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  1. 1. Hashing
  2. 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. 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. 4. Applications of hashing• File management – working out where to store records• Comparing complex values• Cryptography – creating digital signatures – eg: md5
  5. 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. 6. Closed Hashing1 23 32 44 End234 33 Hash table is supplemented by5 a linked list, which is used to store colliding entries.67 Therefore, some values are found outside of the standard hash table (in the linked list)
  7. 7. ‘Open’ Hashing Some strategy is used to fit colliding entries in a predictable way inside the1 23 existing table2 323 44 For this to work, the size of4 33 the table needs to be5 significantly bigger than the total number of records67 At least 3:2
  8. 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