Queues Fall 2018 Margaret Reid-Miller

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1 Queues Fall 2018 Margaret Reid-Miller

2 Today Exam 2 is next Tuesday, October 30 Writing methods various classes that implement Lists. Methods using Lists and Big-O w/ ArrayList or LinkedLists Prove f(n) in O(g(n)) using the Big-O definition Recursion call tree, trace, implement Interfaces Stacks & Queues (conceptual, trace code, big-o) Evaluate post-fix expressions Fall (Reid-Miller) 2

3 Today Today: Finish converting infix to postfix Quiz 6 & solutions Queues ArrayQueue Exercise: Reverse queue values Fall (Reid-Miller) 3

4 Fall (Reid-Miller) 4

5 Stack ADT last in, first out (LIFO) Operations: PUSH adds an element onto the top of the stack POP removes the element from the top of the stack PEEK returns the element on the top of the stack without removing it (optional operation). Test if the stack is EMPTY Why have a Stack ADT? Less power than arrays or Lists Use them for more discipline, simple, fast operations Fall (Reid-Miller) 5

6 Stack Implementations Want O(1) for all operations, so what underlying data structure can we use? array? Yes, if top is last element of array ArrayList? Yes, if top is size()-1 linked list? Yes, with top at head of the list Fall (Reid-Miller) 6

7 Converting Infix to Postfix Note: Assume the infix expression is valid. Each entry in a infix expression is a token. 1. Let S be an empty stack. 2. Let postfix be an empty string. 3. For each token in the infix expression: a. If the token is a number, append it to the postfix string. b. Otherwise (the token is an operator) Process the operator (see next 2 slides) 4. While the stack S is not empty: a. Pop an operator off the stack S and append it to the posfix string. Fall (Reid-Miller) 7

Processing Parentheses (converting infix to postfix, cont d) Each pair of parentheses marks a subexpression that must be completely converted before previous operators are processed.

8 Processing Parentheses (converting infix to postfix, cont d) Each pair of parentheses marks a subexpression that must be completely converted before previous operators are processed. Assign the lowest precedence to left and right parentheses so only a right parenthesis can pop off a left parenthesis. Do not put parentheses in the postfix string. Operator Precedence * 2 / ( -1 ) -1 Fall (Reid-Miller) 8

9 Process the operator - revised (converting infix to postfix, cont d) Let nextop be the operator token. 1. If stack S is empty or nextop is (, push nextop on stack S. 2. Otherwise: a. Let topop = peek(s). b. If prec(nextop) > prec(topop), push nextop on stack S. c. Otherwise: i. While S is not empty and prec(nextop) prec(topop): a) Let topop = pop(s). b) If topop is (, exit loop immediately. c) Append topop to postfix string. d) If stack S is not empty, let topop = peek(s). ii. If nextop is not ), push nextop on stack S. Fall (Reid-Miller) 9

10 Converting: An example Infix: * ( 4 / ) - 6 / + ( ( ( ( ( * * * * * * * Postfix: / 1 + * Fall (Reid-Miller) 10

11 Invalid expressions Assume that tokens are only operators and integers. Evaluating a postfix expression: How would you know that the postfix expression is not valid? Converting an infix expression to postfix: How would you know that the infix expression is not valid? Fall (Reid-Miller) 11

12 Queues Fall (Reid-Miller) 12

13 Queue ADT last in last out Operations: ENQUEUE adds an element to the BACK of the queue DEQUEUE removes the element from the FRONT of the queue PEEK returns the element in the front of the queue without removing it (optional?) Test if the queue is EMPTY Fall (Reid-Miller) 13

14 Uses: Queue A store checkout line A playlist of songs on a jukebox, mp3 player, etc. Putting a new bottle of milk behind the old one. Fall (Reid-Miller) 14

15 Queue Operations public interface FIFOQueue<E> { void enqueue(e obj); E dequeue(); E peek(); boolean isempty(); } Ideally, each of these operations should be O(1) time. Fall (Reid-Miller) 15

16 Queue Implementations Want O(1) for all operations, so what underlying data structure can we use? ArrayList? No, one of the enqueue or dequeue must be O(1) array? Yes, surprsingly linked list? Singly, Doubly, Singly with reference to the tail? Fall (Reid-Miller) 16

17 Queues using an array FRONT REAR Store the elements of the queue from front to rear in order in the array. What happens if we store the front of the queue always in position 0? Fall (Reid-Miller) 17

18 Queues using an array FRONT REAR Store the elements of the queue from front to rear in order in the array. What happens if we store the rear of the queue always in last position in the array? Fall (Reid-Miller) 18

