Cấu trúc dữ liệu và thuật toán dsa ch12 hash

Hash Dr Rang Nguyen Basic concepts Hash functions Direct Hashing Modulo division Digit extraction Mid square Mid square Folding Collision resolution Open addressing Linked list resolution 12 1 Chapter[.]

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Basic concepts Hash functions

Direct HashingModulo divisionDigit extractionMid-squareMid-squareFolding

Collision resolution

Open addressingLinked list resolution

Chapter 12

Hash

Data Structures and Algorithms

Dr Rang Nguyen Faculty of Computer Science and Engineering

University of Technology, VNU-HCM

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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

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Basic concepts

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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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Basic concepts

Is there a search algorithm

whose complexity is O(1) ?

YES

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Basic concepts

Is there a search algorithm

whose complexity is O(1) ?

YES

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Open addressingLinked list resolutionBasic concepts

Hình: Each key has only one address

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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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Hash functions

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Direct Hashing

The address is the key itself:

hash(Key) = Key

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Direct Hashing

• Advantage : there is no collision.

• Disadvantage : the address space (storage

size) is as large as the key space.

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Modulo division

Address = Key mod listSize

• Fewer collisions if listSize is a prime

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Mid-square

Address = middle digits of Key 2

Example:

9452 * 9452 = 89 3403 04→ 3403

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Folding

The key is divided into parts whose size

matches the address size.

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Folding

The key is divided into parts whose size

matches the address size.

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• 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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Open addressing

When a collision occurs, an

for placing the new element in.

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Open Addressing

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

Inserts key k into table T.

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Open Addressing

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

Searches for key k in table T.

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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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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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Open addressingLinked list resolutionLinear Probing

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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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Quadratic Probing

• The address increment is the collision probe

number squared:

hp(k, i) = (h(k) + i 2 ) mod m

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Quadratic Probing

• Advantages :

• works much better than linear probing

• Disadvantages :

• time required to square numbers

• produces secondary clustering

h(k 1 ) = h(k 2 ) → hp(k 1 , i) = hp(k 2 , i)

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Double Hashing

• Using two hash functions:

hp(k, i) = (h 1 (k) + ih 2 (k)) mod m

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Linked List Resolution

• Major disadvantage of Open Addressing :

each collision resolution increases the

probability for future collisions.

→ use linked lists to store synonyms

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Open addressingLinked list resolutionLinked list resolution

Tiêu đề	Hash
Tác giả	Dr. Rang Nguyen
Trường học	University of Technology, VNU-HCM
Chuyên ngành	Computer Science and Engineering
Thể loại	Chương

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