Dictionaries

DictionariesA Dictionary is a set S made up of n elements: x0 x1 x2 x3 … xn-1 that has

the following functions.

Functions:createEmptySet() returns a newly created empty setlookUp(S, k) returns the node in S that has the key k insert(S, x) returns S with x added delete(S, k) returns S with x (found using x.k) removedisEmptySet(S) returns true if S is empty and false if it is

not

Homework 7

• Describe how to implement a dictionary that has an average lookUp, insert, and delete time that is constant, but uses an array of no more than 2*n elements.

• Do the five Dictionary functions.

A Node

NameLast: SmartFirstName: Joe

StudentNumber: 8SSN: 123341112

Grade: 95

Hash Table

11232876446898674312

Hash Table

11232876446898674312

hash function

Hash Function

h(key) position in the array

• Last 4 of SSN for an array of size 10,000.• The modulo function is good to use for two

reasons.– Lets you fit key to any size array.– If you use a prime number, it helps your

distribution.

h(key) = key mod 17

11232876446898674312

Collisions

11232876446898674312

3454

Separate Chaining

Linear Probing

Add:5714222439

Linear Probing

Add:714222439

5

Linear Probing

Add:14222439

5

7

Linear Probing

Add:222439 5

7

14

Linear Probing

Add:2439

5

7

14

22

Linear Probing

Add:2439

5

7

14

22

Linear Probing

Add:39

5

7

14

22

24

Linear Probing

Add:

5

7

14

22

2439

Primary Clustering

5

7

14

22

2439

Double Hashing

H(key, 0) = h(key)H(key, p+1) = (H(key, p) + h2(key)) mod m

Double Hashing

5

7

14

22

24

39

h2(key) = addDigits(key)

Double Hashing

Add:5714222439

Double Hashing

Add:714222439

5

Double Hashing

Add:14222439

5

7

Double Hashing

Add:222439 5

7

14

Double Hashing

Add:2439

5

7

14

22

Double Hashing

Add:2439

5

7

14

22

Double Hashing

Add:39

5

7

14

22

24

Double Hashing

Add:

5

7

14

22

24

39