Hashing involves using an algorithm to generate a numeric key from input data. It maps keys to integers in order to store and retrieve data more efficiently. A simple hashing algorithm uses the modulus operator (%) to distribute keys uniformly. Hashing is commonly used for file management, comparing complex values, and cryptography. Collisions occur when different keys hash to the same value, requiring strategies like open hashing, closed hashing, or deleting data. Closed hashing supplements the hash table with linked lists to store colliding entries outside the standard table.

1. Hashing

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