Transcript Hash Table - Prince of Songkla University

Chapter 9
Hash Table
Aree Teeraparbseree, Ph.D
1
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 called
the hash value of
the key

2
Simple example of Hash table (1)

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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
http://www.sparknotes.com/cs/searching/hashtables/
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
3
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/
4
Simple example of Hash table (3)
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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!!
http://www.sparknotes.com/cs/searching/hashtables/
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
5
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.

6
Hash function
Direct
 Subtraction
 Modulo-Division
 Digit Extraction
 Etc..

7
address
Direct
data
001
John Smith
005
Joey Bill
007
Lisa Smith
Key
001
100
007
001
Hash
100
007
Key = Hash value
…
100
Sandra dee
8
address
Subtraction
data
001
John Smith
005
Joey Bill
007
Lisa Smith
5410001-5410000 = 1
5410701-5410000 = 701
5410005-5410000 = 5
Key
5410001
5410701
5410005
Hash
001
701
005
hash(5410001) = 1
hash(5410701) = 701
hash(5410005) = 5
…
701
Anna Lee
9
address
Modulo-Division
data
001
John Smith
005
Joey Bill
007
Lisa Smith
14020%701 + 1 = 1
07009%701 + 1 = 701
11220%701 + 1 = 5
Key
14020
07009
11220
Hash
001
701
005
hash(14020) = 1
hash(07009) = 701
hash(11220) = 5
…
701
Anna Lee
10
address
Digit Extraction
data
000
…
Index from 000-999
310025239725 = 035
390980552321 = 951
310150234821 = 131
035
Henry James
131
Eddy Brown
Key
310025239725
390980552321
310150234821
Hash
035
951
131
…
951
hash(310025239725) = 035
hash(390980552321) = 951
hash(310150234821) = 131
Jamie Ben
…
999
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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 open
 Linear
Probing
 Double Hashing
12
Separate Chaining
13
http://www.sparknotes.com/cs/searching/hashtables/section1.rhtml
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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14
Double Hashing

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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.
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