CS Data Structures I Chapter 6 Stacks I

2 Topics ADT Stack Stack Operations Using ADT Stack Line editor Bracket checking Special-Palindromes Implementation of ADT Stack Using Arrays

3 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

4 Stack Of Cups Add a cup to the stack. bottom top C A B D E F Remove a cup from new stack. bottom top C A B D E

5 Introduction Real-life examples: Trays Pennies Folded shirts Books... Very useful in computer science Converting numeric strings into equivalent values Evaluating algebraic expressions

6 LIFO A stack is a LIFO (Last-in-first-out) list push pop top bottom stack depth = 5

7 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

8 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

9 Introduction Writing the line: First Draft: // Write the line while (the ADT is not empty) { Remove most recently added item from the ADT Write item } // 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 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 }

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

13 Using ADT Stack Write Backwards using ADT stack operations: +displayBackward ( in aStack ; Stack) // Displays input line in reverse order by writing // the contents of stack aStack while ( ! aStack.isEmpty ( ) ) {aStack.pop ( newChar ) write newChar } // end while

14 Stack Application Example: Balanced Braces Assumption 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

15 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

16 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 elsebalancedSoFar = false // ignore all characters other that braces }// end while if ( balancedSoFar && aStack.isEmpty( ) ) aString has balanced braces else aString doesnt have balanced braces

17 Stack Application Balanced Braces: Examples { a { b } c } { a { b c } { a b } }

18 Stack Application How about math expression with 3 types of brackets () [] {}

19 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

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

21 Stack Application 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

22 Stack Application Special-Palindromes: Pseudocode using ADT Stack aStack.createStack ( ) // Push characters preceding $ onto stack i = 0ch = character at position i in string while ( ch != $) {aStack.Push ( ch ) ++ich = character at position i in string } // end while ++i// Skip the $ // match the reverse of w inLanguage = true // assume string is in language while ( inLanguage && i < length of aString) try {aStack.pop (StackTop) ch = character at position i in string if ( StackTop = ch ++i // Characters match elseinLanguage = false } // end try catch {// pop failed, stack empty (1st half of string shorter than 2nd half inLanguage = false } // end catch If (inLanguage && isEmpty()) aString is in language Else aString is not in language

23 ADT Stack Implementation implementations Arrays Linked lists ADT List Vector

24 ADT Stack Implementation ArrayLinked ListADT List Top Top Top

25 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 Pseudo-code: int size(): return t +1 boolean isEmpty(): return t < 0 Object top(): if isEmpty() then throw StackEmptyException else return s [t ]

26 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() throws StackException; } // end StackInterface

27 Stack Exception public class StackException extends java.lang.RuntimeException { public StackException(String s) { super(s); } // end constructor } // end StackException

28 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

29 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

30 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 { if (!isEmpty()) { return items[top]; } else { throw new StackException("Stack exception on " + "peek - stack empty"); } // end if } // end peek } // end ArrayStack

31 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

32 Array Stack Test Output Pushing: Popping:

33 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