1. 1 Stacks & Queues CSC212

2. 2 Stacks & Queues Stack: Last In First Out (LIFO). –Used in procedure calls, to compute arithmetic expressions etc. Queue: First In First Out (FIFO). –Used in operating systems, simulations etc. Priority Queues: Highest priority item is served first. –Used in operating systems, printer servers etc.

3. 3 Stack (Linked Implementation) TOP

4. 4 ADT Stack: Specification Elements: The elements are of a variable type. In a linked implementation an element is placed in a node. public class Node extends Object { public T data; public Node next; public Node () { data = null; next = null; } public Node (T val) { data = val; next = null; } }

5. 5 ADT Stack: Specification Structure: the elements are linearly arranged, and ordered according to the order of arrival, most recently arrived element called top. Domain: the number of elements in the stack is bounded therefore the domain is finite. Type of elements: Stack

6. 6 ADT Stack: Specification Operations: 1.Procedure Push (Stack S, Type e) requires: Stack S is not full. input: Stack S, Type e. results: Element e is added to the stack as its most recently added elements. output: none. 2.Procedure Pop (Stack S, Type e) requires: Stack S is not empty. input: Stack S. results: the most recently arrived element in S is removed and its value assigned to e. output: Type e. 3.Procedure Empty (Stack S, boolean flag) input: Stack S. results: If Stack S is empty then flag is true, otherwise false. output: flag.

7. 7 ADT Stack: Specification Operations: 4.Procedure Full (Stack S, Boolean flag). requires: input: Stack S. results: If S is full then Full is true, otherwise Full is false. output: flag.

8. 8 ADT Stack (Linked Implementation) TOP Data Element Pointer A Linked Implementation of the Stack.

9. 9 ADT Stack (Linked Implementation) public class LinkStack { private Node top; /* Creates a new instance of LinkStack */ public LinkStack() { top = null; } public boolean empty(){ return top == null; }

10. 10 ADT Stack (Linked Implementation) public boolean full(){ return false; } public void push(T e){ Node tmp = new Node(e); tmp.next = top; top = tmp; }

11. 11 ADT Stack (Linked Implementation) public T pop(){ Node tmp = top; T e = top.data; top = top.next; return e; }

12. 12 Stack: Array Implementation public class ArrayStack { private int maxsize; private int top; private T[] nodes; /** Creates a new instance of ArrayStack */ public ArrayStack(int n) { maxsize = n; top = 0; nodes = (T[]) new Object[n]; }

13. 13 Stack: Array Implementation public boolean empty(){ return top == 0; } public boolean full(){ return top == maxsize; }

14. 14 Stack: Array Implementation public void push(T e){ nodes[top++] = e; } public T pop(){ return nodes[--top]; }

15. 15 Applications of Stacks Some applications of stacks are: –Balancing symbols. –Computing or evaluating postfix expressions. –Converting expressions from infix to postfix.

16. 16 1. Balancing Symbols Expressions: mathematical (a + ((b-c)*d)) or programs have delimiters. begin{S1 S2{ beginS2S3 begin} ….S4 end} end

17. 17 1. Balancing Symbols Delimiters must be balanced. [()] is legal but [(]) illegal. A stack can be used to check if the delimiters are balanced. –Read characters from the start of the expression to the end. –If the token is a starting delimiter, push on to the stack, if closing delimiter pop the corresponding start delimiter from the stack.

18. 18 1. Balancing Symbols –If the stack is empty or if the popped symbol does not correspond to the closing symbol: report error. –If stack is not empty at the end of file report an error.

19. 19 2. Postfix Expressions Evaluating Postfix Expressions: –Infix expression: 4.99*1.06+5.99+6.99*1.06 –Value 18.69 correct  parenthesis used. –Value 19.37 incorrect  no parenthesis used. –In postfix form, above expression becomes: 4.99 1.06 * 5.99 + 6.99 1.06*+  Advantage: no brackets are needed and a stack can be used to compute the expression.

20. 20 2. Postfix Expressions Example: –infix: 6*(5+((2+3)*8)+3) –postfix: 6 5 2 3 + 8 * + 3 + *. Algorithm to compute postfix expression: –Read the postfix expression left to right. When a number is read push it on the stack; when a operator is read, pop two numbers from the stack and carry out the operation on them, push the result back on the stack.

21. 21 3. Infix to Postfix Conversion A stack can also be used to convert an infix expression to postfix expression. (See handout) Example: infix expression a + b * c + (d * e + f) * g to postfix expression a b c * + d e * f + g * +

22. 22 Queues Front Tail

23. 23 ADT Queue: Specification Elements: The elements are of a variable type. In a linked implementation elements are placed in nodes. public class Node extends Object { public T data; public Node next; public Node () { data = null; next = null; } public Node (T val) { data = val; next = null; } }

24. 24 ADT Queue: Specification Structure: the elements are linearly arranged, and ordered according to the order of arrival, most recently arrived element is called the tail and least recently arrived element the front or head. Domain: the number of elements in the queue is bounded therefore the domain is finite. Type of elements: Queue

25. 25 ADT Queue: Specification Operations: 1.Procedure Enqueue (Queue Q, Type e) requires: Queue Q is not full. input: Queue Q, Type e. results: Element e is added to the queue at its tail. output: none. 2.Procedure Serve (Queue Q, Type e) requires: Queue Q is not empty. input: Queue Q. results: the element at the head of Q is removed and its value assigned to e. output: Type e. 3.Procedure Length (Queue Q, int length) input: Queue Q. results: The number of element in the Queue Q is returned. output: length.

