An array in which TableNodes are not stored consecutively

Their place of storage is calculated using the key and a hash function

Keys and entries are scattered throughout the array.

Implementation 6: Hashing

key entry

Key hash function

array index

4

10

123

insert: calculate place of storage, insert TableNode; (1)

find: calculate place of storage, retrieve entry; (1)

remove: calculate place of storage, set it to null; (1)

Hashing

key entry

4

10

123

All are constant time (1) !

Hashing

We use an array of some fixed size T to hold the data. T is typically prime.

Each key is mapped into some number in the range 0 to T-1 using a hash function, which ideally should be efficient to compute.

Example: fruits

Suppose our hash function gave us the following values: hashCode("apple") = 5

hashCode("watermelon") = 3hashCode("grapes") = 8hashCode("cantaloupe") = 7hashCode("kiwi") = 0hashCode("strawberry") = 9hashCode("mango") = 6hashCode("banana") = 2

kiwi

bananawatermelon

applemango

cantaloupegrapes

strawberry

0

1

2

3

4

5

6

7

8

9

Example

Store data in a table array: table[5] = "apple"

table[3] = "watermelon" table[8] = "grapes" table[7] = "cantaloupe" table[0] = "kiwi" table[9] = "strawberry" table[6] = "mango" table[2] = "banana"

kiwi

bananawatermelon

applemango

cantaloupegrapes

strawberry

0

1

2

3

4

5

6

7

8

9

Example

Associative array: table["apple"]

table["watermelon"] table["grapes"] table["cantaloupe"] table["kiwi"] table["strawberry"] table["mango"] table["banana"]

kiwi

bananawatermelon

applemango

cantaloupegrapes

strawberry

0

1

2

3

4

5

6

7

8

9

Example Hash Functions

If the keys are strings the hash function is some function of the characters in the strings.

One possibility is to simply add the ASCII values of the characters:

TableSizeABChExample

TableSizeistrstrhlength

i

)%676665()(:

%][)(1

0

Finding the hash function

int hashCode( char* s ){

int i, sum;sum = 0;for(i=0; i < strlen(s); i++ ) sum = sum + s[i]; // ascii value

return sum % TABLESIZE;

}

Example Hash Functions

Another possibility is to convert the string into some number in some arbitrary base b (b also might be a prime number):

TbbbABChExample

Tbistrstrhlength

i

i

)%676665()(:

%][)(

210

1

0

Example Hash Functions

If the keys are integers then key%T is generally a good hash function, unless the data has some undesirable features.

For example, if T = 10 and all keys end in zeros, then key%T = 0 for all keys.

In general, to avoid situations like this, T should be a prime number.