1. The Queue Data Structure Mugurel Ionu Andreica Spring 2012

2. 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

3. Queue - Example

4. Queue – Array-based Implementation (queue1.h) #define NMAX 100 template 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 } };

5. Using the Queue #include #include “queue1.h” int main() { Queue q; q.enqueue(7); q.enqueue(8); q.enqueue(6); 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; }

6. 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

7. Circular Array-based Queue - Example Circular array with NMAX=3 entries

8. Queue – Circular Array-based Implementation (queue2.h) #define NMAX 100 template 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; } };