26. 26 ADT Queue: Specification Operations: 4.Procedure Full (Queue Q, Boolean flag). requires: input: Queue Q. results: If Q is full then flag is set to true, otherwise flag is set to false. output: flag.

27. 27 ADT Queue (Linked Implementation) public class LinkQueue { private Node head, tail; private int size; /** Creates a new instance of LinkQueue */ public LinkQueue() { head = tail = null; size = 0; }

28. 28 ADT Queue (Linked Implementation) public boolean full() { return false; } public int length (){ return size; }

29. 29 ADT Queue (Linked Implementation) public void enqueue (Type e) { if (tail == null){ head = tail = new Node(e); } else { tail.next = new Node(e); tail = tail.next; } size++; }

30. 30 ADT Queue (Linked Implementation) public Type serve() { Node tmp; Type x; tmp = head; x = head.data; head = head.next; size--; if (size == 0) tail = null; return x; }

31. 31 ADT Queue (Array Implementation) Array implementation of the queue…a fixed size array is used to store the data elements. As data elements are enqueued & served the queue crawls through the array from low to high index values. As the queue crawls forward, it also expands and contracts.

32. 32 ADT Queue (Array Implementation) HeadTail HeadTail After one En-queue and one Serve

33. 33 ADT Queue (Array Implementation) HeadTail Where to En-queue this?

34. 34 ADT Queue (Array Implementation) HeadTail Wrap Round 0 MaxSize-1

35. 35 ADT Queue (Array Implementation) 0MaxSize - 1 Head Tail

36. 36 ADT Queue (Array Implementaion) public class ArrayQueue { private int maxsize; private int size; private int head, tail; private T[] nodes; /** Creates a new instance of ArrayQueue */ public ArrayQueue(int n) { maxsize = n; size = 0; head = tail = 0; nodes = (T[]) new Object[n]; }

37. 37 ADT Queue (Array Implementation) public boolean full () { return size == maxsize ? true : false; } public int length () { return size; } public void enqueue(T e) { nodes[tail] = e; tail = (tail + 1) % maxsize; size++; }

38. 38 ADT Queue (Array Implementation) public T serve () { T e = nodes[head]; head = (head + 1) % maxsize; size--; return e; }

39. 39 Priority Queue Each data element has a priority associated with it.Highest priority item is served first. Real World Priority Queues: hospital emergency rooms…most sick patients treated first, events in a computer system, etc. Priority Queue can be viewed as: –View 1: Priority queue as an ordered list. –View 2: Priority queue as a set.

40. 40 ADT Priority Queue Specification: Elements: The elements are of type PQNode. Each node has in it a data element of variable type and priority of type Priority ( which could be int type). public class PQNode { private T data; private Priority priority; public PQNode next; public PQNode() { next = null; } public PQNode(T e, Priority p) { data = e; priority = p; }

41. 41 ADT Priority Queue Structure: the elements are linearly arranged, and may be ordered according to a priority value, highest priority element is called the tail and least priority element the front or head. Domain: the number of nodes in the queue is bounded therefore the domain is finite. Type of elements: PriorityQueue

42. 42 ADT Priority Queue Operations: 1.Procedure Enqueue (PriorityQueue PQ, Type e, Priority p) requires: PQ is not full. input: PQ, e. results: Element e is added to the queue according to its priority. output: none. 2.Procedure Serve (PriorityQueue PQ, Type e, Priority p) requires: PQ is not empty. input: PQ. results: the element at the head of PQ is removed and returned. output: e, p. 3.Procedure Length (PriorityQueue PQ, int length) input: PQ. results: The number of element in the PQ is returned. output: length.

43. 43 ADT Priority Queue Operations: 4.Procedure Full (PrioriytQueue PQ, Flag flag). requires: input: PQ. results: If PQ is full then flag is set to true, otherwise flag is set to false. output: flag.

44. 44 ADT Priority Queue el 10 el 108775 HeadTail Array Implementation el 7 Insert Where? el 10 el 10 el 8 7 5 7 Head Tail Linked Implementation el

45. 45 ADT Priority Queue (Linked) public class LinkPQ { private int size; private PQNode head, tail; /* tail is of no use here. */ public LinkPQ() { head = tail = null; size = 0; } public int length (){ return size; }

46. 46 ADT Priority Queue (Linked) public int length (){ return size; } public boolean full () { return false; }

47. 47 ADT Priority Queue (Linked) public void enqueue(T e, int pty) { PQNode p, q, tmp; if ((size == 0) || (pty > head.Priority())) { tmp = new PQNode (e, pty); tmp.next = head; head = tmp; } else { p = head; q = null; while ((p != null) && (p.Priority() > pty)) { q = p; p = p.next; } tmp = new PQNode (e, pty); tmp.next = p; q.next = tmp; } }

48. 48 ADT Priority Queue (Linked) public T serve (Priority pty){ T e = head.get_data(); pty.set_value(head.get_priority().get_value()); head = head.next; size--; return(e); }

49. 49 ADT Priority Queue Implementations –Array Implementation: Enqueue is O(n), Serve is O(1). –Linked List: Enqueue is O(n), Serve is O(1). –Heap: Enqueue is O(log n), Serve is O(log n)  Heaps to be discussed later.