1. Hash Tables Computer Science and Engineering
Chapter 8 of Goodrich and Tomassia’s Text
2/22/2019
B. Ramamurthy

2. Topics Hashing Hash functions Hash Tables Collision
Collision resolution
Chaining, linear probing, quadratic probing, double hashing
Java Hash table
Example
2/22/2019
B. Ramamurthy

3. Hashing Concept Another approach for storing and searching elements.
Used in applications where add and delete, besides search, are used.
Worst case linear but can get O(1) best case.
2/22/2019
B. Ramamurthy

4. Hash Function
A hash function h maps keys of a given type into an integer interval {0, N-1}
A simple function:
h(x) = x mod N
A good hash function will uniformly disperse the keys in the range {0, N-1}
2/22/2019
B. Ramamurthy

5. Hash Table Hash table ADT:
Has a hash function h
Array of size N
Collision occurs when two keys map to the same array index.
Two major collision resolution schemes are: chaining and open addressing
2/22/2019
B. Ramamurthy

6. Example Item(name, ssn) where ssn is 9 digit positive integer.
Hash table N =
Hash function: last four digits of of x
Use chaining to handle collision.
2/22/2019
B. Ramamurthy

7. Hash Table: Example 1 2 3 .
9996
9997
9998
9999
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B. Ramamurthy

8. Hash Functions Usually specified as two components:
Component1 called the hash code map, collects the parts of the data and maps them to integers (numeric data)
H1: keys  integers
Component2 called the compression map, takes the integers and maps them to 0 to N-1.
H2: integers {0, N-1}
2/22/2019
B. Ramamurthy

9. Hash Code Maps Memory address of data
Integer cast of non-numeric data: bit/byte pattern of data
Sum of all components: add the ascii values of your last name
Polynomials of various parts of data.
2/22/2019
B. Ramamurthy

10. Compression maps Reminder of division (mod) h(y) = y mod N
Multiple, Add and Divide (MAD)
h(y) = (a*y + b) mod N where
a mod N <> 0 (otherwise everything will map to b!)
2/22/2019
B. Ramamurthy

11. Linear Probing
Linear probing resolves collision by placing the colliding item in the next available empty cell.
Each entry inspected is referred to as the “probe”
Example: h(x) = x mod 13
Insert keys: 18, 41, 22, 44, 59, 32, 31, 73, in that order
2/22/2019
B. Ramamurthy

12. Search with linear probing: find(k)
j = h(k); probe = 0;
while (p < N)
2.1 c = A[j]
2.2 if (c == null) return NOT_FOUND;
else if (c.key() == k)
return c.element();
else j = (j+1) mod N
p = p +1;
3. return NOT_FOUND;
2/22/2019
B. Ramamurthy

13. Double Hashing h1: primary hash function
If it results in collision, resolve by applying another hash function, secondary hash function; here is an example of such a function.
d(k) = q – k mod q
Where q < N,
Possible values of d(k) are 1,2,3,..q
It cannot be 0
When collision occurs: (h(k)+j*d(k)) mod N
j = 0, 1, ..N-1
2/22/2019
B. Ramamurthy

14. Example h(k) = k mod 13 d(k) = 7 – k mod 7
Insert 18, 41, 22, 44, 59, 32, 31, 73.
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B. Ramamurthy

15. Java support for Hashing
Java1.4 API
Hashtable since jdk1.0
HashMap since jdk1.2
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B. Ramamurthy

16. Hashtable/HashMap Array of Entry
Chaining is the collision resolution policy
Entry is an inner class; Entry is a list;
Entry holds a key, value and a link to next Entry
Key Object should implement hashcode() and equals() methods
hashcode() of the Key class is the hash code map that converts key attributes to an integer
Compression map/function is hashcode mod array.length
Loadfactor (how full it can get before expanding), initial capacity can be specified
2/22/2019
B. Ramamurthy

17. Hashtable vs HashMap Dictionary extends
Hashtable Map, Cloneable, Serailizable
Dictionary
extends
implements
AbstractMap
extends
Hashtable Map, Cloneable, Serailizable
implements
2/22/2019
B. Ramamurthy

18. Hashtable vs HashMap
Hashtable implements Dictionary which is deprecated and has been superceded by AbstractMap
Hashtable implementation is a synchronized for concurrent access. HashMap leaves synchronization to the application.
Hashtable is slower (due to synchronized implementation)
2/22/2019
B. Ramamurthy

19. HashMap
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B. Ramamurthy

20. Using HashMap
Problem: An employee data is made up of Name (first, last), employee number (Integer), and salary. Maintain a set of 50 employee data for a “temp agency” so that employees can be added, removed and searched easily.
Solution: Choice of data structure: HashMap
Key? We will consider name as the key
Name is a class of two attributes: first, last
2/22/2019
B. Ramamurthy