (int i = 0; i < str.size(); i++) { state = F((int) str.charAt(i), state); return state % n;

8. Choosing F Bad choice (checksum): + (why?) Better choices: functions involving bitwise operators (they run fast!), prime numbers (why?) Assume arithmetic operators don’t overflow (java does calculations mod the word size!) Example: F(v, s) = v*31+s There are a lot of ways to choose F – check wikipedia for some examples.

9. Example Supposed A = 1, B = 2, …, what is the hash of: “ABC” “ACB” “CB” Where F(c, s) = 5 * c + s?

10. Hash Tables The following interface describes a Hash table: public interface HashTable extends Iterable { public Value get(Key k); // null if not found public void set(Key k, Value v); public int size(); }

11. Hash Tables Let’s simplify by assuming that the Key is a string: public interface HashTable extends Iterable { public Value get(String s); public void set(String s, Value v); public int size(); }

12. Caching the Hash public class Hashed { public Value value; public int hash; } Note that we can remove the Value if we only hash strings. How would you compare hashed values for equality?

13. Factoring Out The Hasher public interface HashFunction { public HashedString hash(String s); } Every hash table needs to keep a hash function around. We can create families of such functions by parameterizing them.

14. A Naïve Hashtable Instead of using hash codes to organize the table, we’ll use direct searches. public class SimpleHashTable implements HashTable ; public ArrayList > values = new ArrayList > (); public HashFunction f; public SimpleHashTable(HashFunction f) { this.f = f; } public Value get(String s) {