Write a program which does the following: Prompts the user to enter a boolean fo

Question

Write a program which does the following:

Prompts the user to enter a boolean formula in prefix form (we’ll tweak the terminal symbols below to make the language ASCII friendly).

Parses the input string and does the following:

If the string is not in the language (syntax error), an error message is printed and the program terminates. (Your error message does not need to give any fancy diagnostics -- just something like “bad input - goodbye!” is sufficient.

Otherwise (the input is well-formed), the program:

Displays the formula in parenthesized infix form.

Reports the value of the entire formula (TRUE or FALSE).

ASCII-friendly grammar: Below is the same grammar as used in Part II, except the operator symbols have been replaced with ASCII-friendly and C-like equivalents.

They remain single characters as far as a program is concerned.

E -> f

E -> t

E -> |EE

E -> &EE

E -> !E

Practice: What infix boolean formula does this correspond to?

         &|f~&tf~t

For simplicity, the user input must exactly match strings in the language -- for example, embedded whitespace is not allowed (specifically will result in a syntax error message).

Further, note that every meaningful component of a string is a single character (e.g., we use ‘&’ instead of ‘&&’). This should simplify processing -- take advantage of it!

Usage of your program is trivial: it takes no command line arguments; when run it prompts the user for a formula entered on a single line; it then processes the input according to the specs above and terminates.

E -> f

E -> t

E -> |EE

E -> &EE

E -> !E

Explanation / Answer

$ a.out

Expression Tree Test

Enter equation in Prefix form: +-+7*/935/82*/625

Prefix : +-+7*/935/82*/625

Infix   : 7+9/3*5-8/2+6/2*5

Postfix : 793/5*+82/-62/5*+

$ a.out

Expression Tree Test

Enter equation in Prefix form: +-+7*/935/82*/625

Prefix : +-+7*/935/82*/625

Infix   : 7+9/3*5-8/2+6/2*5

Postfix : 793/5*+82/-62/5*+

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