The document discusses stacks as a last in, first out (LIFO) data structure, outlining their advantages, basic operations, and usage in applications like undo/redo features and string reversal. It includes implementation examples, coding explanations for push and pop functions, and applications of stacks in converting decimal to binary, as well as infix to postfix notation. Additionally, it touches on the Towers of Hanoi problem as a stack-based application.

1. Chapter 4
Stacks
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2. This is stacks
A data structure in
which the
elements are
added and
removed from the
top only; a Last In
First Out (LIFO)
data structure.

3. Why People use stacks?
Say you are writing a notepad application. A
good use for a stack would be the undo/redo
feature. Every time the user enters
something, save the state (in this case, the
text) on a stack and if you need to reverse
something, just pop it off the top of the undo
stack and push it onto the redo stack.
Stacks are also used for reversing things. If
you push something, say a String onto a Stack
one character at a time, and then construct a
String from the members popped off the
Stack, then the String is reversed.

4. Last In First Out
B
A
D
C
B
A
C
B
A
D
C
B
A
E
D
C
B
A
top
top
top
top
top
A

5. Stacks
Advantages
Advantages
Simplest one
Easy to
implement
Fast operation
Insertion/deletion
from one place
Disadvantages
Disadvantages
Only can be
inserted/removed
from the top
Problem when
accessing “the one
that on the top”
Recursive Function

6. BASIC OPERATION

7. BASIC
OPERATION
• InitializeStacks – initializes
the stack to an empty state
• DestroyStack – removes all
the elements from the
state
• IsEmptyStack – Check the
stack whether is empty or
not
• IsFullStack – Check
whether the stack is full or
not

8. Push and Pop
PUSH – You add
something at the
top
POP – You remove
something at the
top

9. Push Operation of Stacks

10. Pop Operation

11. Simple Example

12. Let us Implement Stacks
First, as usual we need to define some maximum stack
content to put our data

13. Let us Implement Stacks
Then, we use Class system called “stack”

14. Let us Implement Stacks
We declare a private inside “stack” class
- arr[MAX] : this is where we put all the data
- top : we assign our “leader” here.

15. Let us Implement Stacks
Then, we declare public
- First we put some constructor.
- Inside this constructor I’ve put a value top = -1 to
indicate that stack is empty for the first time.

16. Let us Implement Stacks
Now, push operation.
- We go through one by one here

17. Let us Implement Stacks
1st – This is where this operation get a value which is
integer type
So, inside main function, we will call using
“push(40)” for example
So, 40 is an integer

18. Let us Implement Stacks
Top++, we increment first because this is top
operation, so we updates the current position from -
1 to 0. (the computer always starts with “0” and not
“1”. So, top is 0 right now

19. Let us Implement Stacks
Then, we check whether top is still lower than MAX.
If the top still lower than MAX, we continue to insert
data at the position according to the top position
arr[0] = 40 (recall that top = 0).

20. Let us Implement Stacks
If it is not, we create a message to display “Stack
Full”.
Remember to set the top back to top– since we
already add top++ at first line of this function.

21. Example push(40)
4
2
12
32
54
5
top = 6
top++
- top = 6
(before this top is equal to 5, top = 5)

22. Example push(40)
4
2
12
32
54
5
top = 6
if(top<MAX)
{
arr[top]=a;
}
- Yes, top is still lower than
MAX which is 10.
- So, arr[6] = 40
(since we receive a = 40)

23. Example push(40)
212
21
23
40
4
2
12
32
54
5
top = 9
else
{
cout<<"STACK FULL!!"<<endl;
top--;
}
- But if top is equal to 10 (already full after top++),
then we put message STACK FULL, and set it back
to top--

24. Let us Implement Stacks
Now, pop operation. We use function type integer (not
void)
- We go through one by one here

25. Let us Implement Stacks
We check whether top is still -1(empty)
- We return NULL is we still do some pop() at the main
function

