The document discusses stacks and their implementation and applications. It defines a stack as a list of elements where elements can only be inserted or removed from one end, called the top. Stacks can be implemented using arrays, with a pointer tracking the top element. The key operations on a stack are push to add an element, pop to remove an element, and peek to access the top element. The document provides algorithms for these operations and discusses applications of stacks like recursion, infix to postfix conversion, and postfix to infix conversion. It includes an example of converting an infix expression to postfix using a stack.

1. Stack
By
Nilesh Dalvi
Lecturer, Patkar-Varde College.Lecturer, Patkar-Varde College.
http://www.slideshare.net/nileshdalvi01
Java and DataJava and Data
StructuresStructures

2. Stack
• A Stack is a list of elements in which an element may
be inserted or deleted at one end which is known as
TOP of the stack.
• Operation Performed On Array:
1. Push: add an element in stack
2. Pop: remove an element in stack
3. Peek :Current processed element
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).
a
b
c TOP

3. Array representation of stacks:
• We can represent a stack in computer in various ways, by
means of one-way-list or linear array.
• Consider Linear array stack:
• TOP : Location of the top element of the stack
• MAXSTK : max elements that can be held by stack
• If TOP = 0 or TOP = NULL indicates that stack is empty.
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).
XX YY ZZ
1 2 3 4 5 6 7 8
TOP MAXSTK

4. Adding element: PUSH()
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).
Algorithm PUSH (STACK, ITEM)
{
if (TOP = MAXSTK) then
write ("Overflow");
else
TOP := TOP + 1;
STACK [TOP] := ITEM;
}

5. Deleting element: POP()
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).
Algorithm POP (STACK, ITEM)
{
if (TOP = 0) then
write ("Underflow");
else
ITEM = STACK [TOP];
TOP := TOP - 1;
}

6. Accessing element: PEEK()
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).
Algorithm PEEK (STACK)
{
if (TOP = 0) then
write ("Underflow");
else
Return STACK [TOP];
}

7. Implementation of Stack operations
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

8. Applications of Stack:
• Recursion
• Infix to postfix conversion
• Postfix to infix conversion
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

9. infixVect
postfixVect
( a + b - c ) * d – ( e + f )
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).
Infix to postfix conversion

10. infixVect
postfixVect
a + b - c ) * d – ( e + f )
(
Infix to postfix conversion
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

11. infixVect
postfixVect
+ b - c ) * d – ( e + f )
(
a
Infix to postfix conversion
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

12. infixVect
postfixVect
b - c ) * d – ( e + f )
(
a
+
Infix to postfix conversion
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

13. infixVect
postfixVect
- c ) * d – ( e + f )
(
a b
+
Infix to postfix conversion
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

14. infixVect
postfixVect
c ) * d – ( e + f )
(
a b +
-
Infix to postfix conversion
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

15. infixVect
postfixVect
) * d – ( e + f )
(
a b + c
-
Infix to postfix conversion
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

16. infixVect
postfixVect
* d – ( e + f )
a b + c -
Infix to postfix conversion
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

17. infixVect
postfixVect
d – ( e + f )
a b + c -
*
Infix to postfix conversion
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

18. infixVect
postfixVect
– ( e + f )
a b + c - d
*
Infix to postfix conversion
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

19. infixVect
postfixVect
( e + f )
a b + c – d *
-
Infix to postfix conversion
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

20. infixVect
postfixVect
e + f )
a b + c – d *
-
(
Infix to postfix conversion
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

21. infixVect
postfixVect
+ f )
a b + c – d * e
-
(
Infix to postfix conversion
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

22. infixVect
postfixVect
f )
a b + c – d * e
-
(
+
Infix to postfix conversion
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

23. infixVect
postfixVect
)
a b + c – d * e f
-
(
+
Infix to postfix conversion
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

24. infixVect
postfixVect
a b + c – d * e f +
-
Infix to postfix conversion
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

25. infixVect
postfixVect
a b + c – d * e f + -
Infix to postfix conversion
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

26. Algorithm for Infix to Postfix
1) Examine the next element in the input.
2) If it is operand, output it.
3) If it is opening parenthesis, push it on stack.
4) If it is an operator, then
i) If stack is empty, push operator on stack.
ii) If the top of stack is opening parenthesis, push operator on stack
iii) If it has higher priority than the top of stack, push operator on stack.
iv) Else pop the operator from the stack and output it, repeat step 4
5) If it is a closing parenthesis, pop operators from stack and output them
until an opening parenthesis is encountered. pop and discard the opening
parenthesis.
6) If there is more input go to step 1
7) If there is no more input, pop the remaining operators to output.
Nilesh Dalvi, Lecturer@Patkar-Varde College, Goregaon(W).

27. Q & A