Cấu trúc dữ liệu và thuật toán dsa ch9 hash 1

Luong The Nhan, Tran Giang SonBasic concepts Hash functions Direct HashingModulo divisionDigit extractionMid-squareMid-squareFoldingRotationPseudo-random Collision resolution Open addres

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Luong The Nhan, Tran Giang Son

Basic concepts Hash functions

Direct HashingModulo divisionDigit extractionMid-squareMid-squareFoldingRotationPseudo-random

Collision resolution

Open addressingLinked list resolutionBucket hashing

9.1

Chapter 9

Hash

Data Structures and Algorithms

Luong The Nhan, Tran Giang Son Faculty of Computer Science and Engineering

University of Technology, VNU-HCM

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9.2

Outcomes

• L.O.5.1 - Depict the following concepts: hashing table,

key, collision, and collision resolution.

• L.O.5.2 - Describe hashing functions using pseudocode

and give examples to show their algorithms.

• L.O.5.3 - Describe collision resolution methods using

pseudocode and give examples to show their algorithms.

• L.O.5.4 - Implement hashing tables using C/C++.

• L.O.5.5 - Analyze the complexity and develop

experiment (program) to evaluate methods supplied for

hashing tables.

• L.O.1.2 - Analyze algorithms and use Big-O notation to

characterize the computational complexity of algorithms

composed by using the following control structures:

sequence, branching, and iteration (not recursion).

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9.4

Basic concepts

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9.5

Basic concepts

• Sequential search: O(n)

• Binary search: O(log 2 n)

→ Requiring several key

comparisons before the

target is found.

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9.7

Basic concepts

Is there a search algorithm

whose complexity is O(1) ?

YES

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9.7

Basic concepts

Is there a search algorithm

whose complexity is O(1) ?

YES

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9.8

Basic concepts

Hình: Each key has only one address

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9.9

Basic concepts

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• Ideal hashing :

• No location collision

• Compact address space

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• Collision : the location of the data to be

inserted is already occupied by the synonym

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• Collision : the location of the data to be

inserted is already occupied by the synonym

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9.11

Basic concepts

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9.12

Basic concepts

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9.13

Basic concepts

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9.14

Basic concepts

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9.15

Hash functions

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9.17

Direct Hashing

The address is the key itself:

hash(Key) = Key

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9.18

Direct Hashing

• Advantage : there is no collision.

• Disadvantage : the address space (storage

size) is as large as the key space.

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9.19

Modulo division

Address = Key mod listSize

• Fewer collisions if listSize is a prime

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9.23

Folding

The key is divided into parts whose size

matches the address size.

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9.23

Folding

The key is divided into parts whose size

matches the address size.

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9.24

Rotation

• Hashing keys that are identical except for

the last character may create synonyms.

• The key is rotated before hashing.

original key rotated key

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9.25

Rotation

• Used in combination with fold shift.

original key rotated key

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9.26

Pseudo-random

For maximum efficiency, a and c should be

prime numbers.

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9.28

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9.29

• Except for the direct hashing, none of the

others are one-to-one mapping

→ Requiring collision resolution methods

• Each collision resolution method can be

used independently with each hash function

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9.30

• A rule of thumb: a hashed list should not

be allowed to become more than 75% full.

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9.31

• As data are added and collisions are

resolved, hashing tends to cause data to

group within the list.

→ Clustering : data are unevenly distributed

across the list.

• High degree of clustering increases the

number of probes to locate an element.

→ Minimize clustering.

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9.32

• Primary clustering : data become clustered

around a home address.

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9.33

• Secondary clustering : data become grouped

along a collision path throughout a list.

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9.35

Open addressing

When a collision occurs, an

for placing the new element in.

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9.38

Open Addressing

Algorithm hashInsert(ref T <array>, val k <key>)

Inserts key k into table T.

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9.39

Open Addressing

Algorithm hashSearch(val T <array>, val k <key>)

Searches for key k in table T.

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9.41

Linear Probing

• When a home address is occupied, go to

the next address (the current address + 1):

hp(k, i) = (h(k) + i) mod m

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9.41

Linear Probing

• When a home address is occupied, go to

the next address (the current address + 1):

hp(k, i) = (h(k) + i) mod m

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9.42

Linear Probing

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9.43

Linear Probing

• Advantages :

• quite simple to implement

• data tend to remain near their home

address (significant for disk addresses)

• Disadvantages :

• produces primary clustering

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Tiêu đề	Cấu trúc dữ liệu và thuật toán dsa ch9 hash 1
Tác giả	Luong The Nhan, Tran Giang Son
Trường học	University of Technology, VNU-HCM
Chuyên ngành	Data Structures and Algorithms
Thể loại	Giáo trình

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