26. Let us Implement Stacks
If it is not
- We give any topmost data inside arr[top] to local
variable int data
- Then, we set the arr[top] = NULL since we actually
remove the data
- We set back the top to top--. Example if top = 5, then
top now is 4.
- We will return the int data

27. Example (pop)
5
64
4
2
12
32
54
5
top = 7
int data = arr[top]
- int data = arr[7]=5

28. Example (pop)
64
4
2
12
32
54
5
top = 7
arr[top]= NULL
- arr[7] = NOTHING
INSIDE

29. Example (pop)
64
4
2
12
32
54
5
top = 7
top--
- Top = 6

30. Example (pop)
64
4
2
12
32
54
5
top = 7
return data
- We return data = 5 to
any function that call
or want to know what
value that the push has
throw away.

31. FULL SOURCE CODE

32. #include <iostream>
using namespace std;
#define MAX 10 // MAXIMUM STACK CONTENT
class stack
{
private:
int arr[MAX]; // Contains all the Data
int top; //Contains location of Topmost Data pushed onto Stack
public:
stack() //Constructor
{
top=-1; //Sets the Top Location to -1 indicating an empty
stack
}

33. void push(int a) // Push ie. Add Value Function
{
top++; // increment to by 1
if(top<MAX)
{
arr[top]=a; //If Stack is Vacant store Value in Array
}
else
{
cout<<"STACK FULL!!"<<endl;
top--;
}
}

34. int pop() // Delete Item. Returns the deleted
item
{
if(top==-1)
{
cout<<"STACK IS EMPTY!!!"<<endl;
return NULL;
}
else
{
int data=arr[top]; //Set Topmost Value in data
arr[top]=NULL; //Set Original Location to NULL
top--; // Decrement top by 1
return data; // Return deleted item
}
}
};

35. int main()
{
stack a;
a.push(3);
cout<<"3 is Pushedn";
a.push(10);
cout<<"10 is Pushedn";
a.push(1);
cout<<"1 is Pushednn";
cout<<a.pop()<<" is Poppedn";
cout<<a.pop()<<" is Poppedn";
cout<<a.pop()<<" is Poppedn";
return 0;
}

36. APPLICATION

37. ALGORITHM CONVERTING
DECIMAL TO BINARY

38. How it works
• Let say you have a number: 148
Is 148 >= 128? Yes, so the 128 bit must be 1. 148 – 128 =
20, which means we need to find bits worth 20 more.
Is 20 >= 64? No, so the 64 bit must be 0.
Is 20 >= 32? No, so the 32 bit must be 0.
Is 20 >= 16? Yes, so the 16 bit must be 1. 20 – 16 = 4,
which means we need to find bits worth 4 more.

39. How it works
• Let say you have a number: 148
Is 4 >= 8? No, so the 8 bit must be 0.
Is 4 >= 4? Yes, so the 4 bit must be 1. 4 – 4 = 0, which
means all the rest of the bits must be 0.

40. How it works
• Let say you have a number: 148
148 = (1 * 128) + (0 * 64) + (0 * 32) + (1 * 16) + (0 * 8) +
(1 * 4) + (0 * 2) + (0 * 1) = 1001 0100

41. Coding
Enter the decimal number

42. Coding
While getnumber is still
bigger than “0”, we will
running this loop

43. Coding
This is to get the remaining
balance after division

44. Coding
Push the balance (which is
the balance of division)
into stack

45. Coding
Save in public array too

46. Coding
Update the counter

47. Coding
Get the result of division
using integer (not
double/floating number)

48. Coding
Display purpose

49. Source
• http://www.learncpp.com/cpp-tutorial/37-
converting-between-binary-and-decimal/

50. CONVERTING INFIX TO POSTFIX AND
PREFIX NOTATION

51. What is…
• Infix is
A*B
• Postfix is
AB*
• Prefix is
*AB

52. Infix to Postfix
• Let use an example
a+b*c-e

53. Infix to postfix Process
a+b*c-e
a
Postfix String
Our Stack
At first, “a” is found and
inserted into Postfix String

54. Infix to postfix Process
+
a+b*c-e
a
Postfix String
Our Stack
Then, we found “+”
So put it into Our Stack

55. Infix to postfix Process
+
a+b*c-e
ab
Postfix String
Our Stack
Next, we scanned another one
“b”. Put it into Postfix String

