Chapter 5. ADTs Stack and Queue

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1 Chapter 5 ADTs Stack and Queue

2 Stacks of Coins and Bills

3 Stacks of Boxes and Books TOP OF THE STACK TOP OF THE STACK

4 Logical (or ADT) level: A stack is an ordered group of homogeneous items (elements), in which the removal and addition of stack items can take place only at the top of the stack A stack is a LIFO last in, first out structure

5 Stack ADT Operations MakeEmpty -- Sets stack to an empty state IsEmpty -- Determines whether the stack is currently empty IsFull -- Determines whether the stack is currently full Push (ItemType newitem) -- Throws exception if stack is full; otherwise adds newitem to the top of the stack Pop -- Throws exception if stack is empty; otherwise removes the item at the top of the stack ItemType Top -- Throws exception if stack is empty; otherwise returns a copy of the top item

6 ADT Stack Operations Transformers Push Pop Observers IsEmpty IsFull change state observe state

7 class StackType { public: StackType( ); bool IsFull () const; bool IsEmpty() const; void Push( ItemType item ); void Pop(); private: ItemType Top(); private: int top; ItemType items[max_items]; }; What are the pre and post conditions?

8 // File: StackTypecpp #include "StackTypeh" #include <iostream> StackType::StackType( ) { top = -1; } bool StackType::IsEmpty() const { return(top == -1); } bool StackType::IsFull() const { return (top = = MAX_ITEMS-1); }

9 void StackType::Push(ItemType newitem) { if( IsFull() ) throw FullStack(): top++; items[top] = newitem; } void StackType::Pop() { if( IsEmpty() ) throw EmptyStack(); top--; } ItemType StackType::Top() { if (IsEmpty()) throw EmptyStack(); return items[top]; }

10 Class Interface Diagram (Memory reversed to better illustrate concept) StackType class StackType IsEmpty IsFull Push Pop Top Private data: top [MAX_ITEMS-1] [ 2 ] [ 1 ] items [ 0 ]

11 Tracing Client Code Private data: top letter [MAX_ITEMS-1] [ 2 ] [ 1 ] items [ 0 ] char letter = ; StackType charstack; charstackpush(letter); charstackpush( C ); charstackpush( S ); if ( charstackisempty( )) charstackpop( ); charstackpush( K ); while (charstackisempty( )) { letter = charstacktop(); charstackpop(0)}

12 Tracing Client Code letter Private data: top -1 [MAX_ITEMS-1] [ 2 ] [ 1 ] items [ 0 ] char letter = ; StackType charstack; charstackpush(letter); charstackpush( C ); charstackpush( S ); if ( charstackisempty( )) charstackpop( ); charstackpush( K ); while (charstackisempty( )) { letter = charstacktop(); charstackpop(0)}

13 Tracing Client Code letter Private data: top 0 [MAX_ITEMS-1] [ 2 ] [ 1 ] items [ 0 ] char letter = ; StackType charstack; charstackpush(letter); charstackpush( C ); charstackpush( S ); if ( charstackisempty( )) charstackpop( ); charstackpush( K ); while (charstackisempty( )) { letter = charstacktop(); charstackpop(0)}

14 Tracing Client Code letter Private data: top 1 [MAX_ITEMS-1] [ 2 ] items [ 0 ] [ 1 ] C char letter = ; StackType charstack; charstackpush(letter); charstackpush( C ); charstackpush( S ); if ( charstackisempty( )) charstackpop( ); charstackpush( K ); while (charstackisempty( )) { letter = charstacktop(); charstackpop(0)}

15 Tracing Client Code letter Private data: top 2 [MAX_ITEMS-1] items [ 0 ] [ 2 ] S [ 1 ] C char letter = ; StackType charstack; charstackpush(letter); charstackpush( C ); charstackpush( S ); if ( charstackisempty( )) charstackpop( ); charstackpush( K ); while (charstackisempty( )) { letter = charstacktop(); charstackpop(0)}

16 Tracing Client Code letter Private data: top 2 [MAX_ITEMS-1] items [ 0 ] [ 2 ] S [ 1 ] C char letter = ; StackType charstack; charstackpush(letter); charstackpush( C ); charstackpush( S ); if ( charstackisempty( )) charstackpop( ); charstackpush( K ); while (charstackisempty( )) { letter = charstacktop(); charstackpop(0)}

