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Chapter 9Hash Table

Aree Teeraparbseree, Ph.D

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What is Hash table? Hash table is an associative array Hash table is made up of 2 parts:

an array a mapping function (hash function)

Hash function convert key to array index

The index is calledthe hash value ofthe key

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Simple example of Hash table (1)

Hash table: array of string

Hash table size is 12 Hash function takes a

string as input Hash value will be

the sum of the ASCII characters that make up the string mod the size of the table

Hash table (strings)0 NULL

1 NULL

2 NULL

3 NULL

4 NULL

5 NULL

6 NULL

7 NULL

8 NULL

9 NULL

10 NULL

11 NULL

http://www.sparknotes.com/cs/searching/hashtables/

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Simple example of Hash table (2)

int hash(char *str, int table_size) {

int sum=0;

if (str == NULL)

return -1;

for( ; *str; str++) // *str != ‘\0’

sum += *str;

return sum%table_size;

}

// covert to integer with its Ascii code

http://www.sparknotes.com/cs/searching/hashtables/

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Simple example of Hash table (3)

Store a string into the table: "Steve".

hash("Steve",12) = 3 Index = 3 Store: "Spark" hash("Spark",12) = 6 Store: "Notes" hash("Notes",12) = 3

Collision with Steve!!

Hash table (strings)0 NULL

1 NULL

2 NULL

3 Steve / Notes !!

4 NULL

5 NULL

6 Spark

7 NULL

8 NULL

9 NULL

10 NULL

11 NULL

http://www.sparknotes.com/cs/searching/hashtables/

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Implementing A Hash Table In C

Create a Hash function. Insert items in a Hash table. Delete items in the table. Search for a specific data-value in the

table.

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Hash function Direct Subtraction Modulo-Division Digit Extraction Etc..

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001 John Smith

005 Joey Bill

007 Lisa Smith

…

100 Sandra dee

Hash001100007

Key

address data

001

100

007

Direct

Key = Hash value

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001 John Smith

005 Joey Bill

007 Lisa Smith

…

701 Anna Lee

Hash541000154107015410005

Key

address data

001

005

701

hash(5410001) = 1hash(5410701) = 701hash(5410005) = 5

5410001-5410000 = 15410701-5410000 = 7015410005-5410000 = 5

Subtraction

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001 John Smith

005 Joey Bill

007 Lisa Smith

…

701 Anna Lee

Hash140200700911220

Key

address data

001

005

701

hash(14020) = 1hash(07009) = 701hash(11220) = 5

14020%701 + 1 = 107009%701 + 1 = 70111220%701 + 1 = 5

Modulo-Division

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000

…

035 Henry James

131 Eddy Brown

…

951 Jamie Ben

…

999

Hash310025239725390980552321310150234821

Key

address data

035

131

951

hash(310025239725) = 035hash(390980552321) = 951hash(310150234821) = 131

Index from 000-999310025239725 = 035390980552321 = 951310150234821 = 131

Digit Extraction

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Collisions: Solution

1. Open Hashing (separate chaining): keeping the colliding record in a linked list.

2. Close Hashing (Open Addressing): place the colliding record in another location that is still openLinear ProbingDouble Hashing

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Separate Chaining

http://www.sparknotes.com/cs/searching/hashtables/section1.rhtml

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Linear Probing Let i = hash(key) If data[i] does not already contain a

record, then store the record in data[i] If data[i] already contains a record then

try data[i+1]. If that location already contains a record, try data[i+2] and so on.

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Double Hashing Let i = hash(key) If data[i] does not already contain a record, then store the record

in data[i] If data[i] already contains a record then

let i = (i+hash2(key))%SIZE, and try new data[i].

If that location already contains a record, then

let i = (i+hash2(key))%SIZE, and try that data[i], until a vacant position is found.

Possible implementation of hash2(key) :- hash2(key) = 1 + (key % (SIZE - 2)- hash2(key) = max(1, (key / SIZE) % SIZE)

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Search for a specific key

Use key to calculate the hash value. Check that location of the array for the

key. Keep moving forward until you find the

key, or you reach an empty spot. (depend on the collision solution)

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Deleting a record

Records may also be deleted from a hash table.

But the location must not be left as an ordinary "empty spot" since that could interfere with searches.

The location must be marked in some special way so that a search can tell that the spot used to have something in it.