19 Queues using a circular array REAR FRONT Allow the queue to wrap around from the last cell of the array back to the first cell so shifting is not necessary. Problem? If the array is full, we can reallocate the array and copy the queue data into the new array starting at position 0 again. Fall (Reid-Miller) 19

20 Array Implementation Fields public class ArrayQueue<E> implements FIFOQueue<E> { private E[] dataarray; private int front; private int rear; private int numelements; indices of front and rear queue elements in array // methods (next slides) } Fall (Reid-Miller) 20

21 Array Implementation Constructor & isempty public ArrayQueue() { } dataarray = (E[])new Object[1]; front = -1; rear = -1; numelements = 0; indicates an empty queue public boolean isempty() { return (numelements == 0); } Fall (Reid-Miller) 21

22 Array Implementation enqueue public void enqueue(e element) { } numelements == dataarray.length if ( ) reallocate(); rear = ; (rear+1) % dataarray.length dataarray[rear] = element; if (front == -1) front = rear; numelements++; Fall (Reid-Miller) 22

23 Array Implementation reallocate REAR FRONT FRONT REAR Fall (Reid-Miller) 23

24 Array Implementation reallocate private void reallocate() { E[] newarray = (E[])new Object[numElements*2]; int j = front; for (int i=0; i<numelements; i++) { newarray[i] = dataarray[j]; } (j + 1) % numelements j = ; } front = 0; rear = numelements-1; dataarray = newarray; Fall (Reid-Miller) 24

25 Array Implementation dequeue public E dequeue() { if ( ) numelements == 0 throw new NoSuchElementException(); E obj = dataarray[front]; dataarray[front] = null; if (front == rear) { front = -1; rear = -1; } else numelements--; return obj; } front = (front+1)%dataarray.length; Fall (Reid-Miller) 25

26 Array Implementation peek public E peek() { if ( ) numelements == 0 throw new NoSuchElementException(); return dataarray[front]; } Fall (Reid-Miller) 26

27 Exercise: Reverse // reverses the queue objects using a stack public static void reverse(queue<string> q) { Fall (Reid-Miller) 27

28 Reverse // reverses the queue objects using a stack public static void reverse(queue<string> q) { Stack<string> s = new Stack<String>(); while (!q.isempty()) s.push(q.dequeue()); } while (!s.isempty()) a.enqueue(s.pop()); Fall (Reid-Miller) 28

29 Reverse (recursively) // reverses the queue objects, recursively public static void reverse(queue<string> q) { } if (!q.isempty()) String front = q.dequeue(); reverse(q); q.enqueue(front); Where s the stack? Fall (Reid-Miller) 29

30 Queues using a singly-linked list null front rear Store the elements of the stack from top to bottom in order in the list. Why do we need an additional reference to the tail? Fall (Reid-Miller) 30

31 Linked List Implementation Fields public class ListQueue<E> implements FIFOQueue<E> { private Node front; private Node rear; // methods (next slides) references to nodes with front and rear queue elements in list } Fall (Reid-Miller) 31

32 Linked List Implementation Constructor & isempty public ListQueue() { front = null; } rear = null; indicates an empty queue public boolean isempty() { } return (front == null); Fall (Reid-Miller) 32

33 Linked List Implementation enqueue public void enqueue(e obj) { Node newnode = new Node(obj); ❶ ❷ if (rear!= null) { rear.next = newnode; rear = newnode; } else { newnode rear = newnode; front = newnode; ❶ } } null front rear ❷ Fall (Reid-Miller) 33 null

34 Linked List Implementation dequeue public E dequeue() { } ❶ ❷ if (front == null) throw new NoSuchElementException(); E element = front.data; front = front.next; if (front == null) rear = null; return element; data element data null ❶ front ❷ rear Fall (Reid-Miller) 34

35 Linked List Implementation peek public E peek() { if (front == null) } throw new NoSuchElementException(); return front.data; Fall (Reid-Miller) 35

36 Other uses for queues Printer queues Packet router Simulating a queuing system Supermarket checkout lanes Highway traffic congestion models Internet traffic Fall (Reid-Miller) 36

Stacks Fall 2018 Margaret Reid-Miller

Stacks Fall 2018 Margaret Reid-Miller Stacks 15-121 Fall 2018 Margaret Reid-Miller Today Exam 2 is next Tuesday, October 30 Today: Quiz 5 solutions Recursive add from last week (see SinglyLinkedListR.java) Stacks ADT (Queues on Thursday) ArrayStack