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What is Hashing?, Lecture notes of Data Structures and Algorithms

Southeastern Community CollegeData Structures and Algorithms

A hash is an into mapping of some input. (number, string) into a usually small and usually integer number. • The input is the hash key.

Typology: Lecture notes

2021/2022

Uploaded on 09/12/2022

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What is Hashing?
A hash is an into mapping of some input
(number, string) into a usually small and
usually integer number
•The input is the hash key
•The mapping is the hash function
•The output is the hash value
•The hash value is frequently used to index
(hash index) a table (hash table)
–Doing a lookup in a table by referencing its index is essentially a one
cycle operation- really, really fast
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Download What is Hashing? and more Lecture notes Data Structures and Algorithms in PDF only on Docsity!

What is Hashing?

A hash is an into mapping of some input (number, string) into a usually small and usually integer number

  • The input is the hash key
  • The mapping is the hash function
  • The output is the hash value
  • The hash value is frequently used to index ( hash index) a table ( hash table) - Doing a lookup in a table by referencing its index is essentially a one cycle operation- really, really fast

Hash Collisions

f x f y x y BUT f x f y x y

Restated, necessarily f (^) onto is into. If it were, but neither necessarily 1 - 1 and onto , there would be no 1 - 1 nor even such thing as a collision.

f (x)= f (y) f

x y

f

z f

f (z)

Hash Function

A good hash function

  • Must map all substrings into the table (index

cannot exceed table size)

  • Spreads the collisions uniformly over the

table, avoiding concentrations of collisions

Issues with a Hash Table

  • Size of hash table
  • Choice of hashing function
  • Hash Collisions
    • Minimize the number of collisions
    • Avoid pockets of collisions the table - i.e., spread collisions evenly over
    • Have a process to handle collisions, both on storage and lookup
      • Chaining
      • Probing
  • Hash table lookup efficiency
    • Rapid generation of hash values