Algorithm to evaluate expression given in postfix notation , Data Structure & Algorithms

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Q. Write down an algorithm to evaluate an expression given to you in postfix notation. Show the execution of your algorithm for the following given expression.

AB^CD-EF/GH+/+*

Ans.

Algorithm to evaluate Post fix Expression is shown as follows

Opndstk = the empty stack;

/*scan the input string reading one */

/*element at a time into symb */

while ( not end of input){

symb = next input character;

if (symb is an operand)

push (opndstk, symb);

else

{

/* symb is an operator */

opnd 2 = Pop (opnd stk);

opnd 1 = Pop (opnd stk);

value = result of applying symb to opnd 1 and opnd 2;

push (opndstk,value);

}/*end else */

}/*end while */

return (pop (opnd stk));

AB^CD-EF/GH+/+*

Symb	Opnd1	Opnd2	Value	Opndstk
A				A
B				A,B
^	A	B	A^B	A^B
C	A	B	A^B	A^B,C
D	A	B	A^B	A^B,C,D
-	C	D	C-D	A^B,C-D
E	C	D	C-D	A^B,C-D,E
F	C	D	C-D	A^B,C-D,E,F
/	E	F	E/F	A^B,C-D,E/F
G	E	F	E/F	A^B,C-D,E/F,G
H	E	F	E/F	A^B,C-D,E/F,G,H
+	G	H	G+H	A^B,C-D,E/F,G+H
/	E/F	G+H	(E/F)/(G+H)	A^B,C-D, (E/F) /(G+H)
+	C-D	(E/F)/(G+H)	(C-D)+(E/F)/(G+H)	A^B,(C-D)+ (E/F)/(G+H)
*	A^B	(C- D)+(E/F)/(G+H)	A^B*((C-D)+ (E/F)/(G+H))	A^B*((C-D)+ (E/F)/(G+H))

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