2. What is hashing
• Simply, generating a numeric key using an
algorithm (hash function)
• Definition: A function that maps keys to
integers, usually to get an even distribution
on a smaller set of values.
• The very simplest hash function is to use the
modulus operator %
• Input range % key range
3. Input and key range
• Example. We want to store 7 digit
telephone numbers so that they can be
quickly retrieved.
– Number of expected entries = 100
– Range of telephone numbers = 0 – 9999999
Simple hashing algorithm
hash = inputNumber % 100
What’s the effect?
4. Applications of hashing
• File management – working out where
to store records
• Comparing complex values
• Cryptography – creating digital
signatures – eg: md5
5. Collisions
• Where the hash value returned for two
keys is the same.
• What to do?
– Open hashing
– Closed hashing
– Deleting
• The 2/3rds rule
6. Closed Hashing
1 23 32 44 End
2
3
4 33 Hash table is supplemented by
5 a linked list, which is used to
store colliding entries.
6
7 Therefore, some values are
found outside of the standard
hash table (in the linked list)
7. ‘Open’ Hashing
Some strategy is used to fit
colliding entries in a
predictable way inside the
1 23
existing table
2 32
3 44
For this to work, the size of
4 33 the table needs to be
5 significantly bigger than the
total number of records
6
7 At least 3:2
8. DJB Hash function
• “An algorithm produced by Professor Daniel J.
Bernstein and shown first to the world on the usenet
newsgroup comp.lang.c. It is one of the most efficient
hash functions ever published. “
def DJBHash(key):
hash = 5381
for i in range(len(key)):
hash = ((hash << 5) + hash) + ord(key[i])
return hash
