In infix notation operators sit between operands (A + B). Postfix places them after (A B +), which removes the need for parentheses because evaluation order is fully determined by position. The shunting-yard algorithm scans left to right, sends operands straight to output, and uses a stack to hold operators whose precedence decides when they can leave.
Shunting-yard algorithm for infix to postfixOperand → copy to output
Operator → pop higher-or-equal precedence operators to output, then push it
( → push
) → pop to output until matching (
^ → right-associative: pop only strictly higher precedence
Why precedence matters
A * B + C converts to A B * C + because * binds tighter. Without precedence rules the stack would not know that the multiplication must be emitted first.