Stacks

1
Stacks Templates

• CS 302 Data Structures
• Sections 5.1 6.1

2
What is a stack?

• It is an ordered group of homogeneous items.
• Items are added to and removed from the top of
  the stack
• LIFO property Last In, First Out
• The last item added would be the first to be
  removed

3
Stack Specification

• include "ItemType.h"
• // Must be provided by the user of the class
• // Contains definitions for MAX_ITEMS and
  ItemType
•  
• class StackType
• public
• StackType()
• void MakeEmpty()
• bool IsEmpty() const
• bool IsFull() const
• void Push(ItemType)
• void Pop(ItemType)
• private
• int top
• ItemType itemsMAX_ITEMS

4
Stack Implementation

• StackTypeStackType()
• top -1
• void StackTypeMakeEmpty()
• top -1

O(1)
O(1)
5
Stack Implementation (cont.)

• bool StackTypeIsEmpty() const
• return (top -1)
• bool StackTypeIsFull() const
• return (top MAX_ITEMS-1)
•  

O(1)
O(1)
6
Push (ItemType newItem)

• Function Adds newItem to the top of the stack.
• Preconditions Stack has been initialized and is
  not full.
• Postconditions newItem is at the top of the
  stack.

7
Stack Implementation (cont.)

•  
• void StackTypePush(ItemType newItem)
• top
• itemstop newItem
•  

O(1)
8
Pop (ItemType item)

• Function Removes topItem from stack and returns
  it in item.
• Preconditions Stack has been initialized and is
  not empty.
• Postconditions Top element has been removed from
  stack and item is a copy of the removed element.

9
Stack Implementation (cont.)

•  
• void StackTypePop(ItemType item)
• item itemstop
• top--

O(1)
10

• Stack overflow
• The condition resulting from trying to push an
  element onto a full stack.
• if(!stack.IsFull())
• stack.Push(item)
• Stack underflow
• The condition resulting from trying to pop an
  empty stack.
• if(!stack.IsEmpty())
• stack.Pop(item)