17 Tracing Client Code letter Private data: top 1 [MAX_ITEMS-1] items [ 0 ] [ 2 ] S [ 1 ] C 0 char letter = ; StackType charstack; charstackpush(letter); charstackpush( C ); charstackpush( S ); if ( charstackisempty( )) charstackpop( ); charstackpush( K ); while (charstackisempty( )) { letter = charstacktop(); charstackpop(0)}

18 Tracing Client Code letter Private data: top 2 [MAX_ITEMS-1] items [ 0 ] [ 2 ] K [ 1 ] C char letter = ; StackType charstack; charstackpush(letter); charstackpush( C ); charstackpush( S ); if ( charstackisempty( )) charstackpop( ); charstackpush( K ); while (charstackisempty( )) { letter = charstacktop(); charstackpop(0)}

19 Tracing Client Code letter Private data: top 2 [MAX_ITEMS-1] items [ 0 ] [ 2 ] K [ 1 ] C char letter = ; StackType charstack; charstackpush(letter); charstackpush( C ); charstackpush( S ); if ( charstackisempty( )) charstackpop( ); charstackpush( K ); while (charstackisempty( )) { letter = charstacktop(); charstackpop(0)}

20 Tracing Client Code letter Private data: top 2 K [MAX_ITEMS-1] items [ 0 ] [ 2 ] K [ 1 ] C char letter = ; StackType charstack; charstackpush(letter); charstackpush( C ); charstackpush( S ); if ( charstackisempty( )) charstackpop( ); charstackpush( K ); while (charstackisempty( )) { letter = charstacktop(); charstackpop(0)}

21 Tracing Client Code letter Private data: top 1 [MAX_ITEMS-1] items [ 0 ] K [ 2 ] K [ 1 ] C char letter = ; StackType charstack; charstackpush(letter); charstackpush( C ); charstackpush( S ); if ( charstackisempty( )) charstackpop( ); charstackpush( K ); while (charstackisempty( )) { letter = charstacktop(); charstackpop(0)}

22 Tracing Client Code letter Private data: top 1 K [MAX_ITEMS-1] items [ 0 ] [ 2 ] K [ 1 ] C char letter = ; StackType charstack; charstackpush(letter); charstackpush( C ); charstackpush( S ); if ( charstackisempty( )) charstackpop( ); charstackpush( K ); while (charstackisempty( )) { letter = charstacktop(); charstackpop(0)}

23 Tracing Client Code letter Private data: top 0 C [MAX_ITEMS-1] items [ 0 ] [ 2 ] K [ 1 ] C char letter = ; StackType charstack; charstackpush(letter); charstackpush( C ); charstackpush( S ); if ( charstackisempty( )) charstackpop( ); charstackpush( K ); while (charstackisempty( )) { letter = charstacktop(); charstackpop(0)}

24 Tracing Client Code letter Private data: top 0 C [MAX_ITEMS-1] items [ 0 ] [ 2 ] K [ 1 ] C char letter = ; StackType charstack; charstackpush(letter); charstackpush( C ); charstackpush( S ); if ( charstackisempty( )) charstackpop( ); charstackpush( K ); while (charstackisempty( )) { letter = charstacktop(); charstackpop(0)}

25 Tracing Client Code letter Private data: top -1 [MAX_ITEMS-1] items [ 0 ] [ 2 ] K [ 1 ] C char letter = ; StackType charstack; charstackpush(letter); charstackpush( C ); charstackpush( S ); if ( charstackisempty( )) charstackpop( ); charstackpush( K ); while (charstackisempty( )) { letter = charstacktop(); charstackpop(0)}

26 End of Trace letter Private data: top -1 [MAX_ITEMS-1] items [ 0 ] [ 2 ] K [ 1 ] C char letter = ; StackType charstack; charstackpush(letter); charstackpush( C ); charstackpush( S ); if ( charstackisempty( )) charstackpop( ); charstackpush( K ); while (charstackisempty( )) { letter = charstacktop(); charstackpop(0)}

27 Another Stack Implementation One advantage of an ADT is that the implementation can be changed without the program using it knowing about it The dynamic array implementation of the stack has a weakness -- the maximum size of the stack is passed to the constructor as parameter Instead we can dynamically allocate the space for each stack element as it is pushed onto the stack

28 ItemType is char class StackType StackType Top IsEmpty IsFull Private data: topptr C Push Pop ~StackType

29 ItemType is float class StackType StackType Top IsEmpty IsFull Push Pop ~StackType Private data: topptr

30 ItemType is string class StackType StackType Top IsEmpty IsFull Private data: topptr cat dog Push Pop ~StackType

31 letter Tracing Client Code char letter = ; StackType mystack; mystackpush(letter); mystackpush( C ); mystackpush( S ); If (mystackisempty() ) { letter = mystacktop( ); mystackpop(); } mystackpush( K );

