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Hashing. Basic Technique Open Hashing Closed Hashing Restructuring Hash Tables. Hashing. Basic Technique Hash Function – h(x) : X  (0, 1, ... , b-1) Given an object x, calculate an “equivalence class” h1(x) = x mod b h2(x) = floor(x / 10) mod b

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Hashing l.jpg

Hashing

Basic Technique

Open Hashing

Closed Hashing

Restructuring Hash Tables

CS 303 – Hashing

Lecture 11


Hashing2 l.jpg

Hashing

  • Basic Technique

  • Hash Function – h(x) : X  (0, 1, ... , b-1)

  • Given an object x, calculate an “equivalence class”

  • h1(x) = x mod b

  • h2(x) = floor(x / 10) mod b

  • h3(s) = ( ord(ci) ) mod b

  • Desiderata

  • h should “hash” x so that:

  • |B0| = |B1| = .... = |Bb-1|

  • x’s should be “randomly” (but repeatably!) dispersed (fast)

  • May need to use domain specific information about the distribution of values for x

CS 303 – Hashing

Lecture 11


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Open Hashing

Set of Sets

  • Member

  • calculate h(x)

  • scan list B(h(x))

  • Insert

  • calculate h(x)

  • add to B(h(x))

  • Delete

  • calculate h(x)

  • remove from B(h(x))

  • Ideally, the lists B(i) are short and uniform in length

  • O(N/B) [NOT O(1)!]

...

1

2

...

...

b-1

CS 303 – Hashing

Lecture 11


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Closed Hashing

  • No linked lists – just the table!

  • Note 0-based addressing

  • Search

  • calculate h(x)

  • inspect B(h(x))

  • if FULL and B(h).v = x

  • then FOUND

  • else ReHash with hi(x)

  • Strategies

  • LINEAR – hi+1(x) = hi(x) + 1 mod b

  • RANDOM – new hi(x) every time?

0

e is one of:

EMPTY

DELETED

FULL

i

b-1

CS 303 – Hashing

Lecture 11


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Restructuring Hash Tables

Insertion

1/(1-a)

  • For Closed Hashing

  • Slow growth until a = 0.8, then explosive growth

  • If a 0.9 (closed) or N/B  2 (open) it pays to

  • 1) create a new table with B’ = 2B

  • 2) re-insert all elements into the new table

Deletion

-(1/a)log(1-a)

a

0.8

CS 303 – Hashing

Lecture 11


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