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Michelle B. Alambra
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What is a stack?Stack RepresentationStack OperationsExample of a Stack
What is a Stack?
A stack is an ordered list where all operations are restricted at one end of the list known as the top.
Imagine the cafeteria tray holder. The type of behavior in list processing is called LIFO or Last-In-First-out.
A pile of Tray
Stack Representation
There are two ways to represent a stack As a one-dimensional array
when using a one-dimensional array to portray a stack, insertion, deletion, and retrieval is done from the last element in the array. This form of representation is used when the maximum size of the stack is known.
As one –dimensional Array
Arr[n]
Arr[n-1]
…
…
…
Arr[3]
Arr[2]
Arr[1]
Top
Bottom
Stack Representation
As a doubly-linked listwhen using a doubly-linked list
to portray a stack, insertion, deletion, and retrieval is done from the tail. This form of representation is used when the maximum size of the stack is unknown. TopBottom
Node1
Node2
Node3
Node n
……
Head Tail
Stack Operations
There are basically three (3) operations associated with stacks.
PushInserts a new element at the top of the
stack. Pop
Retrieves the element at the top of the stack and deletes it from the stack.
TopMostRetrieves the element at the top of the
stack
Pushing an Element into a StackPush (Arr, N, Top, Value)
{ If (Top = N) then { Print (“Error: Stack is Full!”) Exit } Increment Top Set Arr[Top] to Value // insert new
element}
Push ( , , , ){ If (Top = N) then { Print (“Error: Stack is Full!”) Exit } Increment Top Set Arr[Top] to Value // insert new
element}
Name of a one Dimensional array representing the stack
The size of an Array
Position of the topmost element in the stack
The value to be inserted into the stack
Arr N Top
Value
Pushing an Element into a Stack
Let us simulate the algorithm by using the following stack.
Arr [10]
Arr [9]
Arr [8]
Arr [7]
Arr [6]
Arr [5]
Arr [4]
Arr [3]
Banana Top
Arr [2]
Orange
Arr [1]
Apple Bottom
Pushing an Element into a StackTo “push” an element into the stack,
we will pass the following parameters to the algorithm:
(Arr, 10, 3, “Mango”)Arr [10]
Arr [9]
Arr [8]
Arr [7]
Arr [6]
Arr [5]
Arr [4]
Arr [3]
Banana
Arr [2]
Orange
Arr [1]
Apple
Mango
Top
Bottom
Increment Top
Set Arr[Top] to Value
Pushing an Element into a Stack (Arr, 10, 4, “Pomelo”)
Arr [10]
Arr [9]
Arr [8]
Arr [7]
Arr [6]
Arr [5]
Arr [4]
Mango
Arr [3]
Banana
Arr [2]
Orange
Arr [1]
Apple
Pomelo
Top
Bottom
Increment Top
Set Arr[Top] to Value
Pushing an Element into a Stack (Arr, 10, 5, “Melon”)
Arr [10]
Arr [9]
Arr [8]
Arr [7]
Arr [6]
Arr [5]
Pomelo
Arr [4]
Mango
Arr [3]
Banana
Arr [2]
Orange
Arr [1]
Apple
Melon
Top
Bottom
Increment Top
Set Arr[Top] to Value
Poping an Element from a StackPop (Arr1, N, Top){ If (Top = 0) then { Print (“Error: Stack is Empty!”) Exit }Print Arr1[Top]Decrement Top}
Pop ( , , ){ If (Top = 0) then { Print (“Error: Stack is Empty!”) Exit }Print Arr1[Top]Decrement Top}
Arr1 N Top
Name of a one Dimensional array representing the stack
The size of an Array
Position of the topmost element in the stack
Poping an element from a stack
Let us use the following stack
Arr1 [10]
Arr 1[9]
Arr 1[8]
Arr 1[7]
Arr 1[6]
Strawberry Top
Arr 1[5]
Pomelo
Arr 1[4]
Mango
Arr 1[3]
Banana
Arr 1[2]
Orange
Arr 1[1]
Apple Bottom
To “pop” an element into the stack, we should have the following parameters:
(Arr1, 10, 7)Arr 1[10]
Arr 1[9]
Arr 1[8]
Arr 1[7]
Arr 1[6]
Melon
Arr 1[5]
Pomelo
Arr 1[4]
Mango
Arr 1[3]
Banana
Arr 1[2]
Orange
Arr 1[1]
Apple
Top
Bottom
Print Arr1[Top] “Strawberry”
StrawberryDecrement Top Top = 6
Poping an element from a stack
Poping an element from a stack (Arr1, 10, 6)
Arr1 [10]
Arr 1[9]
Arr 1[8]
Arr 1[7]
Arr 1[6]
Arr 1[5]
Pomelo
Arr 1[4]
Mango
Arr 1[3]
Banana
Arr 1[2]
Orange
Arr 1[1]
Apple
Top
Bottom
Melon
Print Arr1[Top] “Melon”
Decrement Top Top = 5
Poping an element from a stack (Arr1, 10, 6)
Arr 1[10]
Arr 1[9]
Arr 1[8]
Arr 1[7]
Arr 1[6]
Arr 1[5]
Arr 1[4]
Mango
Arr 1[3]
Banana
Arr 1[2]
Orange
Arr 1[1]
Apple
Top
Bottom
Pomelo
Print Arr1[Top] “Pomelo”
Decrement Top Top = 4
Retrieving an element from a stack
TopMost (Arr1, Top){ Print Arr1[Top]}
Function Calls One natural example of stacks which
arises in computer programming is the processing of function calls and their returns.
Suppose we have the following procedure which indirectly combines two (2) functions:
Function Calls
PROC1 calls FUNC1, and FUNC1 calls FUNC2.
When FUNC2 has completed, processing will continue at statement b in FUNC1.
When FUNC1 has completed, processing will resume at statement a in PROC1.
Generally, the variables used in a program are assigned by the compiler to machine registers.
When another function called the variables used by this new function are also assigned to the same machine registers, thereby erasing all previous content.
Once the new function has completed, the invoking procedure would have lost all relevant procedure prior to the call.
Function Calls
When PROC1 begins executing, the stack will contain the following information:
Top and BottomOperating System
It relinquishes control to the operating system. As with function calls, there must
be a way for PROC1 to know “where to go” when it is done. This is why the bottom of
the stack always contains information about the operating system.
Function Calls
When FUNC1 is invoke by PROC1 , the stack contains the following:
Bottom
a:
Contents of Machine Registers
Operating System
Top
When FUNC1 was called, the system
pushed the return address, a, and the contents of the machine registers into
the stack.
Function Calls
When FUNC1 will reference FUNC2, the stack will contain the following information:
Bottom
b:
Contents of Machine Registers
a:
Contents of Machine Registers
Operating System
Top
After the FUNC2 has completed, the system will determine where processing
should continue by POPing the information from the stack. Since the top
of the stack contains, b, processing will
continue with statement b in FUNC1.
Function Calls
BottomOperating System
Top
The system will return the values of all variables by once again POPing the
stack.
b:
Contents of Machine Registers
a:
Contents of Machine Registers
Function Calls
BottomOperating System
Topa:
Contents of Machine Registers
Once PROC1 has completed, the stack is POPed once more and control will
return to the operating system.
Function Calls
Top and BottomOperating System
THANK YOU
