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CSE 246 Data Structures and Algorithms. Spring2011 Lecture#11. Stack Application. Run time Stack procedures Postfix Calculator Interpret infix with precedence. Stack Application.

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stack application
Stack Application
  • Run time Stack procedures
  • Postfix Calculator
  • Interpret infix with precedence


stack application1
Stack Application
  • Almost invariably, programs compiled from modern high level languages (even C!) make use of a stack frame for the working memory of each procedure or function invocation.
  • When any procedure or function is called, a number of words - the stack frame - is pushed onto a program stack.


arithmetic expression
Arithmetic Expression
  • Infix, Postfix and Prefix notations are three different but equivalent ways of writing expressions.


arithmetic expressions
Arithmetic Expressions

Infix Expressions

An expression in which every binary operation appears between its operands


(i) a+b “+” is a binary operation and a and b are its operands

(ii) (a+b)*c

Prefix Expressions

An expression in which operator comes before its operands


(i) a+b = +ab

(ii) (a+b)*c = *+abc

(iii) a+(b*c) =+a*bc

Postfix Expressions

An expression in which operator comes after its operands


(i) a+b = ab+

(ii) (a+b)*c = ab+c*

(iii) a+(b*c) = abc*+


arithmetic expression validate
Arithmetic Expression validate
  • Pushing an item on to stack correspond to opening a scope, and popping an item from the stack corresponds to closing a scope.
  • When the stack is empty and scope ender encountered, so the parenthesis pattern is invalid.


infix notation
Infix notation
  • Infix notation: A * ( B + C ) / D
  • Infix notation needs extra information to make the order of evaluation of the operators clear: rules built into the language about operator precedence and associativity, and brackets ( ) to allow users to override these rules.


postfix notation
Postfix notation
  • The order of evaluation of operators is always left-to-right, and brackets cannot be used to change this order.
  • Operators act on values immediately to the left of them.
  • RPN has the advantage of being extremely easy, and therefore fast, for a computer to analyze.


  • In the 1920's, Jan Lukasiewicz developed a formal logic system which allowed mathematical expressions to be specified without parentheses by placing the operators before (prefix notation) or after (postfix notation) the operands.
  • postfix notation for a calculator keyboard.
  • computer scientists realized that RPN or postfix notation was very efficient for computer math.
  • As a postfix expression is scanned from left to right, operands are simply placed into a last-in, first-out (LIFO) stack and operators may be immediately applied to the operands at the bottom of the stack.
  • Another advantage is consistency between machines.


practical implications
Practical implications
  • Calculations proceed from left to right
  • There are no brackets or parentheses, as they are unnecessary.
  • Operands precede operator. They are removed as the operation is evaluated.
  • When an operation is made, the result becomes an operand itself (for later operators)
  • There is no hidden state. No need to wonder if you hit an operator or not.


precedence of operators
Precedence of Operators
  • The five binary operators are: addition, subtraction, multiplication, division and exponentiation.
  • The order of precedence is (highest to lowest)
  • Exponentiation 
  • Multiplication/division *, /
  • Addition/subtraction +, -
  • The calculation: ((1 + 2) * 4) + 3 can be written down like this in RPN:
  • The expression is evaluated in the following way (the Stack is displayed after Operation has taken place):
  • Input Stack Operation

1 1 Push operand

2 1, 2 Push operand

+ 3 Addition

4 3, 4 Push operand

* 12 Multiplication

3 12,3 Push operand

+ 15 Addition

1 2 + 4 * 3 +


infix to postfix conversion algorithm
Infix to Postfix conversion Algorithm

Opstk = the empty stack

while(not end of input) {

symb=next input char;

if (symbol is operand)

add symb in postfix string

else {

while(!empty(opstk)&& prcd(stacktop(opstk), symb)) {

topsymb=pop(opstk); add topsymb to postfix string;



while(!empty(opstk)) {


add topsymb to postfix string;



algorithm for postfix evalution
Algorithm for postfix evalution

Opndstk = the emty stack;

While (not end of input)


Symb = next input character;

If (symb is an operand)






Value = result of applying symb to opnd1 and opnd2;

Push(opndstk, value);



Return (pop(opndstk));


a stack interface in java
A Stack Interface in Java
  • The stack data structure is included as a "built-in" class in the java.util package of Java.
  • it is instructive to learn how to design and implement a stack "from scratch.“
  • Implementing an abstract data type in Java involves two steps
    • Define interface
    • Define exceptions for any error conditions that can arise.
    • Provide a concrete class that implements the methods of the interface associated with that ADT.


stack interface
Stack interface

public interface Stack <E> {

public int size();

public booleanisEmpty();

public E top() throws EmptyStackException;

public void push( E element);

public E pop() throws EmptyStackException;