Chapter 5 ADTs Stack and Queue Fall 2013 Yanjun Li CS2200

Outline Stack Queue Comparison Array-based Implementation Linked Implementation Queue Comparison Fall 2013 Yanjun Li CS2200

Stacks of Coins and Bills Fall 2013 Yanjun Li CS2200

Stacks of Boxes and Books TOP OF THE STACK Fall 2013 Yanjun Li CS2200

Stacks Logical level What do these composite objects all have in common ? Fall 2013 Yanjun Li CS2200

Stacks Stack An abstract data type in which elements are added and removed from only one end. A “last in, first out” (LIFO) structure. Fall 2013 Yanjun Li CS2200

Stacks Logical level What operations would be appropriate for a stack? Fall 2013 Yanjun Li CS2200

Stacks Transformers Observers Push Pop IsEmpty IsFull Top change state observe state What about an iterator? Fall 2013 Yanjun Li CS2200

Stacks Application Level For what type of problems would stacks be useful? LIFO: A stack is great for reversing data. Operating system function calls Finding palindromes Expression evaluation & syntax parsing Fall 2013 Yanjun Li CS2200

Stack Applications Operating system function calls void DrawSquare(int x, int y, int edge) { DrawLine(x, y, edge, HORIZONTAL); DrawLine(x, y, edge, VERTICAL); DrawLine(x+edge, y, edge, VERTICAL); DrawLine(x, y+edge, edge, HORIZONTAL); } int main () DrawSquare(1,2,3); return 0; Fall 2013 Yanjun Li CS2200

Stack Applications Finding palindromes (Lab!) Fall 2013 Yanjun Li CS2200

Stack Applications Help Converting Decimal to Binary (pseudocode) Read (number) Loop (number > 0) 1) digit = number modulo 2 (number%2) 2) print (digit) 3) number = number / 2 // from Data Structures by Gilbert and Forouzan Problem: The binary numbers are printed backwards. 19 becomes 11001 instead of 10011 Solution: push each binary number onto the stack and pop the digit out of the stack and print it at the end. Fall 2013 Yanjun Li CS2200

Stacks class StackType { public: StackType(); ~StackType(); bool IsEmpty() const; bool IsFull() const; void Push(ItemType item); void Pop( ); ItemType Top() const; Fall 2013 Yanjun Li CS2200

Stacks Implementation Level Array-based Implementation Linked Structure Fall 2013 Yanjun Li CS2200

Array-Based Implementation private: int top; ItemType items[MAX_ITEM]; }; [0] [1] [2] …. [M..] stack .items .top Fall 2013 Yanjun Li CS2200

Array-Based Implementation Give a series of operations that could produce this situation Fall 2013 Yanjun Li CS2200

Array-Based Implementation To what do we initialize top ? 0 or -1 Do we increment or store first? 0: store and increment -1: increment and store Which is better? (what does top represent?) StackType::StackType() { top = -1; } Fall 2013 Yanjun Li CS2200

Array-Based Implementation Before we code, we must consider error conditions Stack overflow The condition that results from trying to push an element on to a full stack Exception class : FullStack Stack underflow The condition that results from trying to pop an empty stack Exception class: EmptyStack Fall 2013 Yanjun Li CS2200

Array-Based Implementation //pre: Stack has been initialized. //post: function value = (stack is empty) bool StackType::IsEmpty() const { return ( top == -1); } //pre: stack has been initialized. //post: function value = (stack is full) bool StackType:: IsFull() const return ( top == MAX_ITEM-1); What does const mean? Fall 2013 Yanjun Li CS2200

Array-Based Implementation //pre: stack has been initialized and is not full //post: newItem is at the top of the stack. void StackType::Push(ItemType newItem) { top++; items[top] = newItem; } Fall 2013 Yanjun Li CS2200

