Chapter 7
– Stacks
Stacks
Infix Notation
Further Stack Examples
Summary Slides (4 slides)
Pushing/Popping a Stack
Class Stack (3 slides)
Using a Stack to Create a Hex #
Uncoupling Stack Elt’s (6 slides)
Activation Records
RPN
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
2
Stacks
A stack is a sequence of items that are
accessible at only one end of the sequence.
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Further Stack Examples
3
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
4
Pushing/Popping a Stack
Because a pop removes the item last added to
the stack, we say that a stack has LIFO (lastin/first-out) ordering.
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CLASS stack
Constructor
<stack>
Operations
<stack>
stack();
Create an empty stack
CLASS stack
bool empty(); const
Check whether the stack is empty. Return true if it is
empty and false otherwise.
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CLASS stack
Operations
void pop();
Remove the item from the top of the stack.
Precondition:
The stack is not empty.
Postcondition: Either the stack is empty or
the stack has a new topmost
item from a previous push.
void push(const T& item);
Insert the argument item at the top of the stack.
Postcondition: The stack has a new item at
the top.
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<stack>
CLASS stack
Operations
<stack>
int size() const;
Return the number of items on the stack.
T& top() const;
Return a reference to the value of the item at the
top of the stack.
Precondition: The stack is not empty.
const T& top() const;
Constant version of top().
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Using a Stack to Create a Hex
Number
'1'
'F'
431 % 16 = 15
431 / 16 = 26
'1'
'A'
'A'
'A'
'F'
'F'
'F'
26 % 16 = 10
26 / 16 = 1
1 % 16 = 1
1 / 16 = 0
'F'
Pop '1'
numStr = "1"
Push Digit Characters
8
'A'
Pop 'A'
Pop 'F'
numStr = "1A" numStr = "1AF"
Pop Digit Characters
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'F'
Uncoupling Stack Elements
A
9
9
B
Train Before Uncoupling E
E
C
D
Main
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Contents
Uncoupling Stack Elements
A
Uncouple E. Move to side track
B
C
D
E
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Uncoupling Stack Elements
Uncouple D. Move to side track
A
B
C
D
E
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Uncoupling Stack Elements
Uncouple C Move aside
A
B
C
D
E
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Uncoupling Stack Elements
Attach D to end of train
A
B
D
C
E
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Uncoupling Stack Elements
A
14
Attach E to end of train
B
D
E
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C
Arguments
int n
Return Address
RetLoc or RetLoc2
Activation Record
System Stack
In main():
call fact(4)
In fact(4):
call fact(3)
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Argument
4
Return
RetLoc1
Argument
3
Return
RetLoc2
Argument
4
Return
RetLoc1
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RPN (Reverse Polish Notation) expression 2 3 +
Scan of Expression and Action Current operandStack
1. Identify 2 as an operand.
Push integer 2 on the stack.
2
2. Identify 3 as an operand.
Push integer 3 on the stack.
3
3. Identify + as an operator
Begin the process of evaluating +.
3
2
2
4. getOperands() pops stack
twice and assigns 3 to
right and 2 to left.
operandStack empty
5. compute() evaluates left + right
and returns the value 5. Return
value is pushed on the stack.
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5
Infix Expression Rules
The figure below gives input precedence, stack precedence, and
rank used for the operators +, -, *, /, %, and ^, along with the
parentheses. Except for the exponential operator ^, the other
binary operators are left-associative and have equal input and
stack precedence.
Precedence
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Symbol
Input
precedence
+ * / %
^
(
)
1
2
4
5
0
Stack
precedence
1
2
3
-1
0
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Rank
-1
-1
-1
0
0
Summary Slide 1
§- Stack
- Storage Structure with insert (push) and erase (pop)
operations occur at one end, called the top of the
stack.
- The last element in is the first element out of the
stack, so a stack is a LIFO structure.
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Summary Slide 2
§- Recursion
- The system maintains a stack of activation records
that specify:
1) the function arguments
2) the local variables/objects
3) the return address
- The system pushes an activation record when
calling a function and pops it when returning.
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Summary Slide 3
§- Postfix/RPN Expression Notation
- places the operator after its operands
- easy to evaluate using a single stack to hold
operands.
- The rules:
1) Immediately push an operand onto the stack.
2) For a binary operator, pop the stack twice, perform the
operation, and push the result onto the stack.
3)
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At the end a single value remains on the stack. This is
the value of the expression.
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Summary Slide 4
§- Infix notation
- A binary operator appears between its operands.
- More complex than postfix, because it requires the
use of operator precedence and parentheses.
- In addition, some operators are left-associative, and
a few are right-associative.
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