chapter 7 stacks dr. youssef harrath yharrath@uob.edu.bh
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Chapter 7
Stacks
Dr. Youssef Harrath
yharrath@uob.edu.bh
Outline
1. Introduction
2. Implementation of Stacks as Arrays
3. Example: Highest GPA
4. Linked Implementation of Stacks
5. Stack as Derived from the class linkedListType
6. Application of Stacks:
A. Postfix Expression Calculator
B. Print a Linked List Backwards
2Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
1. Introduction
3Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
Stack of coins
Stack of books
1. Introduction
4Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
A stack is a list of homogenous elements, wherein the addition
and deletion of elements occurs only at one end (top of the stack).
The bottom element of the stack is the earliest added one.
The top element is the last added item.
The last added item will be the first one to be deleted.
A stack is called a LIFO data structure.
1. Introduction: Stack operations
5Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
A
push box A
AB
push box B
AB
C
push box C
AB
C
Retrieve the top element
AB
pop stack
1. Introduction: Stack operations
6Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
The basic operations on a stack are:
initializeStack: intializes the stack to an empty state.
destroyStack: Removes all the elements from the stack,
leaving the stack empty.
isEmptyStack: Checks whether the stack is empty.
isFullStack: Checks whether the stack is full.
push: Adds a new element to the top of the stack.
top: returns the top of the stack.
pop: Removes the top of the stack.
2. Implementation of Stacks as Arrays
7Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
template<class Type>class stackType{public:
const stackType<Type>& operator=(const stackType<Type>&);void initializeStack();bool isEmptyStack();bool isFullStack();void destroyStack();void push(const Type& newItem);Type top();void pop();stackType(int stackSize = 100);stackType(const stackType<Type>& otherStack);~stackType();
private:int maxStackSize;int stackTop; // variable to point to the top of the stackType *list;void copyStack(const stackType<Type>& otherStack);
};
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2. Implementation of Stacks as Arrays
8Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
A
B
C
D
.
.
.
100
4
maxStackSize
stackTop
list
stack
2. Implementation of Stacks as Arrays
9Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
template<class Type>
void
stackType<Type>::initializeStack()
{
stackTop = 0;
}template<class Type>
void stackType<Type>::destroyStack()
{
stackTop = 0;
}
2. Implementation of Stacks as Arrays
10Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
template<class Type>
bool stackType<Type>::isFullStack()
{
return(stackTop == maxStackSize);
}
template<class Type>
bool stackType<Type>::isEmptyStack()
{
return(stackTop == 0);
}
2. Implementation of Stacks as Arrays: push
11Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
Store newItem in the array component indicated by stackTop.
Increment stackTop.
S
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100
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maxStackSize
stackTop
list
stack
u
n
n
S
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100
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maxStackSize
stackTop
list
stack
u
n
n
y
push(‘y’)
2. Implementation of Stacks as Arrays: push
12Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
template<class Type>
void stackType<Type>::push(const Type& newItem)
{
if(!isFullStack())
{
list[stackTop] = newItem;
stackTop++;
}
else
cout<<"Cannot add to a full stack."<<endl;
}
2. Implementation of Stacks as Arrays: top
13Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
template<class Type>
Type stackType<Type>::top()
{
assert(stackTop != 0);
return list[stackTop - 1];
}
2. Implementation of Stacks as Arrays: pop
14Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
B
.
.
.
[99]
[3]
[2]
[1]
[0]
100
4
maxStackSize
stackTop
list
stack
o
l
d
B
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[99]
[3]
[2]
[1]
[0]
100
3
maxStackSize
stackTop
list
stack
o
l
d
pop()
2. Implementation of Stacks as Arrays: pop
15Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
template<class Type>
void stackType<Type>::pop()
{
if(!isEmptyStack())
stackTop--;
else
cout<<"Cannot remove from an empty stack."<<endl;
}
2. Implementation of Stacks as Arrays: copyStack
16Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
template<class Type>
void stackType<Type>::copyStack(const stackType<Type>& otherStack)
{
delete [] list;
maxStackSize = otherStack.maxStackSize;
stackTop = otherStack.stackTop;
list = new Type[maxStackSize];
assert(list != NULL);
for(int j = 0; j < stackTop; j++)
list[j] = otherStack.list[j];
}
2. Implementation of Stacks as Arrays: constructor
17Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
template<class Type>stackType<Type>::stackType(int stackSize)
{if(stackSize <= 0){
cout<<"The size must be positive!"<<endl;maxStackSize = 100;
}else
maxStackSize = stackSize;stackTop = 0;list = new Type[maxStackSize];assert(list != NULL);
}
2. Implementation of Stacks as Arrays: destructor & copy constructor
18Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
template<class Type>
stackType<Type>::~stackType()
{
delete [] list;
}
template<class Type>stackType<Type>::stackType(const stackType<Type>& otherStack)
{
list = NULL;
copyStack(otherStack);
}
2. Implementation of Stacks as Arrays: overloading(=)
19Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
template<class Type>
const stackType<Type>& stackType<Type>::operator=
(const stackType<Type>&
otherStack)
{
if(this != &otherStack)
copyStack(otherStack);
return *this;
}
3. Example: Highest GPA
20Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
Write a C++ program that reads a data file consisting of
each student’s GPA followed by the student’s name. The
program then prints the highest GPA and the names of
all the students who received that GPA. The program
scans the input file only once.3.9 Marwa3.1 Ali3.9 Ahmad2.1 Salma3.9 Zahra1.8 Salah
3. Example: Highest GPA: Algorithm
21Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
• Read the 1st GPA, the name of the 1st student, and assign the 1st
GPA to the highestGPA.