Array-Based Implementation //pre: stack has been initialized. //post: if stack is full, throw an exception; //Else newItem is at the top of the stack. void StackType::Push(ItemType newItem) { if (IsFull()) throw FullStack(); top++; items[top] = newItem; } What is FullStack( ) ? Fall 2013 Yanjun Li CS2200

Array-Based Implementation //pre: stack has been initialized and is not empty. //post: top element has been removed from stack. void StackType::Pop() { top--; } //post: A copy of the top element is returned. ItemType StackType:: Top() const return (items[top]); Fall 2013 Yanjun Li CS2200

Array-Based Implementation //pre: stack has been initialized. //post: if stack is empty, throw an exception; else top element //has been removed from stack. void StackType::Pop() { if (IsEmpty()) throw EmptyStack(); top--; } //post: if stack is empty, throw an exception; else a copy of the //top element is returned. ItemType StackType::Top() const if (IsEmpty()) throw EmptyStack(); return (items[top]); What is EmptyStack ? Fall 2013 Yanjun Li CS2200

Array-Based Implementation Which functions have to be changed if we dynamically allocate the array items ? Do we need to add any new functions? Fall 2013 Yanjun Li CS2200

Test Plan Clear-box strategy to check each operation. Push() & Pop() while it is empty or full. Fall 2013 Yanjun Li CS2200

Linked Implementation The logical level (public part of the class declaration) stays the same; class StackType { public: StackType(); ~StackType(); bool IsEmpty() const; bool IsFull() const; void Push(ItemType item); void Pop( ); ItemType Top() const; Fall 2013 Yanjun Li CS2200

Linked Implementation The implementation level (private part of the class declaration) changes private: NodeType* topPtr; }; ‘D’ .info .next Pointer to the next node in the stack .topPtr Stack Can we “borrow” code from UnsortedType for Push and Pop ? Fall 2013 Yanjun Li CS2200

Linked Implementation //pre: the stack is not full //post: the new item is added on top of the stack void StackType::Push(ItemType newItem) { NodeType* location; location = new NodeType; location->info = newItem; location>next = topPtr; topPtr = location; } newItem .info .next .info .next ‘D’ location .topPtr Fall 2013 Yanjun Li CS2200

Linked Implementation //pre: the stack is not empty //post: the top item is removed from the top of the //stack void StackType::Pop() { NodeType* tempPtr; tempPtr = topPtr; topPtr = topPtr->next; delete tempPtr; } Does this work for stacks of one item? More than Fall 2013 Yanjun Li CS2200

Linked Implementation More than one item Fall 2013 Yanjun Li CS2200

Linked Implementation One item Fall 2013 Yanjun Li CS2200

Linked Implementation What about the constructor, destructor, and observer functions? We can borrow all but Top() from class UnsortedType List //pre: the stack is not empty //post: the item on the top of the stack is //returned. ItemType StackType::Top() { return topPtr->info; } Fall 2013 Yanjun Li CS2200

Other Member Functions Constructor Destructor Free all the node spaces. isEmpty isFull Fall 2013 Yanjun Li CS2200

Array vs. Linked Structure A serious drawback of array-based implementation: the size of a stack must be determined when a stack object is declared. Size is not enough or Space is wasted. Fall 2013 Yanjun Li CS2200

Big-O Comparison Time Array-Based Implementation Linked Implementation Class constructor Class destructor O(1) O(n) IsFull() IsEmpty() Push() Pop() Fall 2013 Yanjun Li CS2200

Queues Fall 2013 Yanjun Li CS2200

Queues Fall 2013 Yanjun Li CS2200

Queues What do these composite objects all have in common? Fall 2013 Yanjun Li CS2200

Queues Queue An abstract data type in which elements are added to the rear and removed from the front; a “first in, first out” (FIFO) structure Fall 2013 Yanjun Li CS2200

Queues What operations would be appropriate for a queue? Fall 2013 Yanjun Li CS2200

Queues Transformers Observers MakeEmpty Enqueue Dequeue IsEmpty IsFull change state observe state What about an iterator? Fall 2013 Yanjun Li CS2200

