Write a C program that takes as input a fully parenthesized, arithmetic expression

of binary operators $+,,*,/,$ and converts the expression into a binary expression

tree. Your program should take input from the command line. The entire

expression should be in a character string without any space in it$.$

An input string only includes floating numbers in the format of Y$.$YY$,$ that is$,$ one

digit to the left of the decimal point and two digits to the right of the decimal

point, and variables of the form of x$1,$ x$2,$ x$3,....$

Your program shall allow for the leaves in the expression tree not only to store

floating values but also to store variables of the form x$1,$ x$2,$ x$3,...,$ For example,

expression $((($ x$1+5\mathrm{.}12)($x$27\mathrm{.}68)/$ x$3)$ will be converted into a binary expression

tree like:

$/$

$|$

$||$

$*$ x$3$

$|$

$||$

$+-$

$||$

$||||$

x$15\mathrm{.}12$ x$27\mathrm{.}68$

Your program should then show a menu with the following options:

$1.$ Preorder

$2.$ Inorder

$3.$ Postorder

$4.$ Calculate

$5.$ Exit

Description:

$($a$)$ If an option of Preorder, Inorder, or Postorder is selected, your

program should print the expression by the corresponding traversal

order $($Note: no parentheses for preorder and postorder traversal but

fully parenthesized for inorder traversal$).$

$($b$)$ Arithmetic calculation is invoked by option Calculate. Your program

should be able to detect errors like divide$-$by$-$zero before the

calculation.

$$ This option supports both expressions with and without

variables. The program first checks for any divide$-$by$-$zero errors

before calculation.

$$ If the expression contains variables, the program prompts the

user to input values for each variable in floating$-$point format

$($Y$.$YY$).$ Once all variable values are entered, they are

substituted into the expression. If a variable for any reason is not

defined or found, the program may use $0$ as the default value for

the variable. Appropriate messages should be displayed to the

users to inform this.

$$ The program then evaluates the expression and provides the

answer in $2$ floating$-$point format $($Y$.$YY$)$

$$ If there$$s an error in the calculation such dividing by $0$ or

unknown operator, the program shall display appropriate

messages and the calculate function can return and output $0.$

$($c$)$ Option Exit terminates your program.

Note: No more than $10$ variables will be passed in a given expression