1. Queue C and Data Structures Baojian Hua bjhua@ustc.edu.cn

2. Linear List Recall that a linear list has the form: The delete and insert operations may insert or delete an arbitrary element e_i If the delete is restricted at one end and insert at the other end, we get a queue

3. Example: Queue of Char ‘a’‘a’ insert ‘b’‘b’ ‘a’‘a’ ‘b’‘b’ ‘a’‘a’ ‘c’‘c’ delete ‘b’‘b’ ‘c’‘c’

4. Abstract Data Types in C: Interface // in file “queue.h” #ifndef QUEUE_H #define QUEUE_H typedef struct queue *queue; queue new (); int size (queue q); int isEmpty (queue q); void enQueue (queue q, poly x); poly deQueue (queue q); poly getHead (queue q); #endif

5. Implementation Using Extensible Array // in file “arrayQueue.c” #include “queue.h” struct queue { arrayList l; }; // Recall the box strategy: l q

6. Operations: “ new ” queue new () { queue q = checkedMalloc (sizeof (*q)); q->l = newArrayList (); return q; } 0 n-1 array max tail l q

7. Operations: “ size ” int size (queue q) { return arrayListLength (q->l); } 0 n-1 array max tail l q

8. Operations: “ isEmpty ” int isEmpty (queue q) { return arrayListIsEmpty (q->l); } 0 n-1 array max tail l q

9. Operations: “ enQueue ” void enQueue (queue q, poly x) { arrayListInsertLast (stk->l, x); return; } 0 n-1 array max tail l q

10. Operations: “ deQueue ” poly deQueue (queue q) { if (! arrayListIsEmpty (q->l)) return arrayListDeleteFirst (q->l); error (“empty queue”); return NULL; }

11. Operations: “ deQueue ” 0 n-1 array max tail l q

12. Operations: “ deQueue ” 0 n-1 array max tail l q

13. Analysis What ’ s the complexity? enQueue: O(1) deQueue: O(n) data movement Can we do better? Lazy approach better amortized performance Circular queue

14. Lazy Approach Instead of moving data when “ deQueue ”, we move data only when reaching the tail of the queue O(n) on n operations which has O(1) amortized cost

15. Lazy Approach What ’ s necessary modification? Leave this as a programming assignment 0 n-1 array max tail l q

16. Circular Queue A refinement of the lazy approach is the circular queue 0 n-1 array max tail l q The formula: tail = (tail+1)%max; head = (head+1)%max; head

17. Implementation Using Linked List // in file “linkedQueue.c” #include “queue.h” struct queue { linkedList l; }; l q data next data next data next …

18. Operations: “ new ” queue new () { queue q = checkedMalloc (sizeof (*q)); q->l = newLinkedList (); return q; } l q /\

19. Operations: “ size ” int size (queue q) { return linkedListLength (q->l); } l q data next data next data next …

20. Operations: “ isEmpty ” int isEmpty (queue q) { return linkedListIsEmpty (q->l); } l q data next data next data next …

21. Operations: “ enQueue ” void enQueue (queue q, poly x) { // note the difference with extensible array- // based representation linkedListInsertLast (q->l, x); return; } l q data next data next data next …

22. Operations: “ deQueue ” poly deQueue (queue) { if (! linkedListIsEmpty (q->l)) return linkedListDeleteFirst (q->l); error (“empty queue”); return NULL; } l q data next data next data next …

23. Analysis What ’ s the complexity of these operations? enQueue: O(n) search the last element deQueue: O(1) Improvement: Circular linked list leave as programming assignment