Lesson 4

Stacks

Readings: chapter 18

Stacks

• Stack: a data structure in which elements are added and removed from one end only

– Addition/deletion occur only at the top of the stack

– Last in first out (LIFO) data structure

• Operations:

– Push: to add an element onto the stack

– Pop: to remove an element from the stack

– isEmpty: to check if the stack is empty

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Stacks (cont’d.)

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Stacks (cont’d.)

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Implementation of Stacks as Arrays

• First element goes in first array position, second in the second position, etc.

• Top of the stack is index of the last element added to the stack

• Stack elements are stored in an array, which is a random access data structure – Stack element is accessed only through top

• To track the top position, use a variable called stackTop

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Implementation of Stacks as Arrays

• The stack elements are stored in an array

– The stack uses a prefix of the array

– The size of the array is the maximum number of elements in the stack

• class stackType implements the functions of the abstract class stackADT

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Implementation of Stacks as Arrays

• C++ arrays begin with the index 0

• If stackTop is 0, stack is empty

• If stackTop is nonzero, stack is not empty

– Top element is given by stackTop – 1

– stackTop is the size of the stack

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Implementation of Stacks as Arrays

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Initialize Stack

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Push

• Store the newItem in the array component indicated by stackTop

• Increment stackTop

• Overflow occurs if we try to add a new item to a full stack

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Push

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Push

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Return the Top Element

• Returns the top element of the stack

• Does not change the state of the stack

• Overflow condition: only allowed if the stack is not empty

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Pop

• Removes the top element and returns it

• To remove an element from the stack, decrement stackTop by 1

• Underflow condition: trying to remove an item from an empty stack

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Pop

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Pop

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Constructor and Destructor

• Constructor:

– Creates array to store stack elements (with default array size)

– Sets stackTop to 0

– Sets stack size to 0

• Destructor:

– Deallocates memory occupied by the array

– Sets stackTop to 0

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Stack Header File

• Place definitions of class and function profiles (stack operations) together in a file

– called ArrayStack.h

• Place implementation of class and function bodies together in a file

– called ArrayStack.cpp

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Linked Implementation of Stacks

• Array only allows fixed number of elements

• If number of elements to be pushed exceeds array size, the program may terminate

• Linked lists can dynamically organize data

• In a linked representation, stackTop is pointer to memory address of top element in stack

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Linked Implementation of Stacks

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Default Constructor

• Initializes the stack to an empty state when a stack object is declared

– Sets stackTop to NULL

– Sets size to 0

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Empty Stack and Full Stack

• In a linked implementation of stacks, function isFullStack does not apply

– Logically, the stack is never full

• Stack is empty if stackTop is NULL

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Initialize Stack

• initializeStack: reinitializes stack to an empty state

– Must deallocate memory occupied by current element

– Sets stackTop to NULL

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Push

• newNode is added at the beginning of the linked list pointed to by stackTop

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Push

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Return the Top Element

• top operation

– returns top element of stack

– returns the element in the node pointed by stackTop

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Pop

• Node pointed to by stackTop is removed

– Second element becomes top element

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Pop

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