Chapter 6: Stacks

STACK APPLICATIONS

STACK IMPLEMENTATIONS

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The stack abstract data type is essentially a list using the LIFO (last-in-first-out) policy for adding and removing elements.The principal stack operations: Create an empty stack.

Copy an existing stack. Destroy a stack.Determine whether a

stack is empty. Add a new element to a stack.Remove the most recently

added element from a stack.Retrieve the most recently added element from a stack.

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When running a program that uses functions, a stack is used to keep track of the function calls, including the status of the variables in each function.

Stack Application:Run-Time Stack

void swap(int &u, int &v){ int temp = u; u = v; v = temp;}

void reorder(int &a, int &b, int &c){ if ((b <= a) && (b <= c)) swap(a,b); else if ((c <= a) && (c <= b)) swap(a,c); if (c <= b) swap(b,c);}

a: 20

b: 30

c: 10

void main(){ int x = 20; int y = 30; int z = 10; if ((x > y) || (y > z)) reorder(x,y,z); cout << x << y << z;}

u: 20

v: 10

temp:20

x: 20

y: 30

z: 10

u: 10

v: 20

a: 10

c: 20

x: 10

z: 20

void swap(int &u, int &v){ int temp = u; u = v; v = temp;}

u: 30

v: 20

temp:30

u: 20

v: 30

b: 20

y: 20

c: 30

z: 30

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Stack Application:Infix-to-Postfix Conversion

Following these rules, then, the infix expression 7 + 6 - 3 * ( 5 + 8 / 2 ) is converted into the postfix expression 7 6 + 3 5 8 2 / + * -

When this is found in the

infix expression...

… do this!

Beginning of infix expression

Push a # onto the stack

Operand Append it to the postfix expression

Right parenthesisRepeatedly pop the stack, appending each entry to the postfix expression,

until a left parenthesis is popped (but not output)

End of infix expression

Repeatedly pop the stack, appending each entry to the postfix expression

Left parenthesis Push it onto the stack

* or / operatorRepeatedly pop the stack, appending all popped * and / operators to the end of the postfix expression, until something else is popped; push this last item

back onto the stack, followed by the new * or / that was encountered

+ or - operator

Repeatedly pop the stack, appending all popped +, -, *, and / operators to the end of the postfix expression, until something else is popped; push this

last item back onto the stack, followed by the new + or - that was encountered

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Stack Application:Postfix Expression Evaluation

Following these rules, then, with the postfix expression 7 6 + 3 5 8 2 / + * - yields:

Following these rules, then, with the postfix expression 7 6 + 3 5 8 2 / + * - yields:

7 7

6

13 13

3

13

3

5

13

3

5

8

13

3

5

8

2

13

3

5

4

13

3

9

13

27

-14

When this is encountered in the postfix expression... … do this!

Operand Push it onto the stack

OperatorPop the stack twice, perform the operation on the two

popped operands, and push the result back onto the stack

End of postfix expression Pop the stack once; the popped value is the final result

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Stack Application:Graphical TransformationsWhen graphically manipulating 2D and 3D objects, it’s often convenient to use a stack to manipulate them at the origin and then translate them to their appropriate locations.

translate

rotate

scale

translate

rotate

scale

translate

translate

rotate

translate

By carefully applying the transformations in the correct order (via the stack), the image is altered in the desired fashion.

translate

scale

rotate

translate

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Stack Implementation Alternatives

An Array ImplementationPositives

Avoids pointers (uses top index)

Trivial implementationNegatives

×Size must be declared in advance A Linked List Implementation

PositivesDynamically allocates

exactly the right amount of memory

Straightforward (if not quite trivial) implementation

Negatives

×Those wonderful pointers

a

b

a

b

c

a

b

b a

c b a

b a

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Linked List Implementation of Stack

// Class declaration file: stack.h// Linked List implementation of the// stack ADT – inherits from LinkedList.

#ifndef STACK_H#include "LinkedList.h"

class stack : protected LinkedList { public: // Class constructors stack(); stack(const stack &s);

// Member functions bool isEmpty(); void push(const elementType &item); elementType pop(); elementType retrieve(); };#define STACK_H#endif

The stack class “inherits” from the LinkedList class, so all LinkedList members are accessible to any

stack.

This derived class has a “protected” access specifier, indicating that the public and protected members of

LinkedList are considered protected in the stack class.

If the access specifier were “private”, then the public and protected

members of LinkedList are considered private in the derived class.

If the access specifier were “public”, then the public and protected

members of LinkedList are considered public and protected (respectively) in

the derived class.Let’s assume that the getNode and head

members in LinkedList were declared protected, not private!

Let’s also assume that the elementType typedef occurred in the LinkedList definition!

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// Class implementation file: stack.cpp// Linked List implementation of the// stack ADT – inherits from LinkedList.

#include "Stack.h"#include "LinkedList.h"#include <assert.h>// Default constructor: //// Inherited from LinkedList. //stack:: stack(): LinkedList(){}

// Copy constructor: //// Inherited from LinkedList. //stack:: stack(const stack &s): LinkedList(s){}

// Empty function: returns a boolean //// value that indicates whether or //// not the stack is empty. //bool stack:: isEmpty(){ return head == NULL;}

// Push function: inserts item at //// the top of the stack. //void stack:: push(const elementType &elt){ nodePtr newHead = getNode(elt); assert(newHead != NULL); newHead->next = head; head = newHead; return;}

// Pop function: removes and returns the //// top stack entry (if there is one). //elementType stack:: pop(){ elementType elt; nodePtr oldHead; assert(head != NULL); oldHead = head; elt = head->item; head = head->next; delete oldHead; return elt;}

// On_top function: returns (w/o removing) //// the top stack entry (if there is one). //elementType stack:: retrieve(){ elementType elt; assert(head != NULL); elt = head->item; return elt;}