56. Infix to postfix Process
*
+
a+b*c-e
ab
Postfix String
Our Stack
Then, we found “ * ”. We put
into Our Stack

57. Infix to postfix Process
*
+
a+b*c-e
abc
Postfix String
Our Stack
We found “C”. So put into
Postfix String

58. Infix to postfix Process
-
+
a+b*c-e
abc*
Postfix String
Our Stack
Next character scanned is '-'. The topmost character in
the stack is '*' which has a higher precedence than '-'.
Thus '*' will be popped out from the stack and added to
the Postfix string.

59. Infix to postfix Process
-
a+b*c-e
abc*+
Postfix String
Our Stack
Even now the stack is not empty. Now the topmost
element of the stack is '+' which has equal priority to '-'.
So pop the '+' from the stack and add it to the Postfix
string. The '-' will be pushed to the stack.

60. Infix to postfix Process
-
a+b*c-e
abc*+e
Postfix String
Our Stack
We found “e”. So put into
Postfix String

61. Infix to postfix Process
a+b*c-e
abc*+e-
Postfix String
Our Stack
Nothing to scan. So, empty Our
Stack and put “ – ” into Postfix
String

62. But
• How to program???
• Let’s code

63. Our main components
• We must have a function to get a input
• Then, we need to have a function to read it in
character form
• And, we need a function to convert it into
postfix
• Of course last one is we want to display the
output

64. Our main components

65. Our Class items

66. Our Class items
We must have two array of stack
(i) One for the *, / , +, and –
(ii) Another one for alphabetic

67. Our Class items
We need to also have two
pointer based data type (char)

68. Our Class items
Set our initial value

69. Our Class items
Set our expression

70. Our Class items
Stack function (push and pop)

71. Our Class items
Convert function

72. Our Class items
Priority function (we will call
this inside convert function)

73. CONCLUSION OF IN/PRE/POST-FIX

74. Source
• http://scriptasylum.com/tutorials/infix_postfi
x/algorithms/infix-postfix/index.htm
• http://electrofriends.com/source-
codes/software-programs/cpp-programs/cpp-
data-structure/c-program-to-convert-an-
expression-from-infix-form-to-postfix-form/
• http://www.cs.man.ac.uk/~pjj/cs212/fix.html

75. A Legend
The Towers of Hanoi
• In the great temple of Brahma in Benares, on a brass plate
under the dome that marks the center of the world, there are
64 disks of pure gold that the priests carry one at a time
between these diamond needles according to Brahma's
immutable law: No disk may be placed on a smaller disk. In
the begging of the world all 64 disks formed the Tower of
Brahma on one needle. Now, however, the process of transfer
of the tower from one needle to another is in mid course.
When the last disk is finally in place, once again forming the
Tower of Brahma but on a different needle, then will come the
end of the world and all will turn to dust.

76. The Towers of Hanoi
A Stack-based Application
– GIVEN: three poles
– a set of discs on the first pole, discs of different sizes, the smallest
discs at the top
– GOAL: move all the discs from the left pole to the right one.
– CONDITIONS: only one disc may be moved at a time.
– A disc can be placed either on an empty pole or on top of a larger
disc.

77. Towers of Hanoi

78. Towers of Hanoi

79. Towers of Hanoi

80. Towers of Hanoi

81. Towers of Hanoi

82. Towers of Hanoi

83. Towers of Hanoi

84. Towers of Hanoi

85. ADDITION TWO INTEGER NUMBERS