• Read the 2nd GPA, the name of the 2nd student. We compare the
second GPA with the highestGPA:
1. The new GPA > highestGPA
a. Update the value of the highestGPA
b. Destroy the stack
c. Insert the name of the new student into the stack.
2. The new GPA = highestGPA: add the name to the stack
3. The new GPA < highestGPA: we do nothing
• Read the next GPA and student name and repeat the steps 1, 2,
and 3 until we rich the end of the file.
3. Example: Highest GPA: Algorithm
22Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
1. Declare the variables
2. Open the input file (treat the exception case)
3. Read the GPA and the student name
4. highestGPA = GPA
5. Initialize the stack
6. while(not end of file)
1. if(GPA > highestGPA)
1. destroyStack(stack)
2. push(stack, student name)
3. highestGPA = GPA
2. else if (GPA = highestGPA)
3. Read the GPA and student name
7. Output the highest GPA
8. Output the names of the students having the highest GPA
3. Example: Highest GPA: Algorithm
23Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
Program
4. Linked Implementation of Stacks: PartI
24Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
template<class Type>struct nodeType {Type info;nodeType<Type> link;}template<class Type>class linkedStackType {public:const linkedStackType <Type>& operator=(const linkedStackType <Type>&);void initializeStack();bool isEmptyStack();bool isFullStack();void destroyStack();void push(const Type& newItem);Type top();…
4. Linked Implementation of Stacks: Part II
25Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
…
void pop();
linkedStackType();
linkedStackType(const linkedStackType <Type>& otherStack);
~ linkedStackType ();
private:
nodeType <Type> *stackTop;
void copyStack(const stackType<Type>& otherStack);
};
4. Linked Implementation of Stacks
26Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
stackTop
stack
Empty linked stack
stackTop
stack
Nonempty linked stack
C
B
A
4. Linked Implementation of Stacks: default constructor
27Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
template<class Type>
linkedStackType<Type>::linkedStackType()
{
stackTop = NULL;
}
4. Linked Implementation of Stacks: destroyStack
28Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
template<class Type>
void linkedStackType<Type>::destroyStack()
{
nodeType<Type> *temp;
while(stackTop != NULL)
{
temp = stackTop;
stackTop = stackTop->link;
delete temp;
}
}
4. Linked Implementation of Stacks: initializeStack
29Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
template<class Type>
void linkedStackType<Type>::initializeStack()
{
destroyStack();
}
4. Linked Implementation of Stacks: isEmptyStack & isFullStack
30Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
template<class Type>
bool linkedStackType<Type>::isEmptyStack()
{
return (stackTop == NULL);
}
template<class Type>
bool linkedStackType<Type>::isFullStack()
{
return false;
}
4. Linked Implementation of Stacks: push
31Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
stackTop
stack
C
B
A
push(D)
stackTop
stack
C
B
A
DnewNode
4. Linked Implementation of Stacks: push
32Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
template<class Type>
void linkedStackType<Type>::push(const Type& newElement)
{
nodeType<Type> *newNode;
newNode = new nodeType<Type>;
assert(newNode != NULL);
newNode->info = newElement;
newNode->link = stackTop;
stackTop = newNode;
}
4. Linked Implementation of Stacks: top
33Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
template<class Type>
Type linkedStackType<Type>::top()
{
assert(newNode != NULL);
return stackTop->info;
}
4. Linked Implementation of Stacks: pop
34Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
stackTop
stack
C
B
A
pop()
stackTop
stack C
B
A
temp
4. Linked Implementation of Stacks: pop
35Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
template<class Type>
void linkedStackType<Type>::pop()
{
nodeType<Type> *temp;
if(stackTop != NULL)
{
temp = stackTop;
stackTop = stackTop->link;
delete temp;
}
else
cout<<“cannot delete from an empty stack!”<<endl;
}
5. Stack as Derived from the class linkedListType
36Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
push insertFirst
initializeStack
isEmptyStack
initializeList
isEmptyList
The class linkedStackType can be derived from the class linkedListType
5. Stack as Derived from the class linkedListType
37Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
Program
• The operator is after/before the operands
• Left to right evaluation
• No precedence
• No need for ()
6. Application of Stacks: Postfix Expression Calculator
38Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
Infix notation
a + b a b + + a b
Postfix notation Prefix notation
• The operator is between
the operands
• Left to right evaluation
• Precedence
• ()
Lukasiewicz (Poland, 1950)
6. Application of Stacks: Postfix Expression Calculator
39Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
Infix Expression
a + b
a + b * c
a * b + c
(a + b) * c
(a - b) * (c + d)
(a + b) * (c - d / e) + f
a b – c d + *
Equivalent Postfix Expression
a b +
a b c * +
a b * c +
a b + c *
a b + c d e / - * f +
6. Application of Stacks: Postfix Expression Calculator
40Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
Infix
(6 + 3) * 2 =
Postfix
6 3 + 2 * =
6
push(6)
6
pop()
9
push(9)
18
push(18)
3
6
push(3)
9
2
push(2)pop() pop()
9
pop()
6. Application of Stacks: Postfix Expression Calculator
41Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
Program will be given as a lab assignment
6. Application of Stacks: Print a Linked List Backwards
42Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
10 155 20first
stackTopstack
10
15
5
20
6. Application of Stacks: Print a Linked List Backwards
43Dr. Youssef Harrath – University of Bahrain – ITCS 215 – 2010/2011
current = first;
while(current != NULL)
{
stack.push(current);
current = current->link;
}
Step 1: save the addresses of the nodes in a stack.
while(!stack.isEmpty())
{
current = stack.top();
stack.pop();
cout<<current->info<<“ “;
}
Step 2: print the linked list in reverse order.
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