1. Java Methods A & AB Object-Oriented Programming and Data Structures Maria Litvin ● Gary Litvin Copyright © 2006 by Maria Litvin, Gary Litvin, and Skylight Publishing. All rights reserved. Lookup Tables and Hashing

2. 24-2 Objectives: Learn about lookup tables Learn about hashing Review java.util.HashSet and java.util.HashMap

3. 24-3 Lookup Tables A lookup table is a one-dimensional array that helps to find data very quickly. The array stores references to data records (or some values). A data record is identified by some key. The value of a key is directly translated into an array index using a simple formula.

4. 24-4 Lookup Tables (cont’d) Only one key can be mapped onto a particular index (no collisions). The index that corresponds to a key must fall into the valid range (from 0 to array.length - 1). Access to data is “instantaneous” (O(1)).

5. 24-5 Lookup Tables: Example 1 Zip codes Corresponding locales Some table entries remain unused

6. 24-6 Lookup Tables: Example 2 private static final int [ ] n_thPowerOf3 = { 1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683 };... // precondition: 0 <= n < 10 public int powOf3 (int n) { return n_thPowerOf3 [ n ]; }

7. 24-7 Lookup Tables: Example 3 256 colors used in a particular image; each of the palette entries corresponds to a triplet of RGB values

8. 24-8 Applications of Lookup Tables Data retrieval Data compression and encryption Tabulating functions Color mapping

9. 24-9 Hash Tables A hash table is similar to a lookup table. The value of a key is translated into an array index using a hash function. The index computed for a key must fall into the valid range. The hash function can map different keys onto the same array index — this situation is called a collision.

10. 24-10 Hash Tables (cont’d) The hash function should map the keys onto the array indices randomly and uniformly. A well-designed hash table and hash function minimize the number of collisions. There are two common techniques for resolving collisions: chaining and probing.

11. 24-11 Chaining Buckets Each element in the array is itself a collection, called a bucket (a list or a BST), which is searched for the desired key

12. 24-12 Probing The probing function recalculates the index If the place where we want to store the key is occupied by a different key, we store the former in another location in the same array, computed using a certain probing formula

13. 24-13 java.util.HashSet and java.util.HashMap Classes These classes implement the Set and Map interfaces, respectively, using hash tables (with chaining). This implementation may be more efficient than TreeSet and TreeMap.

14. 24-14 HashSet and HashMap (cont’d) Collisions are resolved through chaining. The sizes of buckets must remain relatively small. Load factor: Load factor = Total number of items Number of buckets

15. 24-15 HashSet and HashMap (cont’d) Fine tuning:  Load factor too large  lots of collisions  Load factor too small  wasted space and slow iterations over the whole set If the load factor exceeds the specified limit, the table is automatically rehashed into a larger table; if possible this should be avoided.

16. 24-16 HashSet and HashMap (cont’d) Objects in a HashSet or keys in a HashMap must have a reasonable int hashCode method that overrides Object’s hashCode and helps calculate the hashing function. The hashCode method returns an int from the entire int range; it is later mapped on the range of indices in a particular hash table. String, Integer, Double each have a reasonable hashCode defined.

17. 24-17 hashCode Examples For String:  (where s i is Unicode for the i-th character in the string) For Person: public int hashCode ( ) { return getFirstName ().hashCode () + getLastName ().hashCode (); }

18. 24-18 Consistency HashSet / HashMap first use hashCode, then equals. TreeSet / TreeMap use only compareTo (or a comparator) For consistent performance, these methods should agree with each other:  x.equals (y)  x.compareTo (y) == 0  x.equals (y)  x.hashCode() == y.hashCode()

19. 24-19 HashSet Constructors Never mind...

20. 24-20 HashMap Constructors

21. 24-21 Review: What is the main difference between a lookup table and a hash table? What is a collision? Name two common techniques for resolving collisions. What is a bucket? What is a load factor?

22. 24-22 Review (cont’d): How is hash table performance affected when the load factor is too high? Too low? What happens to a HashSet or a HashMap when the load factor exceeds the specified limit? HashSet’s no-args constructor sets the initial capacity to 16 and the load factor limit to 0.75. How many values can be stored in this table before it is rehashed?

23. 24-23 Review (cont’d): What is the sequence of values returned by an iterator for a HashSet? What is the range of values for the hashCode method? Which method(s) of an object are used to find it in a TreeSet? A HashSet?