1. Week 6 - Monday
CS221

2. Last time What did we talk about last time? More recursion examples
Recursive running time

3. Questions?

4. Assignment 3
Recursion

5. Project 2
Infix to Postfix Converter

6. Wittman's Guide to Quick Debugging
a = b;
a and b have to have the same type
Exception: b is a subtype of a
== is a comparison operator that produces a boolean, = is a left-pointing arrow
if statements always have parentheses
No semicolons after if or while headers (and rarely after for headers)
The following is always wrong:
x = y;
x = z;
Know your String methods
A non-void method has to return something
The new keyword is always followed by a type and either parentheses (possibly with arguments) or square brackets with integers inside
Local variables cannot be declared private, public, or protected
Don't use the name of the type for method arguments

7. Know your syntax By now, you should know your syntax inside and out
If you don't know how something in Java works, find out!
Syntax is your basic tool for everything
Read about some syntax once? Doesn't help! Write some code to see it in practice!
CS121
CS122
CS221
Syntax
Problem Solving
Design

8. Merge Sort

9. Merge Sort algorithm (recursive)
Beautiful divide and conquer
Base case: List has size 1
Recursive case:
Divide your list in half
Recursively merge sort each half
Merge the two halves back together in sorted order

10. Let’s code that up…
Great. Now, how long does it take?

11. Student Lecture: Symbol Tables

12. Symbol Tables

13. Symbol tables A symbol table goes by many names:
Map
Lookup table
Dictionary
The idea is a table that has a two columns, a key and a value
You can store, lookup, and change the value based on the key

14. Example A symbol table can be applied to almost anything:
The key doesn't have to be a String
But it should be unique
Key
Value
Spiderman
Climbing and webs
Wolverine
Super healing
Professor X
Telepathy
Human Torch
Flames and flying
Deadpool
Mr. Fantastic
Stretchiness
Key
Value
121
Programming I
122
Programming II
221
Data Structures and Algorithms
322
Formal methods
361
Computer Graphics
363
Computer Security

15. Symbol table ADT
We can define a symbol table ADT with a few essential operations:
put(Key key, Value value)
Put the key-value pair into the table
get(Key key):
Retrieve the value associated with key
delete(Key key)
Remove the value associated with key
contains(Key key)
See if the table contains a key
isEmpty()
size()
It's also useful to be able to iterate over all keys

16. Ordered symbol tables
The idea of order in a symbol table is reasonable:
You want to iterate over all the keys in some natural order
Ordering can give certain kinds of data structures (like a binary search tree) a way to organize

17. Ordered symbol table ADT
An ordered symbol table ADT adds the following operations to a regular symbol table ADT:
Key min()
Get the smallest key
Key max()
Get the biggest key
void deleteMin()
Remove the smallest key
void deleteMax()
Remove the largest key
Other operations might be useful, like finding keys closest in value to a given key or counting the number of keys in a range between two keys

18. Implementations
Like other ADTs, a symbol table can be implemented in a number of different ways:
Linked list
Sorted array
Binary search tree
Balanced binary search tree
Hash table
Note that a hash table cannot be used to implement an ordered symbol table
And it's inefficient to use a linked list for ordered

19. Sorted array We know how to make a sorted array symbol table
A search is Θ(log n) time, which is great!
The trouble is that doing an insert takes Θ(n) time, because we have to move everything in the array around
A sorted array is a reasonable model for a symbol table where you don't have to add or remove items

20. Trees
Trees will allow us to make a sorted symbol table with the following miraculous properties:
Θ(log n) get
Θ(log n) put
Θ(log n) delete
Θ(n) traversal (iterating over everything)
Unfortunately, only balanced binary search trees will give us this property
We'll start this week with binary search trees and then built up to balanced ones

21. Upcoming

22. Next time… Binary search trees BST implementation
Keep reading Chapter 3.1

23. Reminders Finish Assignment 3 Keep working on Project 2
Due Wednesday, October 4
Keep working on Project 2
Due Friday, October 13