1. IKI 10100I: Data Structures & Algorithms Ruli Manurung (acknowledgments to Denny & Ade Azurat) 1 Fasilkom UI Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Implementing Stacks & Queues

2. 2 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Outline ADT: Stacks Basic operations Examples of use Implementations Array-based and linked list-based ADT: Queues Basic operations Examples of use Implementations Array-based and linked list-based

3. 3 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Linear Data Structures A collection of components that are arranged along one dimension, i.e in a straight line, or linearly. Stack: a linear data structure where access is restricted to the most recently inserted item. Queue: a linear data structure where access is restricted to the least recently inserted item. Both of these abstract data types can be implemented at a lower level using a list: either an array or a linked list.

4. 4 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Stack The last item added is pushed (added) to the stack. The last item added can be popped (removed) from the stack. The last item added can be topped (accessed) from the stack. These operations all take constant time: O(1). A typical stack interface: void push(Thing newThing); void pop(); Thing top();

5. 5 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Stack Implementation: Array A stack can be implemented as an array A and an integer top that records the index of the top of the stack. For an empty stack, set top to -1. When push(X) is called, increment top, and write X to A[top]. When pop() is called, decrement top. When top() is called, return A[top].

6. 6 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Example top(-1) Atop(0) A Btop(1) Push A Push B MyStack myStack = new MyStack(); myStack.push(A); myStack.push(B);

7. 7 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Array Doubling When array-based stack is constructed, instantiate an array with a “default” size. When the array underlying the stack is full (not the stack itself!), we can increase the array through array doubling. Allocate a new array twice the size, and copy the old array to the first half of the new array: Thing[] newA = new Thing[oldA.length*2]; for(int ii=0; ii<oldA.length; ii++) newA[ii] = oldA[ii]; oldA = newA;

8. 8 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Running Time Without array doubling, all stack operations take constant time – O(1). With array doubling, push() may be O(N), but this happens quite rarely: array doubling due to data size N must be preceded by N/2 push() non-doubling calls. Effectively, still constant time  Amortization.

9. 9 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Stack Implementation: Array public class MyArrayStack { private T[] array; private int topOfStack; private static final int DEFAULT_CAPACITY = 10; public MyArrayStack() … public boolean isEmpty() … public void makeEmpty() … public T top() … public void pop() … public T topAndPop() … public void push(T x) … private void doubleArray() … }

10. 10 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Stack Implementation: Linked List First item in list = top of stack (if empty: null ) push(Thing x) : Create a new node containing x Insert it as the first element pop() : Delete first item (i.e. move “top” to the second item) top() : Return the data of the first element dcba topOfStack

11. 11 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Stack Implementation: Linked List public class MyLinkedListStack { private ListNode topOfStack; public MyLinkedListStack() … public boolean isEmpty() … public void makeEmpty() … public T top() … public void pop() … public T topAndPop() … public void push(T x) … }

12. 12 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Queue Last item added is enqueued (added) to the back. First item added is dequeued (removed) from the front. First item added can be accessed: getFront. These operations all take constant time – O(1). A typical queue interface: void enqueue(Thing newThing); void dequeue(); Thing getFront();

13. 13 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Queue Implementation: Simple Idea Store items in an array A Maintain index: back Front of queue = A[0] Back of queue = A[back] Enqueue is easy & fast: store at A[back], back++ Dequeue is inefficient: A[1] to A[back] needs to be shifted (and back-- )  O(N) X back enqueue(X) XY back enqueue(Y) XYZ back enqueue(Z) YZ back dequeue()

14. 14 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Queue Implementation: Better Idea Add another index: front, which records the front of the queue Dequeue is now done by incrementing front Both enqueue and dequeue are now O(1). XYZ back enqueue(X) enqueue(Y) enqueue(Z) front YZ back dequeue() front Z back dequeue() front Question: what happens if we enqueue then dequeue array.length-1 items?

15. 15 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Queue Implementation: “Circular” Array After the array.length-1 -th item is enqueued, the underlying array is full, even though the queue is not  logically, it should be (almost?) empty. Solution: wraparound Re-use cells at beginning of array that are ‘empty’ due to dequeue. When either front or back is incremented and points “outside array” ( ≥array.length ), reset to 0.

16. 16 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Circular Example Both front and back indexes “wraparound” the array. Think of the array as a circle… PQR frontback PQRS frontback PQRS front T back QRS front T back RS front T back S front T back T frontback

17. 17 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Java Implementation Fairly straightforward. Basically, maintain Front Back Number of items in queue When is the underlying array really full? How do we do array doubling?

18. 18 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Queue Implementation: Array public class MyArrayQueue { private T[] array; private int front,back,currentSize; private static final int DEFAULT_CAPACITY = 10; public MyArrayQueue() … public boolean isEmpty() … public void makeEmpty() … public T getFront() … public void dequeue() … public T getFrontAndDequeue() … public void enqueue(T x) … private void doubleQueue() … private int increment(int x) … }

19. 19 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Queue Implementation: Linked List Maintain 2 node references: front & back An empty queue: front = back = null. enqueue(Thing X) : Create a new node N containing X If queue empty: front = back = N Else append N and update back dequeue() : Delete first item (referenced by front ) getFront() : Return data of first element abcd frontback

20. 20 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Queue Implementation: Linked List public class MyLinkedListQueue { private ListNode front; private ListNode back; public MyLinkedListQueue() … public boolean isEmpty() … public void makeEmpty() … public T getFront() … public void dequeue() … public T getFrontAndDequeue() … public void enqueue(T x) … }

21. 21 Ruli Manurung (Fasilkom UI)IKI10100I: Data Structures & Algorithms Week 7 Summary Both versions, array and linked-list, run in O(1) Linked-list implementation requires extra overhead due to next reference at each node (Circular) array implementation of queues can be quite tricky Array space doubling needs memory at least 3x size of actual data.