Queues For what type of problems would stacks be useful? Print server maintains a queue of print jobs. Disk driver maintains a queue of disk input/output requests. Scheduler (e.g., in an operating system) maintains a queue of processes awaiting a slice of machine time. Fall 2013 Yanjun Li CS2200

Queues class QueueType Logical Level { public: QueueType(int max); bool IsEmpty() const; bool IsFull() const; void Enqueue(ItemType item); //add newItem to the rear of the queue. void Dequeue(ItemType& item); //remove front item from queue Logical Level Fall 2013 Yanjun Li CS2200

Array-Based Implementation private: ItemType* items; // Dynamically allocated array int maxQue; // Whatever else we need }; Implementation level Fall 2013 Yanjun Li CS2200

Array-Based Implementation One data structure: An array with the front of the queue fixed in the first position Enqueue A, B, C, D Dequeue Move elements down What’s wrong with this design? Fall 2013 Yanjun Li CS2200

Array-Based Implementation Another data structure: An array where the front floats What happens if we add X, Y, and Z ? Fall 2013 Yanjun Li CS2200

Array-Based Implementation We can let the queue wrap around in the array; i.e. treat the array as a circular structure Fall 2013 Yanjun Li CS2200

Array-Based Implementation (a) Initial conditions front = 2 rear = 2 (b) queue.Dequeue(item) front = 3 A [0] [1] [2] [3] [4] Empty Queue Full Queue How can we tell the difference? Fall 2013 Yanjun Li CS2200

Array-Based Implementation A third data structure:Front indicates the slot preceding the front item;it is reserved and not used Empty Queue Full Queue Fall 2013 Yanjun Li CS2200

Array-Based Implementation private: int front; int rear; int maxQue; ItemType* items; }; Complete implementation level To what do we initialize front and rear ? Fall 2013 Yanjun Li CS2200

Array-Based Implementation QueueType::QueueType( int max) { maxQue = max + 1; front = maxQue - 1; rear = maxQue - 1; items = new ItemType[maxQue]; } QueueType::QueueType( ) { maxQue = 500 + 1; QueueType::~QueueType( ) { delete [] items; Why is the array declared max + 1 ? Fall 2013 Yanjun Li CS2200

Array-Based Implementation //Pre: the queue is not full //Post: newItem is at the rear of the queue void QueueType::Enqueue(ItemType newItem) { rear = (rear + 1) % maxQue; items[rear] = newItem; } Fall 2013 Yanjun Li CS2200

Array-Based Implementation //pre: the queue is not empty //post: the front of the queue has been removed // and a copy returned in item void QueueType::Dequeue(ItemType& item) { front = (front + 1) % maxQue; item = items[front]; } Fall 2013 Yanjun Li CS2200

Array-Based Implementation //returns true if the queue is empty bool QueueType::IsEmpty( ) { return ( rear == front ); } //returns true if the queue is full bool QueueType::IsFull( ) return ( (rear + 1) % maxQue == front ) Fall 2013 Yanjun Li CS2200

Linked Implementation Data structure for linked queue What data members are needed? Fall 2013 Yanjun Li CS2200

Linked Implementation Enqueue(newItem) Set newNode to the address of newly allocated node Set Info(newNode) to newItem Set Next(newNode) to NULL Set Next(rear) to newNode If queue is empty Set front to newNode else Fall 2013 Yanjun Li CS2200

Linked Implementation Dequeue(item) Set tempPtr to front Set item to Info(front) Set front to Next(front) if queue is now empty Set rear to NULL Deallocate Node(tempPtr) Fall 2013 Yanjun Li CS2200

Storage Requirements What does this table tell you ? Fall 2013 Yanjun Li CS2200

Reference Reproduced from C++ Plus Data Structures, 4th edition by Nell Dale. Reproduced by permission of Jones and Bartlett Publishers International. Fall 2013 Yanjun Li CS2200