1. CS 221 Analysis of Algorithms Data Structures

2. Portions of the following slides are from  Goodrich and Tamassia, Algorithm Design: Foundations, Analysis and Internet Examples, 2002  and  Material provided by the publisher’s John Wiley & Son, Inc.) companion website for this book

3. Remember this  “Algorithms + Data Structures = Programs”  Niklaus Wirth, Swiss Computer Scientist  Or, perhaps- Programs = Programming_language(Algoritms + Data Structures)

4. Data Structures  What are they and  Why do we care?

5. Stacks  Stack – container for a collection of objects where you add objects to one end and retrieve those objects from the same end  -- add object to the top of the stack and must retrieve from the top of the stack

6. Stacks  Last-In-First-Out -- LIFO  Think Stack of dishes in the cafeteria  Put a plate on top  take a plate from the top Stack of poker chips Stack of anything Bread-crumbs

7. Stacks  Algorithms - Stack Operations Push(o) Pop()

8. Stacks  Other Stack Operations size()  how many objects are on the stack? isEmpty() boolean  is the stack empty? top()  what is on top of stack? but don’t pop it

9. Stacks  What do we use stacks for? Web – Browsers  session visit history Text Editors – Word Processors  edit/undo Procedure Calls  transfer of execution/return

10. Stacks  What do we use stacks for? Web – Browsers  session visit history Text Editors – Word Processors  edit/undo Procedure Calls  transfer of execution/return

11. Stack - Array implementation Algorithm push(o) if t = S.length  1 then throw “StackFullError” else t  t + 1 S[t]  o  A simple way of implementing the Stack ADT uses an array  We add elements from left to right  A variable keeps track of the index of the top element S 012 t from: Goodrich and Tamassia, 2002

12. Stack - Array implementation Algorithm pop() if isEmpty() then throw “StackEmptyError” else t  t  1 return S[t + 1]  A simple way of implementing the Stack ADT uses an array  We add elements from left to right  A variable keeps track of the index of the top element S 012 t from: Goodrich and Tamassia, 2002

13. Stacks for procedure calls  To call a procedure Push state of procedure (local variables and PC) on stack  To return from a procedure Pop state of calling procedure from stack main() { int i = 5; foo(i); } foo(int j) { int k; k = j+1; bar(k); } bar(int m) { … } bar PC = 1 m = 6 foo PC = 3 j = 5 k = 6 main PC = 2 i = 5 from: Goodrich and Tamassia, 2002

14. Stack – array implementation  Issues run-time?  size()  isEmpty()  top()  push(o)  pop() Algorithm push(o) if t = S.length  1 then throw “StackFullError” else t  t + 1 S[t]  o Algorithm pop() if isEmpty() then throw “StackEmptyError” else t  t  1 return S[t + 1]

15. Stack – array implementation  Memory limitations? growth?  How would you handle this? Algorithm push(o) if t = S.length  1 then throw “StackFullError” else t  t + 1 S[t]  o Algorithm pop() if isEmpty() then throw “StackEmptyError” else t  t  1 return S[t + 1]

16. Queues  Queue – container for objects Objects are added/retrieved from queue on First-In-First-Out rule FIFO That is, oldest thing in container must be removed first, then next oldest thing, etc. Objects are added to the end of queue, retrieved from front of queue

17. Queues  Queue – conceptually parts on a conveyer belt standing line to buy movie tickets  In Computer systems Printer queues job scheduling process scheduling Web page request service

18. Queues  Queue algorithms – main operations enqueue(o) – placing object at end of queue dequeue() – retreiving object from front of queue  Other queue operations front(): returns the element at the front without removing it integer size(): returns the number of elements stored boolean isEmpty(): indicates whether no elements are stored

19. Queues  Array-based Queue Algorithm enqueue(o) if size() = N-1 then throw “QueueFullError” Q[r] <- o r <- r + 1 Q 012rf queue

20. Queues  Array-based Queue Algorithm dequeue(o) if isEmpty() then throw “QueueEmptyError” temp <- Q[f] Q[f] <- Null f <- f + 1 return temp Q 012rf queue

21. Queues  Array-based Queue Algorithm dequeue(o) if isEmpty() then throw “QueueEmptyError” temp <- Q[f] Q[f] <- Null f <- f + 1 return temp Q 012rf queue Algorithm enqueue(o) if size() = N-1 then throw “QueueFullError” Q[r] <- o r <- r + 1 Issues?  Run-time?  Memory?

22. Queues  Array-based Queue circular  Use an array of size N in a circular fashion  Two variables keep track of the front and rear f index of the front element r index immediately past the rear element  Array location r is kept empty Q 012rf normal configuration Q 012fr wrapped-around configuration

23. Queue - circular  We use the modulo operator (remainder of division) Algorithm size() return (N  f + r) mod N Algorithm isEmpty() return (f  r) Q 012rf Q 012fr

24. Queue - circular Algorithm enqueue(o) if size() = N  1 then throw FullQueueException else Q[r]  o r  (r + 1) mod N  Operation enqueue throws an exception if the array is full Q 012rf Q 012fr

25. Queue - circular  Operation dequeue throws an exception if the queue is empty Algorithm dequeue() if isEmpty() then throw EmptyQueueException else o  Q[f] f  (f + 1) mod N return o Q 012rf Q 012fr