11
Tracing Client Code
letter
V
char letter V StackType charStack charStac
k.Push(letter) charStack.Push(C) charStack.P
ush(S) if ( !charStack.IsEmpty( ))
charStack.Pop(letter) charStack.Push(K) whil
e (!charStack.IsEmpty( )) charStack.Pop(letter)
Private data top
MAX_ITEMS-1 .
.
. 2
1 items 0
12
Tracing Client Code
letter
V
char letter V StackType charStack charStac
k.Push(letter) charStack.Push(C) charStack.P
ush(S) if ( !charStack.IsEmpty( ))
charStack.Pop( letter) charStack.Push(K) whi
le (!charStack.IsEmpty( )) charStack.Pop(letter)
Private data top -1
MAX_ITEMS-1 .
.
. 2
1 items 0
13
Tracing Client Code
V
letter
char letter V StackType charStack charStac
k.Push(letter) charStack.Push(C) charStack.P
ush(S) if ( !charStack.IsEmpty( ))
charStack.Pop( letter) charStack.Push(K) whi
le (!charStack.IsEmpty( )) charStack.Pop(letter
)
Private data top 0
MAX_ITEMS-1 .
.
. 2
1 items 0 V
14
Tracing Client Code
V
char letter V StackType charStack charStac
k.Push(letter) charStack.Push(C) charStack.P
ush(S) if ( !charStack.IsEmpty( ))
charStack.Pop(letter ) charStack.Push(K) whi
le (!charStack.IsEmpty( )) charStack.Pop(letter)
letter
Private data top 1
MAX_ITEMS-1 .
.
. 2
1 C items
0 V
15
Tracing Client Code
V
char letter V StackType charStack charStac
k.Push(letter) charStack.Push(C) charStack.P
ush(S) if ( !charStack.IsEmpty( ))
charStack.Pop( letter) charStack.Push(K) whi
le (!charStack.IsEmpty( )) charStack.Pop(letter)
letter
Private data top 2
MAX_ITEMS-1 .
.
. 2 S
1 C
items 0 V
16
Tracing Client Code
V
letter
char letter V StackType charStack charStac
k.Push(letter) charStack.Push(C) charStack.P
ush(S) if ( !charStack.IsEmpty( ))
charStack.Pop( letter) charStack.Push(K) whi
le (!charStack.IsEmpty( )) charStack.Pop(letter
)
Private data top 2
MAX_ITEMS-1 .
.
. 2 S
1 C
items 0 V
17
Tracing Client Code
S
char letter V StackType charStack charStac
k.Push(letter) charStack.Push(C) charStack.P
ush(S) if ( !charStack.IsEmpty( ))
charStack.Pop( letter) charStack.Push(K) whi
le (!charStack.IsEmpty( )) charStack.Pop(letter)
letter
Private data top 1
MAX_ITEMS-1 .
.
. 2 S
1 C
items 0 V
18
Tracing Client Code
S
char letter V StackType charStack charStac
k.Push(letter) charStack.Push(C) charStack.P
ush(S) if ( !charStack.IsEmpty( ))
charStack.Pop(letter ) charStack.Push(K) whi
le (!charStack.IsEmpty( )) charStack.Pop(letter)
letter
Private data top 2
MAX_ITEMS-1 .
.
. 2 K
1 C
items 0 V
19
Tracing Client Code
S
char letter V StackType charStack charStac
k.Push(letter) charStack.Push(C) charStack.P
ush(S) if ( !charStack.IsEmpty( ))
charStack.Pop( letter) charStack.Push(K) whi
le (!charStack.IsEmpty( )) charStack.Pop(letter
)
letter
Private data top 2
MAX_ITEMS-1 .
.
. 2 K
1 C
items 0 V
20
Tracing Client Code
K
char letter V StackType charStack charStac
k.Push(letter) charStack.Push(C) charStack.P
ush(S) if ( !charStack.IsEmpty( ))
charStack.Pop( letter) charStack.Push(K) whi
le (!charStack.IsEmpty( )) charStack.Pop(letter)
letter
Private data top 1
MAX_ITEMS-1 .
.
. 2 K
1 C
items 0 V
21
Tracing Client Code
K
char letter V StackType charStack charStac
k.Push(letter) charStack.Push(C) charStack.P
ush(S) if ( !charStack.IsEmpty( ))
charStack.Pop( ) charStack.Push(K) while
(!charStack.IsEmpty( )) charStack.Pop(letter)
letter
Private data top 1
MAX_ITEMS-1 .
.
. 2 K
1 C
items 0 V
22
Tracing Client Code
C
char letter V StackType charStack charStac
k.Push(letter) charStack.Push(C) charStack.P
ush(S) if ( !charStack.IsEmpty( ))
charStack.Pop( letter) charStack.Push(K) whi
le (!charStack.IsEmpty( )) charStack.Pop(letter)
letter
Private data top 0
MAX_ITEMS-1 .
.
. 2 K
1 C
items 0 V
23
Tracing Client Code
C
char letter V StackType charStack charStac
k.Push(letter) charStack.Push(C) charStack.P
ush(S) if ( !charStack.IsEmpty( ))
charStack.Pop( ) charStack.Push(K) while
(!charStack.IsEmpty( )) charStack.Pop(letter)
letter
Private data top 0
MAX_ITEMS-1 .
.
. 2 K
1 C
items 0 V
24
Tracing Client Code
V
char letter V StackType charStack charStac
k.Push(letter) charStack.Push(C) charStack.P
ush(S) if ( !charStack.IsEmpty( ))
charStack.Pop( letter) charStack.Push(K) whi
le (!charStack.IsEmpty( )) charStack.Pop(letter)
letter
Private data top -1
MAX_ITEMS-1 .
.
. 2 K
1 C
items 0 V
25
Tracing Client Code
V
char letter V StackType charStack charStac
k.Push(letter) charStack.Push(C) charStack.P
ush(S) if ( !charStack.IsEmpty( ))
charStack.Pop( ) charStack.Push(K) while
(!charStack.IsEmpty( )) charStack.Pop(letter)
letter
Private data top -1
MAX_ITEMS-1 .
.
. 2 K
1 C
items 0 V
26
Implementing stacks using templates

• Templates allow the compiler to generate multiple
  versions of a class type or a function by
  allowing parameterized types.
• Essentially, we can pass the data type as a
  parameter to a class !!

