1. Chapter 4
Stacks

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 C B A D C B A E D C B A top D C B A top top top

5. Stacks Advantages Disadvantages Advantages Disadvantages Simplest one
Easy to implement
Fast operation
Insertion/deletion from one place
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) top++ top = 6 4 2 12 32 54 5 top = 6
(before this top is equal to 5, top = 5)

22. Example push(40) if(top<MAX) { arr[top]=a; }2 12 32 54 5
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)
top = 6

23. Example push(40) else { cout<<"STACK FULL!!"<<endl; top--;
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) int data = arr[top] - int data = arr[7]=5 5 64 4 2 12 3254
top = 7
int data = arr[top]
- int data = arr[7]=5

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

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

30. Example (pop) return data64 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
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 Pushed\n";
a.push(10);
cout<<"10 is Pushed\n";
a.push(1);
cout<<"1 is Pushed\n\n";
cout<<a.pop()<<" is Popped\n";
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 – 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 – 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) =

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

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

53. Infix to postfix Processa
Postfix String
At first, “a” is found and inserted into Postfix String
Our Stack

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

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

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

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

58. Infix to postfix Process- +
abc*
Postfix String
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.
Our Stack

59. Infix to postfix Process-
abc*+
Postfix String
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.
Our Stack

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

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

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

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