How to iterate over an arithmetic formula of arbitrary length?

Question

C++ / C#

Hey!
It is necessary to enumerate all formulas of arbitrary length P.
The formula uses the constants 0, 1, 2, the variable X, as well as the operations -, +, * and brackets.
"formula length" is the number of operations i.e. if size No. formulas will be as follows:
1.) 0 + 1; x * 2
4.) x * x + 2 * x + 1; (1 + x) * 1 * 2 + 0
This is how to implement =) ?
ps Apparently, the request was set incorrectly. I didn’t find anything similar to the word at all (unless, of course, we consider the “combination without repetitions” of two declared arrays)

Answer 1

You need a Cartesian product of these features.

public bool onlyOneVariable(params string[] values) => values.Count(char.IsLetter) == 1;

from num1 in new[] { '0', '1', '2', 'X' }
from num2 in new[] { '0', '1', '2', 'X' }
from op1 in new[] { '-', '+', '*' }
where onlyOneVariable(num1, num2)
select $"{num1} {op1} {num2}";

Execution example: https://repl.it/repls/TrustyAptInstitution