Hashing

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# Hashing - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Hashing' - rebekah

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Presentation Transcript

### Hashing

Basic Technique

Open Hashing

Closed Hashing

Restructuring Hash Tables

CS 303 – Hashing

Lecture 11

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

Open Hashing

Set of Sets

• Member
• calculate h(x)
• scan list B(h(x))
• Insert
• calculate 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

Closed Hashing
• No linked lists – just the table!
• 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

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