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ADT Stacks

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Stacks

Principle: LIFO

Definition: An ordered collection of

data items which can be accessed atonly one location, called the top of

the stack

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Basic Operations

Push

Pop

Make Null Empty

Full

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Representation:

char STACK[10];

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1. Push

-inserts the data item at the top of thestack, returns the modified stack.

{

if (Top >= (MaxStack - 1))

Success = False; //no room on stack

else

{

Top++; //increment stack top pointer

STACK[Top] = X; //copy X to stack

Success = True;

}}

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2.Pop

-retrieves and removes the element at the top of the

stack, returns the top element of the stack and themodified stack

{

if (Top < 0)

Success = False; //empty stack

else

{

X = STACK[Top]; //pop top of stack into X

Top--; //decrement top of stack pointer

Success = True;

}

}

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3. Make Null

{ Top = -1; }

4. Empty Stack

{ return (Top < 0); }

5. Full Stack

{ return(Top >= MaxStack);

}

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Array Implementation

for a Stack of ints

public class ArrayStack

{

int store[];

int top;

static final int MAX = 100;

public ArrayStack()

{

store = new int[MAX];

top = 0;}

// ...

}

4top

12 24 37 17

top = index of thefirst FREEslot

...

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ArrayStack class, continued

public class ArrayStack

{ // ...

public boolean empty()

{

return (top == 0);

}

public void push(int entry)

{

if (top < MAX)

store[top++] = entry;}

// ...

}

...

4top

12 24 37 17

Remember:top = index of the

first FREEslot

// in the code that uses

// the stack

stack.push( 95 );

95

5

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ArrayStack class, continuedpublic class ArrayStack

{

// ...

public int pop()

throws Exception

{if ( empty() )

throw new Exception();

else

return store[--top];

}

}

...

5top

12 24 37 17 95

4

// in the code that uses

// the stack

int x = stack.pop();

// x gets 95,

// slot 4 is now free

Remember:top = index of the

first FREE slot

Store[4] still contains95, but its nowconsidered free.

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Using the Stack

try

{

ArrayStack st = new ArrayStack();

st.push( 1 ); st.push( 3 ); st.push( 2 );

System.out.println( st.pop() );st.push( 5 );

System.out.println( st.pop() );

System.out.println( st.pop() );

}

catch ( Exception e ){

System.out.println( pop() on empty stack );

}

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Application of Stacks

Checking for unpaired or paired (),{} in a

programming language

Evaluation of expressions.

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A. Evaluation of Expression

To understand how stacks can be used in evaluatingexpressions, we first need to know some underlying principles ofbinary expressions, that is notation of expressions.

Notations of Expressions

Let X=A+B be an expression. Then the notations of expressions aredefined as:

1. Prefix notation: the operator is written before the two operands.Ex. +AB

2. Infix notation: the operator is written in between the twooperands. Ex. A+B

3. Postfix notation: the operator is written after the two operands.Ex. AB+

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Illustration:

X=A+B/C-D

Find the 3 notations of the above expression.

Prefix: -+A/BCD

Infix: A+B/C-D

Postfix: ABC/+D-

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Knowing the underlying principles on the

3 notations of expressions, we now areready to use stacks to evaluate expressions.

There are 2 possible ways to evaluate

expressions

1. Prefix method

2. Postfix method

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A. Prefix method

Algo:

1. Let there be 2 stacks X and S. Assume that X contains

the prefix notation of the expression and S be initially

empty.S will be used to do the evaluation.

2. Get the top of X.

3. If x [i] is an operand, push the element into S.

If x[i] is an operator, pop the 2 topmost element of S.

Apply the operation defined by x[i] then push the result

into S

4. Repeat steps 2-3 until X is empty or S is left with only

one element.That element

Must be the result of the evaluation process.

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Conversion of infix to postfix notation using stacks

.push only operations onto the stack.push the operator if the incoming operator has

a higher precedence than the top operator in the

stack.

.If the incoming operator has a priority

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Priority table

Symbol instack priority Incoming Priority

^ 3 4

*, / 2 2

+, - 1 1

( 0 4

) - -

Example: A+(B*C) + D