27
Implementing stacks using templates
(cont.)

• templateltclass ItemTypegt
• class StackType
• public
• StackType()
• void MakeEmpty()
• bool IsEmpty() const
• bool IsFull() const
• void Push(ItemType)
• void Pop(ItemType)
• private
• int top
• ItemType itemsMAX_ITEMS

28
Example using templates

• // Client code
• StackTypeltintgt myStack
• StackTypeltfloatgt yourStack
• StackTypeltStrTypegt anotherStack
• myStack.Push(35)
• yourStack.Push(584.39)
•  
• Passing a parameter to a template has an effect
  at compile time.
• The compiler generates distinct class types and
  gives its own internal name to each of the types.

29
Function templates

• The definitions of the member functions must be
  rewritten as function templates.
• templateltclass ItemTypegt
• StackTypeltItemTypegtStackType()
• top -1
• templateltclass ItemTypegt
• void StackTypeltItemTypegtMakeEmpty()
• top -1

30
Function templates (cont.)

•  templateltclass ItemTypegt
• bool StackTypeltItemTypegtIsEmpty() const
• return (top -1)
• templateltclass ItemTypegt
• bool StackTypeltItemTypegtIsFull() const
• return (top MAX_ITEMS-1)
•  
• templateltclass ItemTypegt
• void StackTypeltItemTypegtPush(ItemType newItem)
• top
• itemstop newItem

31
Function templates (cont.)

• templateltclass ItemTypegt
• void StackTypeltItemTypegtPop(ItemType item)
• item itemstop
• top--

32
Compiling templates

• We cannot compile StackType.cpp separately from
  the application (i.e., client code)!
• Compiler needs to know the data type of the stack
  to instantiate the class!
• But ... the data type is provided in the clients
  code!
• To address this problem, compile StackType.cpp
  and client code together!
• (1) Append StackType.cpp at the end of
  StackType.h
• or include StackType.cpp at the end of
  StackType.h
• (2) include StackType.h in clients code
• (3) Compile client code

33
Implementing stacks using dynamic array
allocation

• templateltclass ItemTypegt
• class StackType
• public
• StackType(int)
• StackType()
• void MakeEmpty()
• bool IsEmpty() const
• bool IsFull() const
• void Push(ItemType)
• void Pop(ItemType)

private int top int maxStack
ItemType items
34
Implementing stacks using dynamic array
allocation (cont.)

• templateltclass ItemTypegt
• StackTypeltItemTypegtStackType(int max)
• maxStack max
• top -1
• items new ItemTypemax
• templateltclass ItemTypegt
• StackTypeltItemTypegtStackType()
• delete items

35
Example using stacks evaluate postfix
expressions

• Postfix notation is another way of writing
  arithmetic expressions.
•  
• In postfix notation, the operator is written
  after the two operands.
•  
• infix 25 postfix 2 5
• Expressions are evaluated from left to right.
•  
• Precedence rules and parentheses are never
  needed!!

36
Example postfix expressions(cont.)
37
Postfix expressions Algorithm using stacks
(cont.)
38
Postfix expressionsAlgorithm using stacks

• WHILE more input items exist
• Get an item
• IF item is an operand
• stack.Push(item)
• ELSE
• stack.Pop(operand2)
• stack.Pop(operand1)
• Compute result
• stack.Push(result)
• stack.Pop(result)

39

• Exercise 15 (page 330) Write the body for a
  client function that replaces each copy of an
  item in a stack with another item. Use the
  following specification.
• ReplaceItem(StackType stack, ItemType oldItem,
  
  ItemType newItem)
• Function Replaces all occurrences of oldItem
  with newItem.
• Precondition stack has been initialized.
• Postconditions Each occurrence of oldItem in
  stack has been replaced by newItem. Order of
  other elements remains unchanged.
• (You may not assume any knowledge of how the
  stack is implemented).

40
Stack
tempStack

• ItemType item
• StackType tempStack
• while (!Stack.IsEmpty())
• Stack.Pop(item)
• if (itemoldItem)
• tempStack.Push(newItem)
• else
• tempStack.Push(item)
• while (!tempStack.IsEmpty())
• tempStack.Pop(item)
• Stack.Push(item)

Stack
oldItem 2 newItem 5