1. School of Computer Science and Engineering
Lecture 7 : Hashing
Bong-Soo Sohn
Assistant Professor
School of Computer Science and Engineering
Chung-Ang University

2. Hashing
Enables access (search, insert, delete operations) to table items in time that is relatively constant (O(1)) and independent of the items

3. Hashing Terminology hash table cell or bucket Hashing
a data structure in which the location of an object is determined by applying a function to its value.
An array that contains the table items, as assigned by a hash function
cell or bucket
a single location in a hash table.
Hashing
applying a function to the value of an object to determine a location.

4. Hashing Terminology hash function : h(k) hash code
maps each value to a unique position or location
perfect hash function
Maps each search key into a unique location of the hash table
hash code
integer value computed for an object by applying a hash function
Requirements for a hash function
Be easy and fast to compute
Place items evenly throughout the hash table
Must allow for any regularities in the data
Modulo 2k is very bad if most keys are even!

5. Hashing Terminology load factor one-way hash function Collision
the fraction of occupancy in a hash table before it is resized
one-way hash function
is a hash function in which given the result of hashing, it is very hard to guess anything about the original value that was hashed
Collision
when two objects are mapped to the same location in a hash table
Collision-resolution schemes
Assign locations in the hash table to items with different search keys when the items are involved in a collision

6. Hash Function We can assume that input parameter is an integer
Simple hash functions for positive integers:
Division (using modulo operator) : h(k) = k % D
D should be a prime number p
Why prime number ? -> see textbook page 398
Mid-Square
Square the number
Take the middle digits as the hash key
Folding
Partition a key into several parts.
Those partitions are then added together to obtain address
Ex) k=
P1=123, P2=203, P3=241, P4=112, P5=20
h(k)= =699

7. String to Integer Converting a character string to an integer
If jimthe search key is a character string, it can be converted into an integer before the hash function is applied
If the conversion is to a fixed-length integer, must be careful that the conversion doesn’t introduce collisions
unsigned int stringToInt(char *key) {
int number=0;
while (*key) {
number += *key++;
if (*key) number += ((int) *key++) << 8; }
return number;

8. Resolving Collisions Two approaches to collision resolution
Approach 1: Open addressing
Approach 2: Chaining

9. Open Addressing
probe for an empty, or open, location in the hash table
Linear probing
Searches the hash table sequentially, starting from the original location specified by the hash function
Quadratic probing
Searches the hash table beginning with the original location that the hash function specifies and continues at increments of 12, 22, 32, and so on
Rehashing
Apply a second (or even third) hash function

10. Chaining
Each location is a reference to a linked list

11. Good Hash Function A good hash function should
Be easy and fast to compute
Scatter the data evenly throughout the hash table
Issues to consider with regard to how evenly a hash function scatters the search keys
How well does the hash function scatter random data?
How well does the hash function scatter nonrandom data?
General requirements of a hash function
The calculation of the hash function should involve the entire search key
If a hash function uses module arithmetic, the base should be prime

12. Hashing is not efficient for
For many applications, hashing provides the most efficient implementation
Hashing is not efficient for
Traversal in sorted order
Finding the item with the smallest or largest value in its search key
Range query