32 letter Private data: topptr NULL Tracing Client Code char letter = ; StackType mystack; mystackpush(letter); mystackpush( C ); mystackpush( S ); If (mystackisempty() ) { letter = mystacktop( ); mystackpop(); } mystackpush( K );

33 letter Private data: topptr Tracing Client Code char letter = ; StackType mystack; mystackpush(letter); mystackpush( C ); mystackpush( S ); If (mystackisempty() ) { letter = mystacktop( ); mystackpop(); } mystackpush( K );

34 letter Private data: topptr C Tracing Client Code char letter = ; StackType mystack; mystackpush(letter); mystackpush( C ); mystackpush( S ); If (mystackisempty() ) { letter = mystacktop( ); mystackpop(); } mystackpush( K );

35 letter Private data: topptr Tracing Client Code S C V char letter = ; StackType mystack; mystackpush(letter); mystackpush( C ); mystackpush( S ); If (mystackisempty() ) { letter = mystacktop( ); mystackpop(); } mystackpush( K );

36 letter Private data: topptr Tracing Client Code S C char letter = ; StackType mystack; mystackpush(letter); mystackpush( C ); mystackpush( S ); If (mystackisempty() ) { letter = mystacktop( ); mystackpop(); } mystackpush( K );

37 letter Private data: topptr S C Tracing Client Code char letter = ; StackType mystack; mystackpush(letter); mystackpush( C ); mystackpush( S ); If (mystackisempty() ) { letter = mystacktop( ); mystackpop(); } mystackpush( K );

38 letter Private data: topptr S C Tracing Client Code char letter = ; StackType mystack; mystackpush(letter); mystackpush( C ); mystackpush( S ); If (mystackisempty() ) { letter = mystacktop( ); mystackpop(); } mystackpush( K );

39 letter Private data: topptr C Tracing Client Code char letter = ; StackType mystack; mystackpush(letter); mystackpush( C ); mystackpush( S ); If (mystackisempty() ) { letter = mystacktop( ); mystackpop(); } mystackpush( K );

40 letter Private data: topptr C Tracing Client Code char letter = ; StackType mystack; mystackpush(letter); mystackpush( C ); mystackpush( S ); If (mystackisempty() ) { letter = mystacktop( ); mystackpop(); } mystackpush( K );

41 letter Private data: topptr Tracing Client Code char letter = ; StackType mystack; mystackpush(letter); mystackpush( C ); mystackpush( S ); If (mystackisempty() ) { letter = mystacktop( ); mystackpop(); } mystackpush( K );

42 letter Private data: topptr Tracing Client Code char letter = ; StackType mystack; mystackpush(letter); mystackpush( C ); mystackpush( S ); If (mystackisempty() ) { letter = mystacktop( ); mystackpop(); } mystackpush( K );

43 letter Private data: topptr char letter = ; StackType mystack; mystackpush(letter); mystackpush( C ); K mystackpush( S ); If (mystackisempty() ) { letter = mystacktop( ); mystackpop(); } mystackpush( K ); Tracing Client Code

44 // DYNAMICALLY LINKED IMPLEMENTATION OF STACK Struct NodeType; //Forward declaration class StackType { public: //Identical to previous implementation private: NodeType* topptr; }; Struct NodeType { ItemType info; NodeType* next; };

45 Adding newitem to the stack newitem B newitem = B ; NodeType* location; location = new NodeType<char>; location->info = newitem; location->next = topptr; topptr = location; topptr X C L

46 Adding newitem to the stack newitem B newitem = B ; NodeType* location; location = new NodeType<char>; location->info = newitem; location->next = topptr; topptr = location; topptr X C L location

47 newitem B Adding newitem to the stack newitem = B ; NodeType* location; location = new NodeType<char>; location->info = newitem; location->next = topptr; topptr = location; topptr X C L location

48 Adding newitem to the stack newitem B newitem = B ; NodeType* location; location = new NodeType<char>; location->info = newitem; location->next = topptr; topptr = location; topptr X C L location B

49 newitem B Adding newitem to the stack newitem = B ; NodeType* location; location = new NodeType<char>; location->info = newitem; location->next = topptr; topptr = location; topptr X C L location B

50 Adding newitem to the stack newitem B newitem = B ; NodeType* location; location = new NodeType<char>; location->info = newitem; location->next = topptr; topptr = location; topptr X C L location B

51 Implementing Push void StackType::Push ( ItemType newitem ) // Adds newitem to the top of the stack { if (IsFull()) throw FullStack(); NodeType* location; location = new NodeType<ItemType>; location->info = newitem; location->next = topptr; topptr = location; } Do we need IsFull?

