This problem requires you to write a program to convert an infix expression to postfix format. The evaluation of an infix expression such as $A+B**C$ requires knowledge of which of the two operations, $+$ or $*,$ should be performed first. In general, $A+B**C$ is to be interpreted as $A+(B**C)$ unless otherwise specified. We say that multiplication takes precedence over addition, Suppose that we would now like to convert $A+B*C$ to postfix. Applying the rules of precedence, we begin by converting the first portion of the expression that is evaluated, namely, the multiplication operation. Doing this conversion in stages, we obtain

$A+B**C$

$A+B{C}^{**}$

$B{C}^{**}+{?}_{?}$

Given infix form

Convert the multiplication

Convert the addition

The part of the expression that has been converted is underlined. The major rules to remember during the conversion process are that the operations with highest precedence are converted first and that, after a portion of an expression has been converted to postfix, it is treated as a single operand. Let us now consider the same example with the precedence of operators reversed by the deliberate insertion of parentheses:

$(A+B{)}^{**}C$

$AB+{?}^{**}{C}_{?}$

$AB+C*{*}_{?}$

Given infix form

Convert the addition

Convert the multiplication

Note that in the conversion from $AB+{?}^{**}C$ to $AB+C**$ the expression $AB+$ was treated as a single operand. The rules for converting from infix to postfix are simple, provided that you know the order of precedence.

We consider four binary operations: addition, subtraction, multiplication, and division. These operations are denoted by the usual operators, $+$dots,$*{*}^{**},$ and $\frac{?}{?},$ respectively. There are two levels of operator precedence. Both $*$ and $/$ have higher precedence than $+$ and $-$ Furthermore, when un: