How do I convert negative numbers from infix to postfix ?
Suppose I have a expression
a = - b - (-c-d)
In some places I read that you can parathesize the negative numbers like
a = (-b) - (-c-d)
But here if I do that, I will get a term like "ab-" at the beginning of the postfix expression which means a-b and is incorrect.
How do I convert this ?
In infix notation, you must distinguish between the binary subtraction operator sub and the unary negation operator neg. Both are represented by a minus sign, but the context tells you which is which.
You've got a negation, when the minus as at the beginning of the expression, or after an opening parenthesis or after a binary operator:
− (x + y) → x y add neg
4 × − x → 4 x neg mult
2 × (− x + y) → 2 x neg y add mult
You've got a subtraction when the minus is after a closing parenthesis or after a symbol, i.e. after a variable or number:
1 − x → 1 x sub
(4 ∗ x) − 1 → 4 x mult 1 sub
Take care that the unary operator neg just takes one argument off the stack. If you want to stick with binary operators, you can push a zero before the second operand and use binary sub:
− (x + y) → 0 x y add sub
4 x neg mult → 4 0 x sub mult
2 x neg y add mult → 2 0 x sub y add mult
Finally, you can apply a similar logic to unary plus, which you can just ignore:
+ x → x
+ (x + y) → x y add