1. Maps, Dictionaries, Hashtables
(chapter 8 in text)

2. Maps, Dictionaries
Store a bunch of elements that need to be looked up quickly
Each element stored as an entry:
{key, value}
Only difference between maps and dictionaries is that the key has to be unique for maps

3. Map ADT
Important methods:
put(k,v)
get(k)
remove(k)

4. Dictionary ADT Important Methods find(k) findAll(k) insert(k,v)
remove(e)

5. Motivating Example
You’ve been hired by a small college to do an online registration webpage for them.
You want a data structure in which you can store all the students, then when they successfully login, you can get the Student object and add/remove classes from it.

6. Idea 1 Hold students in a list Downside:
Searching for a student takes time 0(n)
Student 1
Student 3
Student 2 …

7. Idea 2
Students have student numbers. Why not create an array to hold all the students and we get a student by student number index
Array –
Good: O(1) time to find a student
Bad: Using space for 10,000,000 students to store a few thousand

8. Solution – Hash Table
Create an array of buckets of size N, where n < N
Expect O(1) performance on average for finding items if well implemented … N
{ , StudentObj2}
{ , StudentObj1}

9. Hash Function Keys not necessarily integers Step 1: Get hashcode
hashcode is the mapping of a key to an integer
Step 2: Use compression function to map hash code to an integer from 0..N-1
note: mapping not necessarily unique. We’ll need to deal with collisions

10. Hashcode Important: Avoid collisions
Our example could just use student number
Let’s consider other strategies

11. Strategy 1 – Summing Components
eg. Suppose key is a String – “hello”
Could get hashcode by summing characters:
int hashcode = ‘h’ + ‘e’ + ‘l’ + ‘l’ + ‘o’
Problem: collision with “olleh”

12. Strategy 2: Polynomial Hash Codes
Form: x0ak-1 + X1ak-2 + … + Xk-2a + X0a + Xk-1
where a is some non-zero constant
Example: “hello”, a =33
int hashcode = ‘h’*334 + ‘e’*333 + ‘l’*332 + ‘l’*33 +’’o’

13. Compression Functions
Map hashcode (some integer) to range 0..N
Simple method: |i| mod N
Note – choice of N important eg. hashCodes {200,205,210,…600}
if N is 100, each code collides with 3 others
if N is 101, no collisions

14. Collision Handling
Two distinct keys mapped to same entry in the hashtable => collision
Makes operations more complicated

15. Separate Chaining When collision occurs, add to end of a list
{0111, “item1”}
{0111, “item1”}
{0314, “item2”}
{0314, “item2”}
{3421,“item3”}

16. Linear Probing (an open addressing scheme)
When collision occurs, go to next bucket
Note: Complicates removals
Try to insert
Final insertion here
{0111, “item1”}
{0111, “item1”}
{0314, “item2”}
{0314, “item2”}

17. Load Factor – n/N Must be < 1 Too small – Waste space
Too large – Too many collisions
Should be < 0.5 for open addressing
Should be < 0.9 for separate chaining