Introduction to stack, its Operations and Applications.

1. DATA STRUCTURE
A data structure is a particular way of organizing data in
a computer so that it can be used effectively.

2. STACK
Stack is a linear data structure which follows a particular order
in which the operations are performed.
It follows the LIFO principle which stands for Last In First Out.
Here, the element which is placed (inserted or added) last, is
accessed first.
It has only one pointer TOP that points the last or top most
element of Stack.
Insertion and Deletion in stack can only be done from top only.

3. EXAMPLES OF STACK

4. OPERATIONS OF STACK
Push() − Pushing (storing) an element on the stack.
Pop() − Removing (accessing) an element from the stack.
We also need to check the status of the stack
to use it efficiently :
Overflow( ) – To check if stack is full.
Underflow( ) – To check if stack is empty.

5. ALGORITHM OF PUSH OPERATION
 Step 1 − Start
 Step 2 – Checks if the stack is full.
 Step 3 − If the stack is full, displays “Overflow”.
 Step 4 − If the stack is not full, increments TOP to point to
next empty space.
 Step 5 − Adds data element to the stack location, where top is
pointing.
 Step 6 − End

6. IMPLEMENTATION OF PUSH
10 10
30
10
30
20
10
30
20
15
10
30
20
15
40
0
1
2
3
4 4
3
2
1
0
4
3
2
1
0
4
3
2
1
0 0
1
2
33
4 4
2
1
0
top = -
1
top =
0
top =
1
top =
2
top =
3
top =
4

7. CODE FOR PUSH OPERATION
void push(int data)
{
if (top == arr.length - 1)
System.out.println("Stack is Full");
else
{
arr[++top] = data;
System.out.println("Pushed data :" + arr[top]);
}
}

8. ALGORITHM OF POP OPERATION
 Step 1 − Start
 Step 2 − Checks if the stack is empty.
 Step 3 − If the stack is empty, displays “Underflow”.
 Step 4 − If the stack is not empty, access the data element at
which TOP is pointing.
 Step 5 − Decrease the value of top by 1.
 Step 6 − End.

9. IMPLEMENTATION OF POP
10
30
20
15
40
3
4
2
1
0
top =
4
10
30
20
15
0
1
2
3
4
top =
3
10
30
20
4
3
2
1
0
top =
2
10
30
4
3
2
1
0
top =
1
10
4
3
2
1
0
top =
0
0
1
2
3
4
top = -
1

10. CODE FOR POP OPERATION
int pop()
{
if (top < 0)
{
System.out.println("Stack Underflow");
return 0;
}
else
{
System.out.println("Popped data : " + arr[top]);
return arr[top--];
}
}

11. APPLICATIONS OF STACK
Conversion of expressions.
Function calling and return procedure.
Recursion handling.
Decimal to Binary conversion.

12. TYPES OF ARITHMETIC EXPRESSIONS
Infix Expression : Operator is placed between the operands.
Example : A+B
Prefix Expression : Operator is placed before the operands.
Example : +AB
Postfix Expression : Operator is placed after the operands.
Example : AB+

13. CONVERSION FROM INFIX TO POSTFIX
1. A + (B * C) – (D / E)
= A + B C * - D E /
= A B C * + - D E /
= A B C * + D E / -

14. 2. (A / B + C) * (D / (E - F))
= (A B / + C ) * (D / E F –)
= (A B / C +) * D E F – /
= A B / C + D E F – / *
3. (M – N )/ (P* ( S – T) + K)
= (M N – ) / (P* (S T – ) + K)
= ( M N –) / ((P S T – *) + K)
= ( M N –) / (P S T – * K +)
= M N – P S T – * K + /

15. CONVERSION FROM INFIX TO PREFIX
1. A + (B * C) – (D / E)
= A + * B C - / D E
= + A * B C - / D E
= - + A * B C / D E

16. 2. (A / B + C) * (D / (E - F))
= (/ A B + C) * (D / - E F)
= (+ / A B C) * ( / D – E F)
= * + / A B C / D – E F
3. (M – N )/ (P* ( S – T) + K)
= ( - M N ) / (P * ( - S T ) + K)
= (- M N ) / ( (* P – S T) + K)
= (- M N ) / (+ * P – S T K)
= / - M N + * P – S T K