What do Push and Pop mean for Stacks?

Question

long story short my lecturer is crap, and was showing us infix to prefix stacks via an overhead projector and his bigass shadow was blocking everything so i missed the importan

Answer 1

The algorithm to go from infix to prefix expressions is:

-reverse input

TOS = top of stack
If next symbol is:
 - an operand -> output it
 - an operator ->
        while TOS is an operator of higher priority -> pop and output TOS
        push symbol
 - a closing parenthesis -> push it
 - an opening parenthesis -> pop and output TOS until TOS is matching
        parenthesis, then pop and discard TOS.

-reverse output

So your example goes something like (x PUSH, o POP):

2*3/(2-1)+5*(4-1)
)1-4(*5+)1-2(/3*2

Next
Symbol  Stack           Output
)       x )
1         )             1
-       x )-            1
4         )-            14
(       o )             14-
        o               14-
*       x *             14-
5         *             14-5
+       o               14-5*
        x +             14-5*
)       x +)            14-5*
1         +)            14-5*1
-       x +)-           14-5*1
2         +)-           14-5*12
(       o +)            14-5*12-
        o +             14-5*12-
/       x +/            14-5*12-
3         +/            14-5*12-3
*       x +/*           14-5*12-3
2         +/*           14-5*12-32
        o +/            14-5*12-32*
        o +             14-5*12-32*/
        o               14-5*12-32*/+

+/*23-21*5-41