1. Plan for Week Linear structures: Stack, Queue
Applications: LIFO, FIFO, other
Canonical examples and view to more
Java specifics of how to use these
Friday: More examples of recursion and alternatives
Blob counting and applications of neighbor-search
Guide to using practice-it for APT-like problems

2. What is a linear structure?
Structure elements have predecessors, successors
Arrays, Linked-lists, ArrayLists
ADT: insert, delete, iterate/traverse, grow, …
Advantages and trade-offs include …
Some linear structures are used to solve problems and are typically studied in courses like 201
We won't look in detail at implementations
We will mention the implementations
Viewed via APIs and problems solved
Discuss that linear structures are not necessarily contiguous, like linked lists, but each element typically has one before and one after. Not necessarily indexable, but can be

3. Stacks Queues and Deques, Oh My!
Linear structures used in problem domains and algorithms: Stack, Queue, Dequeue.
Similar abstractions with different semantics
Mention stacks and queues, continued on next slides. These are in the real-world versions of the terms

6. Why don't we just use arrays?
Stacks used in implementing recursion, postscript language, Java language, graph algorithms
Stacks implemented using array/ArrayList
Queues used in simulation, graph algorithms, scheduling
Queues implemented using array/LinkedList
Deque (dequeue) double ended queue, Gradescope
Implemented using LinkedList or other
Key ideas here are that operations on these structures should be fast: O(1). So add to end of array or arraylist, not at front. Add at front or back of linked-list e.g., for queue.

7. Stacks: Java and Otherwise
See StackDemo.java
Note that Stack is in java.util
Stack is generic, e.g., Stack<String>
See API documentation for details on methods
In code example: push, pop, create, size
Also noted isEmpty and peek
Note that isEmpty is shorthand for .size() == 0. Note that peek looks at top element, but leaves it on the stack

8. Simple stack example Stack is part of java.util.Collections hierarchy
Typically avoid .peek(), but can be useful
Stack<String> s = new Stack<>();
s.push("panda");
s.push("grizzly");
s.push("brown");
System.out.println("size = "+s.size());
System.out.println(s.peek());
String str = s.pop();
System.out.println(s.pop());
Go over what code prints: size = 3, "brown", stores grizzly in str, but doesn't print. Prints "panda" since "grizzly" was popped, then prints "panda" again. What would happen if .pop() called again? Error

9. Two applications of stacks
Manage runtime of method invocations, e.g., in implementing compiler. Note that Java Virtual machine is a stack-based machine
Postfix notation for arithmetic expressions
Can be used in evaluating expressions
What is * 7 ? This is NOT 56
Without precedence, need parentheses, e.g., we'd write (3 + 5) * 7
Postfix is sometimes called Reverse Polish Notation or RPN

10. Postfix, prefix, and infix notation
Postfix notation used in some HP calculators
No parentheses needed, precedence rules work
* *
Read expression
For number/operand: push onto stack
For operator: pop, pop, operate, push
To evaluate prefix: (3 + 5) * 7 we'd use *
What is * +
Discuss first expression is 8, why. Discuss second by explicitly detailing stack: 4 2 (stack has two elements). Then 8 on stack, then (8,7), then 15 then 15 3, then 12
The last expression is an error: pops an empty stack since only 16 on stack when * encountered

11. Postfix.java To evaluate a postfix expression:
If number, push. If operator: pop, pop, op, push
Things to look at in program: What exceptions are caught? When do these occur?
Number format and Stack exceptions
How does StringTokenizer work:
Like .split(), but delivers tokens or chunks one at a time. Delimiters or separators are tokens too
Run program a few times. First try expressions like 3 5 * 7 + or * +, then try some with errors, e.g., 3 + or and talk about why the errors are identified
Can mention that StringTokenizer can return delimiters or ignore them. The TRUE in constructor means return the delimiters.
Walk through the hasNextToken and nextToken code to remind students this is like the hasNextLine and nextLine used in the readLoop – this general iterator pattern shows up often in Java

12. Modifying Postfix.java
How can we add exponentiation to the program
2 3 ^ would be 8 and 3 2 ^ would be 9
Must add new delimiter
What happens before we add ^ when ^ entered?
What happens after we add ^ when ^ entered?
Must add new line in method operator
How do we return appropriate value? Test?
Run through adding ^, first just typing it, then adding as a delimiter and typing it, then adding if (op.equals("^") return Math.pow(lhs,rhs)
Talk about testing with 2 3 ^ and 3 2 ^
Ask students how to commit this to git, but DO NOT commit it

13. http://bit.ly/201fall16-stacks WOTO
Look at source code for Postfix.java to understand both RPN and parsing using tokens in Java

14. Barbara Liskov
Turing Award Winner in 2008 for For contributions to practical and theoretical foundations of programming language and system design, especially related to data abstraction, fault tolerance, and distributed computing.
The advice I give people in general is that you should figure out what you like to do, and what you can do well—and the two are not all that dissimilar, because you don’t typically like doing something if you don’t do it well. … So you should instead watch—be aware of what you’re doing, and what the opportunities are, and step into what seems right, and see where it takes you.

