The Queue Data Structure

Mugurel Ionuț Andreica

Spring 2012

Operations

• enqueue(x)– Adds the element x at the tail of the queue

• dequeue()– Removes the element from the head of the queue and returns it– Returns an error if the stack is empty

• peek()– Returns (but does not remove) the element at the head of the

queue• isEmpty()

– Returns 1 if the queue is empty and 0 otherwise• The axioms are given implicitly – they determine the

expected behavior of the queue for a given sequence of operations– See the examples on the upcoming slides

Queue - Example

enqueue(7) 7 enqueue(8) 7 8 enqueue(6) 7 8

dequeue()returns 7

6

8 6 dequeue()returns 8

6peek()returns 8

enqueue(4) 6 4

Queue – Array-based Implementation (queue1.h)

#define NMAX 100

template<typename T> class Queue { private: T queueArray[NMAX]; int head, tail; public: void enqueue(T x) { if (tail >= NMAX) { fprintf(stderr, "Error 101 - The queue is full!\n"); return; } queueArray[tail] = x; tail++; }

T dequeue() { if (isEmpty()) { fprintf(stderr, "Error 102 - The queue is empty!\

n"); T x; return x; } T x = queueArray[head]; head++; return x; }

T peek() {

if (isEmpty()) {

fprintf(stderr, "Error 103 - The queue is empty!\n");

T x;

return x;

}

return queueArray[head];

}

int isEmpty() {

return (head == tail);

}

Queue() {

head = tail = 0; // the queue is empty in the beginning

}

};

Using the Queue

#include <stdio.h>#include “queue1.h”

int main() {

Queue<int> q;

q.enqueue(7); q.enqueue(8); q.enqueue(6); printf("%d\n", q.dequeue()); printf("%d\n", q.dequeue()); printf("%d\n", q.peek()); q.enqueue(4);

q.enqueue(2);

printf("%d\n", q.dequeue());

printf("%d\n", q.isEmpty());

printf("%d\n", q.peek());

q.dequeue();

printf("%d\n", q.dequeue());

printf("%d\n", q.isEmpty());

return 0;

}

Disadvantages of the Array-based Queue Implementation

• The head and tail variables are constantly increasing

• As elements are removed from the queue, the portion of the array which is effectively used shifts to the right

• We may reach the end of the array and be unable to enqueue any other elements, although a large fraction of the array (its left part) is empty (unused)

• Improved solution: circular array

Circular Array-based Queue - Example

• Circular array with NMAX=3 entries

- - - enqueue(7) 7 - - enqueue(8) 7 8 -

enqueue(6) 7 8 6 dequeue()returns 7

- 8 6peek()

returns 8

dequeue()returns 8

- - 6 enqueue(4) 4 - 6 enqueue(10)

4 10 6 dequeue()returns 6

4 10 - enqueue(13) 4 10 13

Queue – Circular Array-based Implementation (queue2.h)

#define NMAX 100

template<typename T> class Queue { private: T queueArray[NMAX]; int head, tail, size; public: void enqueue(T x) { if (size == NMAX) { fprintf(stderr, "Error 101 - The queue is full!\n"); return; } queueArray[tail] = x; tail = (tail + 1) % NMAX; size++; }

T dequeue() { if (isEmpty()) { fprintf(stderr, "Error 102 - The queue is empty!\n"); T x; return x; } T x = queueArray[head]; head = (head + 1) % NMAX; size--; return x;}

T peek() {

if (isEmpty()) {

fprintf(stderr, "Error 103 - The queue is empty!\n");

T x;

return x;

}

return queueArray[head];

}

int isEmpty() {

return (size == 0);

}

Queue() {

head = tail = size = 0;

}

};