This document defines and provides an example of multiplicative hashing. Multiplicative hashing sets the hash index as the fractional part of multiplying the key by a large random number. The formula takes the key, multiplies it by a constant between 0 and 1, takes the fractional part of the result, and multiplies that by the size of the hash table to obtain the hash value. Mid-square hashing is also discussed, which generates unique keys by taking the square of a seed value and extracting digits from the middle as the new seed.

2. DEFINITION:-
Multiplicative hashing sets the
hash index from the fractional
part of multiplying k by a large
real number. It's faster if this
computation is done using fixed
point rather than floating point.

3. Formula:
h(K) = floor (M (kA % 1))
Here,
M is the size of the hash table. K is the key
and A can be any constant value between 0
and 1. Both k and A are multiplied and their
fractional part is separated. This is then
multiplied with M to get the hash value.

4. Example:
k = 12345
A = 0.357840
M = 100
h(K)=floor(M (KA % 1))
h(12345) = floor[ 100 (12345*0.357840 %
1)]
= floor[ 100 (4417.5348 mod 1) ]
= floor[ 100 (0.5348) ]
= floor[ 53.48 ]
= 53

6. Mid-Square hashing is a hashing
technique in which unique keys are
generated. In this technique, a seed value is
taken and it is squared. Then, some digits
from the middle are extracted. These
extracted digits form a number which is
taken as the new seed.

7. Suppose a 4-digit seed is taken.
seed = 4765
Hence,
square of seed is = 4765 * 4765 = 22705225
So, the new seed value becomes seed = 7052
square of this new seed is = 7052 * 7052 = 49730704
So, the new seed value becomes seed = 7307
.
.
.
.
This process is repeated as many times as a key is
required.

8. BY
TONIA C.S