Evaluation of postfix

Question

Result for evaluating the following post fix

105+606/*8-

I'm confused whether it is correct postfix expression.

Comments

142??

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Yes but how?

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Here Initially

stack contains 10 5

on +,  stack = 15

then stack = 15 60 6

on /,  stack = 15 10 (60/6)

on *, stack = 150

then stack = 150 8

on -, stack = 142 (150-8)

Answer 1

It is indeed a correct postfix expression. Visualize it as an input sequence which begins with 10 and the input comes in the order:- 

10, 5, +, 60, 6, /, *, 8, -

as soon as 10 is seen it is pushed onto the stack. 

10

after 10 the next input is 5 which is again pushed onto the stack:

5

10

 The next input is a + operator, whenever a binary operator is seen, the top two values on the stack are popped and the expression formed by the operator and the operand is evaluated: 10+5, the result of this expression( which in this case is 15) will be pushed back onto the stack. Now the stack should look like:

15

the next inputs 60 and then 6 are similarly pushed onto the stack :

6

60

15

The next operator seen is /, which will be evaluated as: 60/6=10 and 10 will be pushed onto the stack;

10

15

Similarly for the * operator: 15*10=150

150

 The next input is 8 which will be pushed onto stack:

8

150

Now the final input is a subtraction operator: 150-8=142

142

This value left on the stack is the evaluation of your postfix expression.

I guess this should have cleared your doubt. If the confusion still persists, feel free to ask for clarification.

Comments

My bad.. Was taking 10 & 5 as 105.

Thanku :)

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I did the same in my first glance but then I realized that + being a binary operator needs two operands before it( since the expression being postfix) so 105 can only broken as 10, 5. the other combination 1, 05 does not make any sense.