1. ADTs so far

2. Lower level ADTs Linked lists (singly- and doubly- linked) Arrays
“Stretchable”, efficient, but…
Sequential access
Arrays
Even more efficient, but not “stretchable”
Random Access
Vectors, Sequences, Lists
All the features, but pay in efficiency
Really, implemented with the above
1/13/2019
Gene Itkis; cs112

3. Higher Level ADTs For all: isEmpty() size() insert(elem) remove()
Stacks
last inserted
Queues
first inserted
Priority Queues
highest priority
1/13/2019
Gene Itkis; cs112

4. Dictionaries
Retrieve by key

5. Dictionary Examples Phone directory Student records Credit cards DB
Name is key; phone # is the info
Reverse lookup: phone # is key
Student records
Credit cards DB
E.g. check that the given credit card is valid
Extra: “Authenticate” the result
ETC.
1/13/2019
Gene Itkis; cs112

6. Dictionary Interface isEmpty() size() insert(elem) find(key)
Using elem.key
find(key)
remove(key)
1/13/2019
Gene Itkis; cs112

7. Simple Implementations
Unordered List
insert
O(1) – fast (delete: the same)
find
O(n) – slow
Ordered list
Linked list implementation – same as unordered
Array
Binary search: O(lg n) – pretty fast
O(n) – slow (delete: the same)
1/13/2019
Gene Itkis; cs112

8. Better Implementations
Ordered trees
Hash tables
Other
Skip-lists
1/13/2019
Gene Itkis; cs112

9. Ordered Trees Order Depth x< y,z : min at root – heap () x
y<x<z : search 
Depth
Shallow  Balanced
There might be exceptions:
e.g., Leftist heaps
“Strong” balance
Approximate 
E.g., depth of leaves within factor of 2 (R-B trees)
heap
1/13/2019
Gene Itkis; cs112

10. Ordered Trees Searching Insert/Delete Easy Destroys balance
Fix balance
How?
AVL trees
Nodes keep children heights
Rotate when needed: when children heights are >1 apart
Red-Black/2-3-4 trees
1/13/2019
Gene Itkis; cs112

11. Hash tables Example Idea Find professors by office number
Find tools in a tool-box
Might not work for everyone
Idea
“Figure” info location from the key
1/13/2019
Gene Itkis; cs112

12. Hash Tables: Idea Hash function If it works… Problem? H(key)=i
Find – O(1)
Insert/Delete – O(1)
Problem?
Collisions:
H(key’)=H(key)
key … H i
key info …
1/13/2019
Gene Itkis; cs112

13. Hash Table: Issues Good Hash functions Collision Resolution…
key H
Hash
table
key’
key”
Good Hash functions
Minimize collision chances
“Random looking”
Collision Resolution
Chaining
Open Addressing
Linear Probing: d=1
Quadratic Probing: d=i2
Double Hashing: d=H2(key’)
key info
key info d
key’ info
key’ info d
key” info
1/13/2019
Gene Itkis; cs112

14. Collision Resolution Methods Comparison
Chaining
Requires extra space
As with linked list
Stretchable
Can degenerate to linked-list search
Open Addressing
No extra space needed
Has size limit
Also can degenerate to unordered list search
1/13/2019
Gene Itkis; cs112