1. Chapter 7 Stacks I CS2006 - Data Structures I COSC 2006 April 22, 2017

2. Tutorial Do not teach new materials Review the lectures
Hand out simple programming problems
Solve them
Use more examples to explain concepts
Answer assignment problems

3. Topics ADT Stack Stack Operations Using ADT Stack
Line editor
Bracket checking
Special-Palindromes
Implementation of ADT Stack

4. Stack Of Cups Remove a cup from new stack. bottom top bottom top
COSC 2006
April 22, 2017
Stack Of Cups
bottom
top C A B D E F
bottom
top C A B D E
Picture is really a stack of cups and saucers.
LIFO = last in first out. The first cup that is removed from a stack of cups is the
Last one that was added to the stack.
Other examples of LIFO lists in real life: stack of trays in a cafeteria; paper stack in a printer or copy machine; newspaper stack at a news stand.
Add a cup to the stack.
Remove a cup from new stack.
Chapter 6: Stacks

5. Introduction Stack: Ordered group of homogeneous items
Only one item can be accessed at a time (top)
Items addition / removal take place only at the top
Inserting an item is known as "pushing" onto the stack.
Removing an item is known as "popping" off the stack.
Has Last-In-First-Out (LIFO) behavior

6. Introduction Real-life examples: Very useful in computer science Books
Pennies
More???
Very useful in computer science
Converting numeric strings into equivalent values
Evaluating algebraic expressions

7. LIFO A stack is a LIFO (Last-in-first-out) list top push pop 5 4 5 4 43 3 3 3 3 2 2 2 2 2 1 1 1 1 1
stack depth = 5
bottom

8. Introduction Example: Line-editor a b c c d d d e   e f f g
 means backspace
will generate the following output:
a b c d e f g
Observations

9. Introduction Example: Line-editor Pseudocode:
// Read the line, correcting mistakes along the way
while (not end of line) {
Read a new character ch
if ( ch is not a ‘ ‘ )
Add ch to the ADT
else
Remove the most recently added item from the ADT
} // end while

10. Introduction Example: Line-editor The following operations are needed
Determine if the line is empty
Add a character
Remove the most-recently added character
Retrieve the most recently added item
These are exactly the operations needed for a stack
The ADT Stack can be used to perform the reading and correction of the line

11. The Stack Interface In Java
COSC 2006
April 22, 2017
The Stack Interface In Java
We can define our own stack interface like this:
public interface StackInterface
{ public boolean isFull(); // returns if the stack is full
public boolean isEmpty(); // return if the stack is empty public Object top() // return the top element throws StackException; // if the stack is empty public void push(Object obj); // push obj onto the stack
public void popAll ();
public Object pop() // return and remove the top element of the stack throws StackException; // if the stack is empty }
Chapter 6: Stacks

12. Using ADT Stack Read & Correct a text of line: Using stack operations
readAndCorrect ( out aStack : Stack)
// Reads input line and either enters characters onto stack S
// or corrects contents if the character is the ‘ ‘ symbol
aStack.createStack
Read newChar
while ( newChar != eoln )
{ if ( newChar != ‘ ‘ )
aStack.Push( newChar)
else if (! aStack.isEmpty())
aStack.Pop( )
read newChar
} // end while
How to write the contents in a stack backwards?

13. Stack Application Example: Balanced Braces Assumption Example:
All braces are of the same type
Example:
a b c { d e f g { i j k } { l { m n } } o p } q r Balanced
a b c { d e f } } { g h I j { k l } m Unbalanced
Any idea to evaluate?

14. Stack Application Balanced Braces Idea:
keep track for unmatched ‘{‘ by pushing them onto a stack
When ‘}’ is encountered , pop one of the unmatched ‘{‘ from the stack
Stop when
The string and stack are both empty
 Success
Stack is empty, but string still contains closing braces (‘}‘)
 Failure: more closing braces
String is empty but stack still contains unmatched opening braces (‘{‘’)
 Failure: more opening braces

15. Stack Application Balanced Braces: Pseudocode aStack.createStack ( )
balancedSoFar = true
i = 0
while ( balancedSoFar and i < length of aString)
{ ch = character at position i
++ i
if ( ch = ‘{‘)
aStack.push( ‘{‘ )
else if ( ch = ‘}’ )
aStack.pop( ) // Pop a matching open brace
else balancedSoFar = false
// ignore all characters other that braces
} // end while
if ( balancedSoFar && aStack.isEmpty( ) )
aString has balanced braces
else
aString doesn’t have balanced braces

16. Stack Application Balanced Braces: Examples { a { b } c } { a { b c }

17. Stack Application How about math expression with 3 types of brackets
() [] {}
{(A+C)*D

18. Stack Application Algorithm Scan expression from left to right
Each time a left bracket is encountered, push it onto stack
When a right bracket is encountered, compare it with the top item on the stack
If it is a match, pop the stack
If not, report illegal bracketing
If the stack id prematurely empty, report illegal
If there are items left on the stack after the expression has been scanned, report illegal bracketing

19. Stack Application
(3+4)*{7+[4/8]}

20. Stack Application Write the pseudo code by yourself
Special-Palindromes
L = { w $ w ' : w is either empty or any string not including $,
and w ' = reverse (w) }
Idea:
Traverse the first half and push its elements onto the stack
When $ is reached, ignore it and start traversing and matching each element from the input string with that on the stack
Termination:
Success:
Both stack and string are empty
Failure:
Character on input doesn't match character on stack top
String empty, but stack isn't
Stack empty, but string isn't
Write the pseudo code by yourself