52 item Deleting item from the stack NodeType* tempptr; item = topptr->info; tempptr = topptr; topptr = topptr->next; delete tempptr; topptr B X C L tempptr

53 Deleting item from the stack item B NodeType* tempptr; item = topptr->info; tempptr = topptr; topptr = topptr->next; delete tempptr; topptr B X C L tempptr

54 item B Deleting item from the stack NodeType* tempptr; item = topptr->info; tempptr = topptr; topptr = topptr->next; delete tempptr; topptr B X C L tempptr

55 item B Deleting item from the stack NodeType* tempptr; item = topptr->info; tempptr = topptr; topptr = topptr->next; delete tempptr; topptr B X C L tempptr

56 item B Deleting item from the stack NodeType<ItemType>* tempptr; item = topptr->info; tempptr = topptr; topptr = topptr->next; delete tempptr; topptr X C L tempptr

57 Implementing Pop / Top void StackType::Pop() // Remove top item from Stack { if (IsEmpty()) throw EmptyStack(); else { NodeType* tempptr; tempptr = topptr; topptr = topptr ->next; delete tempptr; } } ItemType StackType::Top() // Returns a copy of the top item in the stack { if (IsEmpty()) throw EmptyStack(); else return topptr->info; }

58 Implementing IsFull bool StackType::IsFull() const // Returns true if there is no room for another // ItemType on the free store; false otherwise { NodeType* location; try { location = new NodeType; delete location; return false; } catch(std::bad_alloc exception) { return true; } }

59 Example of a Queue

60 Logical (or ADT) level: A queue is an ordered group of homogeneous items (elements), in which new elements are added at one end (the rear), and elements are removed from the other end (the front) A queue is a FIFO first in, first out structure

61 Queue ADT Operations MakeEmpty -- Sets queue to an empty state IsEmpty -- Determines whether the queue is currently empty IsFull -- Determines whether the queue is currently full Enqueue (ItemType newitem) -- Adds newitem to the rear of the queue Dequeue (ItemType& item) -- Removes the item at the front of the queue and returns it in item

62 ADT Queue Operations Transformers MakeEmpty Enqueue Dequeue Observers IsEmpty IsFull change state observe state

63 Public Interface of QueType typedef char ItemType; class QueType { public: QueType(int max); // max is the size of the queue QueType(); // Default size of 500 ~QueType(); void MakeEmpty(); bool IsEmpty() const; bool IsFull() const; void Enqueue(ItemType item); void Dequeue(ItemType& item);

64 class QueType SIMPLE ARRAY IMPLEMENTATION QueType ~QueType Enqueue Dequeue Private Data: front 1 rear 4 maxque 5 items RESERVED C X J items [0] [1] [2] [3] [4]

65 What is the private part of class QueType for this design? What troubles do we encounter?

66 class QueType DYNAMIC ARRAY IMPLEMENTATION QueType ~QueType Enqueue Dequeue Private Data: front 1 rear 4 maxque 5 items RESERVED C X J items [0] [1] [2] [3] [4]

67 What is the private part of class QueType for this design? Does this design have the same problems as the previous design?

68 class QueType QueType ~QueType Enqueue Private Data: qfront qrear C Z T Dequeue

69 What is the private part of class QueType for this design?

70 CountedQueType inherits from QueType // DERIVE CLASS CountedQueType FROM BASE CLASS QueType class CountedQueType : QueType; { public: CountedQueType( ); void Enqueue( ItemType newitem ); void Dequeue( ItemType& item ); int GetLength( ) const; // Returns number of items on the counted queue private: int length; };

71 What additional fields does CountedQueType need? What functions must be changed?

Definition of Stack. 5 Linked Structures. Stack ADT Operations. ADT Stack Operations. A stack is a LIFO last in, first out structure.

Definition of Stack. 5 Linked Structures. Stack ADT Operations. ADT Stack Operations. A stack is a LIFO last in, first out structure. 5 Linked Structures Definition of Stack Logical (or ADT) level: A stack is an ordered group of homogeneous items (elements), in which the removal and addition of stack items can take place only at the