1. Introduction. Lecture Content

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1 Lecture 6 Queues 1

2 Lecture Content 1. Introduction 2. Queue Implementation Using Array 3. Queue Implementation Using Singly Linked List 4. Priority Queue 5. Applications of Queue 2

3 1. Introduction A queue is a data structure where items are inserted at one end (the rear, tail, last) and deleted at the other end (the front, head, first). Another name for a queue is FIFO (first-in firstout) or FCFS (first-come first-serve). Queues are used in operating systems such as print queue, process scheduling queue. Queue is used to implement Breadth-First Search (BFS) 3

4 1. Introduction The graphical representation of a queue is shown below. 4

5 1. Array-Based Queue enqueue() operation 5

6 1. Array-Based Queue dequeue() operation 6

7 1. Array-Based Queue After some items are removed, Front will point at a cell with a higher index. 7

8 Queue Problem When you insert a new item into the queue, Rear moves upward, toward higher indices in the array. When you remove an item, Front also moves upward. Consequently, there are empty cells at the beginning of the array, because you ve removed them, you still can not insert a new item because Rear can not go any further. 8

9 Queue Problem. 9

10 Solution to Queue Problem To avoid the problem of not being able to insert more items into the queue even when it is not full, Front and Rear wrap around to the beginning of the array. The result is a circular queue (sometimes called a ring buffer). Dealing with wrapping around if (rear == maxsize - 1) rear = -1; if (front == maxsize) front = 0; 10

11 Solution to Queue Problem. 11

12 1. Array-Based Queue class Queue { private int maxsize; private int[] aqueue; private int front; private int rear; private int n; // number of items... // end class Queue 12

13 1. Array-Based Queue public Queue(int s) { // constructor maxsize = s; aqueue = new int[maxsize]; front = 0; rear = -1; n = 0; 13

14 isempty and isfull Operations public boolean isempty() { // returns true if queue is empty return (n == 0); public boolean isfull() { // returns true if queue is full return (n == maxsize); 14

15 enqueue Operation public void enqueue(int data) { // insert item at rear of queue // check whether queue is full if (rear == maxsize - 1) // deal with wraparound rear = -1; aqueue[++rear] = data; // increment rear and insert n++; // one more item 15

16 dequeue Operation public int dequeue() { // remove item from front of queue // check whether queue is empty int temp = 0; temp = aqueue[front++]; if (front == maxsize) // deal with wraparound front = 0; n--; // one less item return temp; 16

17 peek Operation public int peek() { // return item at front of queue // check whether queue is empty return aqueue[front]; 17

18 Display Queue Data public void displayqueue() { int temp = front, count = 0; if (isempty()) System.out.println( "Queue is empty"); else { System.out.print( "Queue (front-->rear): "); 18

19 Display Queue Data while (count < n) { // deal with wraparound if (temp == maxsize) temp = 0; int data = aqueue[temp++]; System.out.print(data + " "); count++; System.out.println(); 19

20 Java Queue Interface import java.util.queue; import java.util.linkedlist; // The LinkedList class implements the Queue interface. 20

21 Java Queue Interface Queue<Integer> Q = new LinkedList<Integer>(); add(x) adds x to the tail of the queue remove() retrieves and removes the head of the queue peek() gets the head of the queue without removing it size() returns the number of queue/list elements isempty() returns true if queue is empty 21

22 Lecture Content 1. Introduction 2. Queue Implementation Using Array 3. Queue Implementation Using Singly Linked List 4. Priority Queue 5. Applications of Queue 22

23 2. SLL-Based Queue - Node Definition class Node { public int data; // data item public Node next; // next node in list public Node(int d) // constructor { data = d; 23

24 2. SLL-Based Queue - Node Definition public void displaynode() { // display node data System.out.println(data + " "); // end class Node 24

25 List Definition class NodeList { private Node first; // ref to first item private Node last; // ref to last item public NodeList() { // constructor first = null; // no items on list yet last = null; // no items on list yet public boolean isempty() { // returns true if list is empty return (first == null); // end class NodeList 25

26 List Definition public void insertlast(int d) { Node newnode = new Node(d); if (isempty()) first = newnode; else last.next = newnode; last = newnode; 26

27 List Definition public int deletefirst() { // (assumes non-empty list) int temp = first.data; if (first.next == null) // if only one item last = null; first = first.next; return temp; 27

28 Display List Data public void displaylist() { Node cur = first; while (cur!= null) { cur.displaynode(); cur = cur.next; System.out.println(); 28

29 List Definition public int First() { // return data member of first node return first.data; 29

30 Queue Definition class SLLQueue { private NodeList List; public SLLQueue() { // constructor List = new NodeList(); public boolean isempty() { // returns true if queue is empty return List.isEmpty(); 30

31 Queue Definition public void enqueue(int data) { // insert at rear of queue List.insertLast(data); public int dequeue() { // remove front item of queue return List.deleteFirst(); 31

