Stacks are used mainly in following applications :

1. Function Calling

Programs compiled from high level languages make use of a stack for the working memory of eachfunction or procedure calling. When any procedure or function is called, function parameters andaddress is pushed into the stack and whenever procedure or function returns, parameters are popped.As a function calls other function, first its argument, then the return address and finally space for localvariables is pushed onto a stack. A function call itself, is known as recursion.

Function a(){ if (condition)

return . .. return b(); }Function b(){ if (condition)

return . .. return a(); }

Note how all the function a and b's environment are found in the stack. When a is called a secondtime from b, a new set of parameters is pushed in the stack on invocation of a.

The stack is a region of main memory within which programs temporarily store data as theyexecute. For example, when a program sends parameters to a function, the parameters are placed onthe stack. When the function executes, these parameters are popped from the stack. When a functioncalls other functions, current contents of the caller function are pushed onto the stack with the addressof the instruction just next to the call instruction, this is done so that after the execution of calledfunction, the compiler can track back the path from where it is sent to the called function.

Applications of Stack

2. To convert an infix expression to postfix

In high level languages, infix notation cannot be used to evaluate expressions. We must analyze theexpression to determine the order in which we evaluate it. A common technique is to convert an infixnotation into postfix notation, then evaluating it.

o Prefix: + a bo Infix: a + bo Postfix: a b +

Infix to postfix conversion can be done easily using stack.

Following are the rules for the infix to postfix conversion of an arithmetic expression:

Rules:o Operands immediately go directly to outputo Operators are pushed into the stack (including parenthesis)o Check to see if stack top operator is less than current operator (Priority of the operator)o If the top operator is less than, push the current operator onto stacko If the top operator is greater than the current, pop top operator and push onto stack,

push current operator onto stacko Priority 2: * /o Priority 1: + -o Priority 0: (

If we encounter a right parenthesis, pop from stack until we get matching left parenthesis. Do notoutput parenthesis.

Example 1 :

A + B * C - D / E

Infix Stack(bot->top) Postfixa) A + B * C - D / Eb) + B * C - D / E Ac) B * C - D / E + Ad) * C - D / E + A Be) C - D / E + * A Bf) - D / E + * A B C

g) D / E + - A B C *

h) / E + - A B C * Di) E + - / A B C * Dj) + - / A B C * D Ek) A B C * D E / - +

Example 2 :

A * B - ( C + D ) + E

Infix Stack(bot->top) Postfixa) A * B - ( C - D ) + E empty emptyb) * B - ( C + D ) + E empty Ac) B - ( C + D ) + E * Ad) - ( C + D ) + E * A Be) - ( C + D ) + E empty A B *f) ( C + D ) + E - A B *g) C + D ) + E - ( A B *h) + D ) + E - ( A B * Ci) D ) + E - ( + A B * Cj) ) + E - ( + A B * C Dk) + E - A B * C D +l) + E empty A B * C D + -m) E + A B * C D + -n) + A B * C D + - Eo) empty A B * C D + - E +

3. To evaluate a postfix expression

The expression may be evaluated by making a left to right scan, stacking operands and evaluatingoperators using the correct number of operands from the stack and finally placing back the result onto the stack.

Algorithm for the evaluation of postfix expression :

1. Scan arithmetic expression from left to right and repeat step 2 and 3 until complete expressionis processed

2. If an operand is found push it into stack

3. If an operator is foundi. Remove two top elements of stack, where X is top element and Y is next-to-topelement.ii. Evaluate X operator Yiii. Place the result of step 3(ii) into stack at top

Example :

Postfix Expression : 1 2 3 + *

Postfix Stack( bot -> top )

a) 1 2 3 + *

b) 2 3 + * 1

c) 3 + * 1 2

d) + * 1 2 3

e) * 1 5 // 5 from 2 + 3

f) 5 // 5 from 1 * 5