21. ADT Stack Implementation
Implementations
Arrays
Linked lists
And?

22. ADT Stack Implementation
Array Linked List ADT List
Where is the top?
Top 10 20 30 10 20 30
Top 10 20 30
Top

23. COSC 2006
April 22, 2017
An Array-Based Stack
We can use arrays for our stacks by requiring a maximum size N for our stack (e.g. N = 50)
The stack would then consist of an N-element array, s, and the array index of the top element, t
Array indices start at 0,so we will initialize t to -1
Chapter 6: Stacks

24. Stack Interface public interface StackInterface {
COSC 2006
April 22, 2017
Stack Interface
public interface StackInterface {
public boolean isEmpty();
public boolean isFull();
public void push(Object newItem) throws StackException;
public Object pop() throws StackException;
public void popAll();
public Object peek/top () throws StackException;
} // end StackInterface
Chapter 6: Stacks

25. Stack Exception public class StackException
COSC 2006
April 22, 2017
Stack Exception
public class StackException
extends java.lang.RuntimeException {
public StackException(String s) {
super(s);
} // end constructor
} // end StackException
Chapter 6: Stacks

26. Array Stack Implementation (1)
COSC 2006
April 22, 2017
Array Stack Implementation (1)
public class ArrayStackBased implements StackInterface {
final int MAX_STACK = 50; // maximum size of stack
private Object items[ ];
private int top;
public ArrayStackBased() {
items = new Object[MAX_STACK];
top = -1;
} // end default constructor
public boolean isEmpty() {
return top < 0;
} // end isEmpty
public boolean isFull() {
return top == MAX_STACK-1;
} // end isFull
Chapter 6: Stacks

27. Array Stack Implementation (1)
COSC 2006
April 22, 2017
Array Stack Implementation (1)
public class ArrayStackBased implements StackInterface {
final int MAX_STACK = 50; // maximum size of stack
private Object items[ ];
private int top;
public ArrayStackBased() {
items = new Object[MAX_STACK];
top = -1;
} // end default constructor
public boolean isEmpty() {
return top < 0;
} // end isEmpty
public boolean isFull() {
return top == MAX_STACK-1;
} // end isFull
Chapter 6: Stacks

28. Array Stack Implementation (2)
COSC 2006
April 22, 2017
Array Stack Implementation (2)
public void push(Object newItem) throws StackException {
if (!isFull()) {
items[++top] = newItem; }
else {
throw new StackException("StackException on " + "push: stack full");
} // end if
} // end push
public void popAll() {
items = new Object[MAX_STACK];
top = -1;
} // end popAll
Chapter 6: Stacks

29. Array Stack Implementation (2)
COSC 2006
April 22, 2017
Array Stack Implementation (2)
public void push(Object newItem) throws StackException {
if (!isFull()) {
items[++top] = newItem; }
else {
throw new StackException("StackException on " + "push: stack full");
} // end if
} // end push
public void popAll() {
items = new Object[MAX_STACK];
top = -1;
} // end popAll
Chapter 6: Stacks

30. Array Stack Implementation (3)
COSC 2006
April 22, 2017
Array Stack Implementation (3)
public Object pop() throws StackException {
if (!isEmpty()) {
return items[top--]; }
else {
throw new StackException("StackException on " + "pop: stack empty");
} // end if
} // end pop
public Object peek() throws StackException {
return items[top];
throw new StackException("Stack exception on " +
"peek - stack empty");
} // end peek
} // end ArrayStack
Chapter 6: Stacks

31. Array Stack Implementation (3)
COSC 2006
April 22, 2017
Array Stack Implementation (3)
public Object pop() throws StackException {
if (!isEmpty()) {
return items[top--]; }
else {
throw new StackException("StackException on " + "pop: stack empty");
} // end if
} // end pop
public Object peek() throws StackException {
return items[top];
throw new StackException("Stack exception on " +
"peek - stack empty");
} // end peek
} // end ArrayStack
Chapter 6: Stacks

32. Array Stack Test public class ArrayStackTest {
COSC 2006
April 22, 2017
Array Stack Test
public class ArrayStackTest {
public static final int MAX_ITEMS = 15;
public static void main(String[ ] args) {
ArrayStackBased stack = new ArrayStackBased();
Integer items[ ] = new Integer[MAX_ITEMS];
System.out.println("Pushing:");
for (int i=0; i<MAX_ITEMS; i++) {
items[i] = new Integer(i);
if (!stack.isFull()) {
System.out.print(" "+i);
stack.push(items[i]);
} // end if
} // end for
System.out.println("\nPopping:");
while (!stack.isEmpty()) {
// cast result of pop to Integer
System.out.print(" "+(Integer)(stack.pop()));
} // end while
System.out.println();
} // end main
} // end ArrayStackTest
Chapter 6: Stacks

33. Array Stack Questions: How to access each object?
COSC 2006
April 22, 2017
Array Stack
Questions:
Can we push/pop primitive type value onto the stack?
Can we push/pop different objects onto the stack?
Student
Car
How to access each object?
Chapter 6: Stacks

34. Review
If the array: 6, 2, 7, 13, 5, 4
is added to a stack, in the order given, which number will be the first number to be removed from the stack? 6 2 5 4

35. Review
The item that is removed first from a stack is called the ______ of the stack.
front
top
Base
prime

36. Review
If the array: 6, 21, 35, 3, 6, 2, 13
is added to a stack, in the order given, which of the following is the top of the stack? 2 6 3 13 35

37. Review
The ______ method of the ADT stack adds an item to the top of the stack.
createStack
push
Pop
peek