1. TK1924 Program Design & Problem Solving Session 2011/2012
L5: Stacks

2. Objectives In this chapter, you will: Learn about stacks
Examine various stack operations
Learn how to implement a stack as an array
Discover stack applications
Learn how to use a stack to remove recursion

3. Stacks Stack: list of homogenous elements Operations:
Addition and deletion occur only at one end, called the top of the stack
Example: in a cafeteria, the second tray can be removed only if first tray has been removed
Last in first out (LIFO) data structure
Operations:
Push: to add an element onto the stack
Pop: to remove an element from the stack

4. Stacks (cont’d.)

5. Stacks (cont’d.)

6. Stack Operations In the abstract class stackADT: initializeStack
isEmptyStack
isFullStack
push
top
pop

7. Implementation of Stacks as Arrays
First element can go in first array position, the second in the second position, etc.
The top of the stack is the index of the last element added to the stack
Stack elements are stored in an array
Stack element is accessed only through top
To keep track of the top position, use a variable called stackTop

8. Implementation of Stacks as Arrays (cont'd.)
Because stack is homogeneous
You can use an array to implement a stack
Can dynamically allocate array
Enables user to specify size of the array
The class stackType implements the functions of the abstract class stackADT

9. UML Class Diagram of class stackType

10. Implementation of Stacks as Arrays (cont'd.)
C++ arrays begin with the index 0
Must distinguish between:
The value of stackTop
The array position indicated by stackTop
If stackTop is 0, the stack is empty
If stackTop is nonzero, the stack is not empty
The top element is given by stackTop - 1

11. Implementation of Stacks as Arrays (cont'd.)

12. Initialize Stack

13. Empty Stack
If stackTop is 0, the stack is empty

14. Full Stack
The stack is full if stackTop is equal to maxStackSize

15. Push Store the newItem in the array component indicated by stackTop
Increment stackTop
Must avoid an overflow

16. Push (cont'd.)

17. Return the Top Element

18. Pop
Simply decrement stackTop by 1
Must check for underflow condition

19. Pop (cont’d.)

20. Pop (cont’d.)

21. Copy Stack

22. Constructor

23. Destructor

24. Stack Header File myStack.h
Place definitions of class and functions (stack operations) together in a file

25. Programming Example: Highest GPA
Input: program reads an input file with each student’s GPA and name
3.5 Bill
3.6 John
2.7 Lisa
3.9 Kathy
3.4 Jason
3.9 David
3.4 Jack
Output: the highest GPA and all the names associated with the highest GPA

26. Programming Example: Problem Analysis and Algorithm Design
Read the first GPA and name of the student
This is the highest GPA so far
Read the second GPA and student name
Compare this GPA with highest GPA so far
New GPA is greater than highest GPA so far
Update highest GPA, initialize stack, add to stack
New GPA is equal to the highest GPA so far
Add name to stack
New GPA is smaller than the highest GPA
Discard

27. Programming Example: Problem Analysis and Algorithm Design (cont’d.)
3.5 Bill
3.6 John
2.7 Lisa
3.9 Kathy
3.4 Jason
3.9 David
3.4 Jack
3.9
[0]
[1]
[2]
[3] :
[98]
[99]
Kathy
David
highestGPA 1
100
list
stackTop
maxStackSize

28. Application of Stacks: Postfix Expressions Calculator
Infix notation: usual notation for writing arithmetic expressions
The operator is written between the operands
Example: a + b
The operators have precedence
Parentheses can be used to override precedence

29. Application of Stacks: Postfix Expressions Calculator (cont'd.)
Prefix (Polish) notation: the operators are written before the operands
Introduced by the Polish mathematician Jan Lukasiewicz
Early 1920s
The parentheses can be omitted
Example: + a b

30. Application of Stacks: Postfix Expressions Calculator (cont'd.)
Reverse Polish notation: the operators follow the operands (postfix operators)
Proposed by the Australian philosopher and early computer scientist Charles L. Hamblin
Late 1950's
Advantage: the operators appear in the order required for computation
Example: a + b * c
In a postfix expression: a b c * +

31. Application of Stacks: Postfix Expressions Calculator (cont'd.)

32. Application of Stacks: Postfix Expressions Calculator (cont'd.)
Postfix notation has important applications in computer science
Many compilers first translate arithmetic expressions into postfix notation and then translate this expression into machine code
Evaluation algorithm:
Scan expression from left to right
When an operator is found, back up to get the operands, perform the operation, and continue

33. Application of Stacks: Postfix Expressions Calculator (cont'd.)
Example: * =

34. Application of Stacks: Postfix Expressions Calculator (cont'd.)
Symbols can be numbers or anything else:
+, -, *, and / are operators
Pop stack twice and evaluate expression
If stack has less than two elements  error
If symbol is =, the expression ends
Pop and print answer from stack
If stack has more than one element  error
If symbol is anything else
Expression contains an illegal operator

35. Application of Stacks: Postfix Expressions Calculator (cont'd.)
Examples:
; 6 - =
; is an illegal operator
* =
Does not have enough operands for + =
Error: stack will have two elements when we encounter equal (=) sign

36. Application of Stacks: Postfix Expressions Calculator (cont'd.)
We assume that the postfix expressions are in the following form:
#6 #3 + #2 * =
If symbol scanned is #, next input is a number
If the symbol scanned is not #, then it is:
An operator (may be illegal) or
An equal sign (end of expression)
We assume expressions contain only +, -, *, and / operators

37. Main Algorithm Pseudocode: We will write four functions:
evaluateExpression, evaluateOpr, discardExp, and printResult

38. Function evaluateExpression

39. Function evaluateOpr

40. Function evaluateOpr (cont’d.)

41. Function discardExp
This function is called whenever an error is discovered in the expression

42. Function printResult
If the postfix expression contains no errors, the function printResult prints the result
Otherwise, it outputs an appropriate message
The result of the expression is in the stack and the output is sent to a file

43. Function printResult (cont’d.)

44. Nonrecursive Algorithm to Print a Linked List Backward
To print the list backward, first we need to get to the last node of the list
Problem: how do we get back to previous node?
Links go in only one direction
Solution: save a pointer to each of the nodes with info 5, 10, and 15
Use a stack (LIFO)

45. Nonrecursive Algorithm to Print a Linked List Backward

46. Nonrecursive Algorithm to Print a Linked List Backward
Let us now execute the following statements:
Output:

47. Summary Stack: items are added/deleted from one end
Last In First Out (LIFO) data structure
Operations: push, pop, initialize, destroy, check for empty/full stack
Can be implemented as array or linked list
Middle elements should not be accessed
Postfix notation: operators are written after the operands (no parentheses needed)