1. Stacks Linear list. One end is called top. Other end is called bottom. Additions to and removals from the top end only.

2. Stack Of Cups Add a cup to the stack. bottom top C A B D E F Remove a cup from new stack. A stack is a LIFO list. bottom top C A B D E

3. The Abstract Class stack template class stack { public: virtual ~stack() {} virtual bool empty() const = 0; virtual int size() const = 0; virtual T& top() = 0; virtual void pop() = 0; virtual void push(const T& theElement) = 0; };

4. Derive From A Linear List Class arrayList chain

5. Derive From arrayList  stack top is either left end or right end of linear list  empty() => arrayList::empty() O(1) time  size() => arrayList::size() O(1) time  top() => get(0) or get(size() - 1) O(1) time 0123456 abcde

6. Derive From arrayList when top is left end of linear list  push(theElement) => insert(0, theElement)  O(size) time  pop() => erase(0)  O(size) time 0123456 abcde

7. Derive From arrayList  when top is right end of linear list push(theElement) => insert(size(), theElement) O(1) time pop() => erase(size()-1) O(1) time  use right end of list as top of stack 0123456 abcde

8. Derive From Chain  stack top is either left end or right end of linear list  empty() => chain::empty() O(1) time  size() => chain::size() O(1) time abcde NULL firstNode

9. Derive From Chain abcde NULL firstNode – when top is left end of linear list  top() => get(0)  O(1) time  push(theElement) => insert(0, theElement)  O(1) time  pop() => erase(0)  O(1) time

10. Derive From Chain abcde null firstNode – when top is right end of linear list top() => get(size() - 1) O(size) time push(theElement) => insert(size(), theElement) O(size) time pop() => erase(size()-1) O(size) time – use left end of list as top of stack

11. Derive From arrayList template class derivedArrayStack : private arrayList, public stack { public: // code for stack methods comes here };

12. Constructor derivedArrayStack(int initialCapacity = 10) : arrayList (initialCapacity) {}

13. empty() And size() bool empty() const {return arrayList ::empty();} int size() const {return arrayList ::size();} 0123456 abcde

14. top() T& top() { if (arrayList ::empty()) throw stackEmpty(); return get(arrayList ::size() - 1); } 0123456 abcde

15. push(theElement) void push(const T& theElement) {insert(arrayList ::size(), theElement);} 0123456 abcde

16. pop() void pop() { if (arrayList ::empty()) throw stackEmpty(); erase(arrayList ::size() - 1); } 0123456 abcde

17. Evaluation Merits of deriving from arrayList  Code for derived class is quite simple and easy to develop.  Code is expected to require little debugging.  Code for other stack implementations such as a linked implementation are easily obtained. Just replace private arrayList with private chain For efficiency reasons we must also make changes to use the left end of the list as the stack top rather than the right end.

18. Demerits Unecessary work is done by the code.  top() verifies that the stack is not empty before get is invoked. The index check done by get is, therefore, not needed.  insert(size(), theElement) does an index check and a copy_backward. Neither is needed.  pop() verifies that the stack is not empty before erase is invoked. erase does an index check and a copy. Neither is needed.  So the derived code runs slower than necessary.

19. Evaluation Code developed from scratch will run faster but will take more time (cost) to develop. Tradeoff between software development cost and performance. Tradeoff between time to market and performance. Could develop easy code first and later refine it to improve performance.

20. A Faster pop() if (arrayList ::empty()) throw stackEmpty(); erase(arrayList ::size() - 1); vs. try {erase(arrayList ::size()-1); catch (illegalIndex {throw stackEmpty();}

21. Code From Scratch Use a 1D array stack whose data type is T.  same as using array element in arrayList Use an int variable stackTop.  Stack elements are in stack[0:stackTop].  Top element is in stack[stackTop].  Bottom element is in stack[0].  Stack is empty iff stackTop = -1.  Number of elements in stack is stackTop + 1.

22. Code From Scratch template class class arrayStack : public stack { public: // public methods come here private: int stackTop; // current top of stack int arrayLength; // stack capacity T *stack; // element array };

23. Constructor template arrayStack ::arrayStack(int initialCapacity) {// Constructor. if (initialCapacity < 1) {// code to throw an exception comes here } arrayLength = initialCapacity; stack = new T[arrayLength]; stackTop = -1; }

24. push(…) template void arrayStack ::push(const T& theElement) {// Add theElement to stack. if (stackTop == arrayLength - 1) {// code to double capacity coms here } // add at stack top stack[++stackTop] = theElement; } 01234 abcde top

25. pop() void pop() { if (stackTop == -1) throw stackEmpty(); stack[stackTop--].~T(); // destructor for T } 01234 abcde top

26. Linked Stack From Scratch See text.

27. Performance 50,000,000 pop, push, and peek operations initial capacity Class 10 50,000,000 arrayStack 2.7s 1.5s derivedArrayStack 7.5s 6.3s STL 5.6s - derivedLinkedStack 41.0s 41.0s linkedStack 40.5s 40.5s

28. Queues Linear list. One end is called front. Other end is called rear. Additions are done at the rear only. Removals are made from the front only.

