CSE 326 Hashing

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CSE 326Hashing

• Richard Anderson
• (instead of Martin Tompa)

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Chaining review
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k H(k)
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B
C
D
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H
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K
H(k) k mod 17
Collect twelve birthdays from students and hash
into the table with chaining
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Open address hashing

• Store all elements in table
• If a cell is occupied, try another cell.
• Linear probing, try cells
• H(k), H(k) 1 mod m, H(k) 2 mod m, . .

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Open Address Hashing
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2 A
3 I
4 J
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6 C
7 B
8 D
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10 K
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k H(k)
A 53 2
B 41 7
C 91 6
D 75 7
E 13 13
F 6 6
G 43 7
H 67 16
I 88 3
J 36 2
K 40 6
H(k) k mod 17
Collect twelve birthdays from students and hash
into the table with chaining
Step through example Emphasize the growing
regions
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Open address hashing
Lookup (K) p H(K) loop if (Ap is
empty) return false if (Ap K) return
true p (p 1) mod m
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Open address hashing issues

• Issues
• Clumping
• Cost per operation
• Deletion

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Double hashing

• Use separate hash functions for the first probe
  and the collision resolution
• H1(k), H1(k) H2(k) mod m, H1(k)
  2H2(k) mod m, H1(k)
  3H2(k) mod m , . . .

Return to earlier slide to update the access code
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Double hashing example
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month day H1(k)
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H1(k) day mod 17
H2(k) month
Collect twelve birthdays (month and day) from
students and hash into the table with
chaining WRITE MONTHS AS NUMBERS
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Double hashing vs.Single hashing
Single

• Load factor a, cost per operation
• Single hashing
• Double hashing

Double
a
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Trade offs between chaining and open addressing
Chaining Open Addressing
Space Time Deletions Coding complexity High load
factor
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Hash Functions

• Function
• Efficient
• Uniform mapping to range
• Avoids systematic collisions

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Hashing strings

• String
• Suppose

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• Fact
• So