15. Queue: another linear ADT
FIFO: first in, first out, used in many applications
Scheduling jobs/processes on a computer
Computer simulations, lines at stores or banks: one line or multiple lines?
Common operations: add (back), remove (front), peek ??
java.util.Queue is an interface
java.util.LinkedList implements the interface
add(), remove(), offer(), poll()
We'll use .add() and.remove() – see API for offer() and poll() but we won't use these. Also have .peek()

16. Stacks: Java and Otherwise
See QueueDemo.java
Note that Queue is in java.util and is an Interface! Typically use LinkedList to create concrete object
See API documentation for details on methods and on many implementing classes
Why use LinkedList? O(1) add back, remove front
Note that isEmpty is shorthand for .size() == 0. Note that peek looks at top element, but leaves it on the stack

17. Simple Queue example Queueis part of java.util.Collections hierarchy
Typically avoid .peek(), but can be useful
Queue<String> q = new LinkedList<>();
q.add("panda");
q.add("grizzly");
q.add("brown");
System.out.println("size = "+q.size());
System.out.println(q.peek());
String str = q.remove();
System.out.println(q.remove());
Go over what code prints: size = 3, "panda", stores grizzly in str, but doesn't print. Prints "brown" since "grizzly" was removed, then prints "brown" again. What would happen if .remove() called again? Error
CAN DO THIS at javarepl.com, i.e., type Queue<String> q = new LinkedList<>() and then play

18. Queue applications Simulation, discrete-event simulation
How many toll-booths do we need? How many express lanes or self-checkout at grocery store? Runway access at airport?
Queues facilitate simulation with mathematical distributions governing events, e.g., Poisson distribution for arrival times
Shortest path, e.g., in word-ladder or Flood-Fill algorithms we'll see on Friday
Get from "white" to "house" one-letter at a time?
white, while, whale, shale, shake, …?

19. Wordladder Story Ladder from ‘white’ to ‘house’
White, while, whale, shale, …
I can do that… optimally
My brother was an English major
My ladder is 16, his is 15, how?
There's a ladder that's 14 words!
The key is ‘sough’
Guarantee optimality!
QUEUE
I heard the puzzle on the way into Duke in the mid 90's. I called my brother and said I'd solve the problem. He said he would too. He used his brain, I wrote a program. Called him an hour alter and said "got it". He said "got it". I said my code was provably optimal and had a 16-word ladder. He said he had 15. WHAT?
I added "sough" to dictionary and got a 14-word ladder 

20. Queue for shortest path – see gitlab
public boolean findLadder(String[] words,
String first, String last){
Queue<String> qu = new LinkedList<>();
Set<String> set = new HashSet<>();
qu.add(first);
while (qu.size() > 0){
String current = qu.remove();
if (oneAway(current,last)) return true;
for(String s : words){
if (! set.contains(s) && oneAway(from,s)){
qu.add(s);
set.(s); } }
return false;

21. Shortest Path reprised
How does Queue ensure we find shortest path?
Where are words one away from first?
Where are words two away from first?
Why do we need to avoid revisiting a word, when?
Why do we use a set for this? Why a HashSet?
Alternatives?
If we want the ladder, not just whether it exists
What's path from white to house? We know there is one.
All words one-away from first are on Q and are added when first is dequeued/removed first time through loop. Each of these 1-away-from-start words comes off the queue and words that are one-away from these, or 2-away from start, are put on the Q. BUT it's a queue so all 2-away words go on after the 1-away.
In general, we remove N-away words before (N+1)-away words because of FIFO structure

22. Shortest path proof
All words one away from start on queue first iteration
What is first value of current when loop entered?
All one-away words dequeued before two-away
See previous assertion, property of queues
Two-away before 3-away, …
Each 2-away word is one away from a 1-away word
So all enqueued after one-away, before three-away
How do we find three-away word?
Any w seen/dequeued that's n-away is:
Seen before every n+k-away word for k >=1!
Don't dwell on this, but walk through it as a semi-formal argument, akin to a hand-wavy proof

23. Keeping track of ladder
Find w, a one-away word from current
Enqueue w if not seen
Call map.put(w,current)
Remember keys are unique!
Put word on queue once!
map.put("lot", "hot")
map.put("dot", "hot")
map.put("hat", "hot")
Remind students that we need to keep track of how words are connected to reconstruct the ladder. Keys in a map are unique, but we only put a word on the queue once! Why? Using a set. We can make this one time the time we make a word the key in a map. The value is what caused the word to be put onto the queue, see examples

24. Reconstructing Word Ladder
Run WordLaddersFull
Notice map and call to map.put(word,current)
What about when returning the ladder, why is the returned ladder in reverse order?
What do we know about code when statement adding (key,value) to map runs?
Run program with "white" "house" and with "voter" "crazy" and with "voter" "smart"

25. http://bit.ly/201fall16-queue WOTO What's your favorite word ladder?
Could you write code to find the longest word ladder?