32 Queue Definition public int peek(int data) { // return data of queue head return List.First(); 32

33 Display Queue Data public void displayqueue() { if (isempty()) System.out.println( Queue is empty"); else { System.out.println( Queue (front-->rear): "); List.displayList(); // end class SLLQueue 33

34 Queue Usage class SLLQueueApp { public static void main( String[] args) { SLLQueue Q = new SLLQueue(); Q.enqueue(20); Q.displayQueue(); Q.dequeue(); Q.displayQueue(); // end main() // end class SLLQueueApp 34

35 Lecture Content 1. Introduction 2. Queue Implementation Using Array 3. Queue Implementation Using Singly Linked List 4. Priority Queue 5. Applications of Queue 35

36 4. Priority Queue In priority queue (PQ), items are ordered by key value so that item with lowest (or highest) key is always at the front. So items are inserted in the proper position to maintain the order. In preemptive multitasking operating system, processes are placed in PQ so the highest-priority process is the next one to receive a time-slice that allows it to execute on CPU. 36

37 4. Array-Based Priority Queue We use a small priority number to indicate a high priority and vice versa. class PQ { // array in sorted order, from max // at index 0 to min at index n - 1 private int maxsize; private int[] apqueue; private int n; // number of items... // end class PQ 37

38 Priority Queue public PQ(int s) { // constructor maxsize = s; apqueue = new int[maxsize]; n = 0; public boolean isempty() { // returns true if queue is empty return (n == 0); 38

39 Priority Queue public boolean isfull() { // returns true if queue is full return (n == maxsize); public int peek() { // return item at front of PQ // small value means high priority return apqueue[n - 1]; 39

40 Priority Queue public int dequeue() { //remove minimum (high priority) item // queue head is at index n - 1 return apqueue[--n]; 40

41 Priority Queue public void displayqueue() { if (isempty()) System.out.println( "Queue is empty"); else { for (int i = n - 1; i >= 0; i--) System.out.print( apqueue[i] + " "); System.out.println(); 41

42 Priority Queue public void enqueue(int data) { // max value (low priority) at index 0, // min value (high priority) at idx n-1 int i = 0; if (n == 0) // if no items in queue, apqueue[n++] = data; else // if queue has items, { // start at end, for (i = n - 1; i >= 0; i--) { // if new item larger, 42

43 Priority Queue if (data > apqueue[i]) apqueue[i+1] = apqueue[i]; // shift right else // if smaller, break; // done shifting // end for apqueue[i+1] = data;// insert it n++; // end enqueue() 43

44 Java PriorityQueue Class import java.util.priorityqueue; PriorityQueue<Integer> pq = new PriorityQueue<Integer>(); 44

45 Java PriorityQueue Class offer(x) / add(x): adds x into priority queue poll() / remove(): retrieves and removes the head of the priority queue peek() gets the head of the priority queue without removing it size() returns the number of elements in queue 45

46 5. Applications of Queue In breadth-first search traversal, when we visit a vertex v we next visit all vertices adjacent to v. The resulting tree is called a breadth-first search tree. This method of traversal can be implemented by a queue to store unexamined vertices. Algorithm BFS for breadth-first search can be applied to directed and undirected graphs. 46

47 5. Applications of Queue Initially, all vertices are marked unvisited. The counter bfn, which is initialized to zero, represents the order in which the vertices are removed from the queue. In the case of undirected graphs, an edge is either a tree edge or a cross edge. If the graph is directed, an edge is either a tree edge, a back edge or a cross edge; there are no forward edges. 47

48 5. Applications of Queue Algorithm BFS Input: A directed or undirected graph G = (V, E). Output: Numbering of the vertices in BFS order. 1. bfn 0 2. for each vertex v V 3. mark v unvisited 4. end for 5. for each vertex v V 6. if v is marked unvisited then bfs(v) 7. end for 48

49 5. Applications of Queue Method bfs(v) 1. Q {v 2. mark v visited 3. while Q 4. v Dequeue(Q) 5. bfn bfn

50 5. Applications of Queue 6. for each edge (v, w) E 7. if w is marked unvisited then 8. Enqueue(w, Q) 9. mark w visited 10. end if 11. end for 12. end while 50

51 5. Applications of Queue An example of the breadth-first search traversal of an undirected graph. 51

52 Exercises 1. Write a program to reverse digits of a nonnegative integer n (e.g., n = 123 will be displayed as 321) by using a. a user-defined queue b. the Java Queue interface and LinkedList class 52

53 References 1. Robert Lafore Data Structures and Algorithms in Java. 2Ed, SAMS. ISBN: M.H. Alsuwaiyel Algorithms Design Techniques and Analysis. World Scientific Publishing. ISBN:

1. Stack Implementation Using 1D Array

Lecture 5 Stacks 1 Lecture Content 1. Stack Implementation Using 1D Array 2. Stack Implementation Using Singly Linked List 3. Applications of Stack 3.1 Infix and Postfix Arithmetic Expressions 3.2 Evaluate