29. The Abstract Class queue template class queue { public: virtual ~queue() {} virtual bool empty() const = 0; virtual int size() const = 0; virtual T& front() = 0; virtual T& back() = 0; virtual void pop() = 0; virtual void push(const T& theElement) = 0; };

30. Revisit Of Stack Applications Applications in which the stack cannot be replaced with a queue.  Parentheses matching.  Towers of Hanoi.  Switchbox routing.  Method invocation and return.  Try-catch-throw implementation. Application in which the stack may be replaced with a queue.  Rat in a maze. Results in finding shortest path to exit.

31. Derive From arrayList  when front is left end of list and rear is right end empty() => queue::empty() –O(1) time size() => queue::size(0) –O(1) time front() => get(0) –O(1) time back() => get(size() - 1) –O(1) time 0123456 abcde

32. Derive From arrayList pop() => erase(0) –O(size) time push(theElement) => insert(size(), theElement) –O(1) time 0123456 abcde

33. Derive From arrayList  when front is right end of list and rear is left end empty() => queue::empty() –O(1) time size() => queue::size(0) –O(1) time front() => get(size() - 1) –O(1) time back() => get(0) –O(1) time 0123456 abcde

34. Derive From arrayList pop() => erase(size() - 1) –O(1) time push(theElement) => insert(0, theElement) –O(size) time 0123456 abcde

35. Derive From arrayList  to perform each opertion in O(1) time (excluding array doubling), we need a customized array representation.

36. Derive From extendedChain abcde NULL firstNode lastNode frontrear  when front is left end of list and rear is right end empty() => extendedChain::empty() – O(1) time size() => extendedChain::size() – O(1) time

37. Derive From ExtendedChain abcde NULL firstNode lastNode frontrear front() => get (0) – O(1) time back() => getLast() … new method

38. Derive From ExtendedChain abcde NULL firstNode lastNode frontrear push(theElement) => push_back(theElement) – O(1) time pop() => erase(0) – O(1) time

39. Derive From extendedChain edcba NULL firstNode lastNode rearfront  when front is right end of list and rear is left end empty() => extendedChain::empty() – O(1) time size() => extendedChain::size() – O(1) time

40. Derive From extendedChain abcde NULL firstNode lastNode rearfront front() => getLast() – O(1) time back() => get(0) – O(1) time

41. Derive From extendedChain abcde NULL firstNode lastNode rearfront push(theElement) => insert(0, theElement) – O(1) time pop() => erase(size() - 1) – O(size) time

42. Custom Linked Code Develop a linked class for queue from scratch to get better preformance than obtainable by deriving from extendedChain.

43. Custom Array Queue Use a 1D array queue. queue[] Circular view of array. [0] [1] [2][3] [4] [5]

44. Custom Array Queue Possible configuration with 3 elements. [0] [1] [2][3] [4] [5] AB C

45. Custom Array Queue Another possible configuration with 3 elements. [0] [1] [2][3] [4] [5] AB C

46. Custom Array Queue Use integer variables theFront and theBack. –theFront is one position counterclockwise from first element –theBack gives position of last element –use front and rear in figures [0] [1] [2][3] [4] [5] AB C front rear [0] [1] [2][3] [4] [5] AB C front rear

47. Push An Element [0] [1] [2][3] [4] [5] AB C front rear Move rear one clockwise.

48. Push An Element Move rear one clockwise. [0] [1] [2][3] [4] [5] AB C front rear Then put into queue[rear]. D

49. Pop An Element [0] [1] [2][3] [4] [5] AB C front rear Move front one clockwise.

50. Pop An Element [0] [1] [2][3] [4] [5] AB C front rear Move front one clockwise. Then extract from queue[front].

51. Moving rear Clockwise [0] [1] [2][3] [4] [5] AB C front rear rear++; if ( rear = = arrayLength) rear = 0; rear = (rear + 1) % arrayLength;

52. Empty That Queue [0] [1] [2][3] [4] [5] AB C front rear

53. Empty That Queue [0] [1] [2][3] [4] [5] B C front rear

54. Empty That Queue [0] [1] [2][3] [4] [5] C front rear

55. Empty That Queue When a series of removes causes the queue to become empty, front = rear. When a queue is constructed, it is empty. So initialize front = rear = 0. [0] [1] [2][3] [4] [5] front rear

56. A Full Tank Please [0] [1] [2][3] [4] [5] AB C front rear

57. A Full Tank Please [0] [1] [2][3] [4] [5] AB C front rear D

58. A Full Tank Please [0] [1] [2][3] [4] [5] AB C front rear DE

59. A Full Tank Please [0] [1] [2][3] [4] [5] AB C front rear DE F When a series of adds causes the queue to become full, front = rear. So we cannot distinguish between a full queue and an empty queue!

60. Ouch!!!!! Remedies.  Don’t let the queue get full. When the addition of an element will cause the queue to be full, increase array size. This is what the text does.  Define a boolean variable lastOperationIsPush. Following each push set this variable to true. Following each pop set to false. Queue is empty iff (front == rear) && !lastOperationIsPush Queue is full iff (front == rear) && lastOperationIsPush