notes80 - CS251 Lecture Notes Feb 21 2005 by Adam...

CS251 Lecture Notes - Feb. 21, 2005
by Adam Muehlhausen
Last class we went over Hash Tables (called 'chaining') and Probing.
-In both chaining and probing hash tables, the expected insertation takes expected time O(1) as long as n is less than N
n number of entries
N size of hash table
In general, the expected time is O(n/N).
Hash Functions
The function that maps keys to the index in the table is called "hash function".
-This is made of 2 parts:
hash code map - translates the key to a number.
compression map - translates that number to an index (that index will be in the range 0 to N-1)
**The Hash Code Map can be
3 things
1)
Integer cast-
It is used for numeric types and we interpret bits as an int. If the key is already an integer, then the identity function is the hash code map.
Example:
2)
Component sum-
This is used for numbers or variables that use multiple 32 bit words. We add the words in the key.
Example:
const int MAX = 100;
char key[MAX];
//seen as sequence of words in memory
//assume key is initialized
unsigned int sum = 0;
unsigned int * p = (unsigned int *) key;
for(int i=0; i < MAX/sizeof(unsigned int); i++) {
sum += p[i];
}
*You can use this approach for hashing strings.
3)
Polynomial accumulation-
This function views the words in the key as coefficients of a polynomial
** Compression Map methods
1) Division: h(k) = |f(k)| mod N
-most common method. N is usually a prime to give an even distribution

2) Multiply and divide: h(k) = |a f(k) + b| mod N
*sometimes this provides a better distribution. (We will use #1 on project 5 though)