Meljun Cortes Data Structures Hash Table

8/21/2019 Meljun Cortes Data Structures Hash Table

1/22

Data Structures and Algorithms

Hash Table

another data structure used to handle large

amount of data that offers fast insertion and

searching

fast searching and deleting

based on arrays, and arrays are difficult to

expand one they’ve been created

Hash Table * Property of STI Page 1 of 22

no convenient way to visit the items in a hash

table in any kind of order


2/22


Keys are Index Numbers


empRecord rec = databaseArray[72];

databaseArray[totalEmployees++] =

newRecord;


3/22


Dictionary

English-language dictionary is a typical exampleof database that can be efficiently handled with

a hash table

computer-language compiler - similar widelyused application for hash tables



4/22


Converting Words to Numbers

computers use various schemes forrepresenting individual characters as numbers

ASCII code - runs from 0 to 255 to

accommodate capitals, punctuation, and so on

How do you combine digits from individualletters into a number that represents an entireword?

Sorts of approaches



5/22


Add the Digits

Add them:

3 + 1 + 20 + 19 =43

C = 3A = 1T = 20S = 19


a wou e co e as

0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 1 = 1

zzzzzzzzzz (ten Zs)

26 + 26 + 26 + 26 +26 + 26 +26 + 26 + 26 +

26 = 260


6/22


Multiply by Powers

another approach of mapping words to numbers

enerates a uni ue number for ever otential

7,546 really means:7*1000 + 5*100 + 4*10 + 6*1

Or writing the multipliers as powers of 10:7*103 + 5*102 + 4*101 + 6*100


word


7/22


Hashing

use modulo operator (%), which finds theremainder when one number is divided byanother

smallNumber = largeNumber %

smallRange;



8/22


Hashing

hash function - hashes (converts) a number in alarge range into a number in a smaller range

An array into which data is inserted using a

hash function is called a hash table

hugeNumber = ch0*27

9

+ ch0*278

+ ch0*277

+ch0*276 + ch0*275 ch0*274 + ch0*273 +ch0*272 + ch0*271 + ch0*270

arraySize = numberWords * 2;


arrayIndex = hugeNumber %

arraySize;


9/22


Collisions

To insert the word melioration into the array, hash theword to obtain its index number, but find that the cellat that number is already occupied by the worddemystify , which happens to hash exact samenumber (for a certain size array).


Open addressing - search the array in somesystematic way for an empty cell, and insert the newitem there

linear probing , quadratic probing , and double

hashing Separate chaining - new item is simply inserted in the

list at that index


10/22


Linear Probing

sequentially search for vacant cells

public DataItem find(int key)

{

int hashVal = hashFunc(key);

while(hashArray[hashVal] != null)

{

if(hashArray[hashVal].getKey() == key)


++hashVal;

hashVal %= arraySize;

}

return null;

}


11/22


Linear Probing

public void insert(DataItem item)

{

int key = item.getKey();


while(hashArray[hashVal] != null &&

hashArray[hashVal].getKey() != -1)

{++hashVal;


}

hashArray[hashVal] = item;


public DataItem delete(int key)

{



{


{

DataItem temp = hashArray[hashVal];

hashArray[hashVal] = nonItem;

return temp;

}++hashVal;


}

return null;

}


12/22


Linear Probing

Sample output



13/22


Quadratic Probing

load factor - ratio of the number of items in atable, to the table’s size

loadFactor = nItems / arraySize;

Quadratic probing is an attempt to keep clusters

from forming



14/22


Quadratic Probing

Step is the Square of the Step Number



15/22


Quadratic Probing

Problem with Quadratic Probes

A quadratic probe eliminates the clusteringproblem seen with the linear probe called as

primary clustering

Secondary clustering - each additional item witha key that hashes to its maximum will require alonger probe



16/22


Double Hashing

Sometimes called as rehashing

The secondary hash function must have certaincharacteristics:

It must not be the same as the primary hashfunction.

It must never output a 0 (otherwise therewould be no step; every probe would land


,go into an endless loop.)

following form work well

stepSize = constant – (key %

constant);

stepSize = 5 – (key & 5);


17/22


Double Hashing


public DataItem find(int key){

int hashVal = hashFunc1(key);

int stepSize = hashFunc2(key);


{


return hashArray[hashVal];

hashVal += stepSize;hashVal %= arraySize;

}

return null;

}


18/22


Double Hashing

public void insert(int key, DataItem item)

{

int hashVal = hashFunc1(key);

int stepSize = hashFunc2(key);

while(hashArray[hashVal] != null &&

hashArray[hashVal].getKey() != -1)

{hashVal += stepSize;


}

hashArray[hashVal] = item;

}


public DataItem delete(int key)

{

int hashVal = hashFunc1(key);int stepSize = hashFunc2(key);


{


{

DataItem temp = hashArray[hashVal];

hashArray[hashVal] = nonItem;

return temp;

}

hashVal += stepSize;


}

return null;

}


19/22


Double Hashing



20/22


Separate Chaining

to install a linked list at each index in the hashtable


Deletion

Table Size

Buckets


21/22


Separate Chaining

public void insert(Link theLink)

{

int key = theLink.getKey();

Link previous = null;

Link current = first;

while( current != null && key > current.getKey() )

{

previous = current;


.

}

if(previous==null)

first = theLink;else

previous.next = theLink;

theLink.next = current;

}


22/22


Separate Chaining

public void delete(int key)

{

Link previous = null;


while( current != null && key != current.getKey()

)

{

previous = current;

current = current.next;

}

Hash Table * Property of STI

public Link find(int key)

{


while(current != null && current.getKey()

Documents

Meljun Cortes Data Structures Hash Table