Unit 3: Queue
Table of Content :
2.1 Definition
2.1 Queue as Abstract Data Type (ADT)
2.3 Primitive operations in Queue: Enqueue and Dequque
2.4 Linear queue, circular queue, priority queue.
Lab: Write a program to implement linear and circular queue operations.
Definition:
A real-world example of a queue can be a single-lane one-way road, where the vehicle enters first, exists first. More real-world examples can be seen as queues at the ticket windows and bus-stops.
Representation of Queue:
As we now understand that in the queue, we access both ends for different reasons. The following diagram given below tires to explain queue representation as a data structure:
As in stacks, a queue can also be implemented using Arrays, Linked-Lists, Pointers, and Structures. For the sake of simplicity, we shall implement queues using a one-dimensional array.
Basic Operations in Queue:
Queue operations may involve initialing or defining the queue, utilizing it, and then completely erasing it from the memory. Here we shall try to understand the basic operations associated with queues-
- enqueue() - add (store) an item to the queue
- dequeue() - remove (access) an item from the queue.
Few more functions are required to make the above-mentioned queue operation efficient. These are-
- peek() - gets the element at the front of the queue without removing it.
- isfull() - checks if the queue is full.
- isempty() - checks if the queue is empty.
In a queue, we always dequeue (or access) data, pointed by a front pointer, and while enquiring (or storing) data in the queue we take the help of the rear pointer.
Let's first learn about supportive functions of a queue -
peek()
This function helps to see the data at the front of the queue. The algorithm of peek() is as follows:-
Algorithm
begin procedure peek return queue[front] end procedure
Implementation of peek() function in C programming language:-
Example
int peek() { return queue[front]; }
isfull()
As we are using dimension array to implement a queue, we just check for the rear pointer to reach at MAXSIZE to determine that the queue is full. In case we maintain the queue in a circular-linked-list, the algorithm will differ. Algorithm of is full() function -
Algorithm
begin procedure isfull if rear equals to MAXSIZE return true else return false endif end procedure
Implementation of isfull() function in C programming language -
Example
bool isfull() { if(rear == MAXSIZE - 1) return true; else return false; }
isempty()
Algorithm of isempty() function-
Algorithm
begin procedure isempty if front is less than MIN OR front is greater than rear return true else return false endif end procedure
If the value of the front is less than MIN or 0, it tells that the queue is not yet initialized, hence empty.
Here's the C programming code-
Example
bool isempty() { if(front < 0 || front > rear) return true; else return false; }
Primitive Operations in Queue:
Enqueue Operation:
The following steps should be taken to enqueue (insert) data into a queue.
- Step 1 - check if the queue is full
- Step 2 - If the queue is full, produce an overflow error and exit.
- Step 3 - If the queue is not full increment the rear pointer to point to the next empty space.
- Step 4 - Add a data element to the queue location, where the rear is pointing.
- Step 5 - return success.
Sometimes, we also check to see if a queue is initialized or not, to handle any unforeseen situations.
Algorithm for enqueue operation
procedure enqueue(data) if queue is full return overflow endif rear ← rear + 1 queue[rear] ← data return true end procedure
Implementation of enqueue() in C programming language-
Example
int enqueue(int data) if(isfull()) return 0; rear = rear + 1; queue[rear] = data; return 1; end procedure
Dequeue Operation:
Accessing data from the queue is a process of two tasks-access the data where the front is pointing and remove the data \after access. The following steps are taken to perform a dequeue operation -
- Step 1 - check if the queue is empty
- Step 2 - If the queue is empty, produce an overflow error and exit.
- Step 3 - If the queue is not empty, access the data where the front is pointing.
- Step 4 - Increment front pointer to point to the next available data element.
- Step 5 - return success.
Algorithm for dequeue operation
procedure dequeue if queue is empty return underflow end if data = queue[front] front ← front + 1 return true end procedure
Implementation of dequeue() in C programming language-
Example
int dequeue() { if(isempty()) return 0; int data = queue[front]; front = front + 1; return data; }
Program to implement Queue Operations:
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <stdbool.h>
#define MAX 6
int intArray[MAX];
int front = 0;
int rear = -1;
int itemCount = 0;
int peek() {
return intArray[front];
}
bool isEmpty() {
return itemCount == 0;
}
bool isFull() {
return itemCount == MAX;
}
int size() {
return itemCount;
}
void insert(int data) {
if(!isFull()) {
if(rear == MAX-1) {
rear = -1;
}
intArray[++rear] = data;
itemCount++;
}
}
int removeData() {
int data = intArray[front++];
if(front == MAX) {
front = 0;
}
itemCount--;
return data;
}
int main() {
/* insert 5 items */
insert(3);
insert(5);
insert(9);
insert(1);
insert(12);
// front : 0
// rear : 4
// ------------------
// index : 0 1 2 3 4
// ------------------
// queue : 3 5 9 1 12
insert(15);
// front : 0
// rear : 5
// ---------------------
// index : 0 1 2 3 4 5
// ---------------------
// queue : 3 5 9 1 12 15
if(isFull()) {
printf("Queue is full!\n");
}
// remove one item
int num = removeData();
printf("Element removed: %d\n",num);
// front : 1
// rear : 5
// -------------------
// index : 1 2 3 4 5
// -------------------
// queue : 5 9 1 12 15
// insert more items
insert(16);
// front : 1
// rear : -1
// ----------------------
// index : 0 1 2 3 4 5
// ----------------------
// queue : 16 5 9 1 12 15
// As queue is full, elements will not be inserted.
insert(17);
insert(18);
// ----------------------
// index : 0 1 2 3 4 5
// ----------------------
// queue : 16 5 9 1 12 15
printf("Element at front: %d\n",peek());
printf("----------------------\n");
printf("index : 5 4 3 2 1 0\n");
printf("----------------------\n");
printf("Queue: ");
while(!isEmpty()) {
int n = removeData();
printf("%d ",n);
}
}If we compile and run the above program, it will produce the following result-
Output
Queue is full! Element removed: 3 Element at front: 5 ---------------------- index : 5 4 3 2 1 0 ---------------------- Queue: 5 9 1 12 15 16
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