Three 2s Maximum Value | Dataford Interview Questions

For a Searce coding screen, determine the largest integer that can be formed using exactly three occurrences of the number 2. You may combine subexpressions with binary operators and apply factorial as a unary operator.

Implement highest_three_twos(max_ops) using at most max_ops mathematical operations.

Allowed operations are:

Binary: +, -, *, exact integer division /, and exponentiation **
Unary: factorial !
Parentheses may be used freely.

Every intermediate result must be an integer with absolute value at most 10^8. Factorial is defined only for integers from 0 through 8. Division is valid only when the divisor is nonzero and the result is integral. Exponents must be nonnegative integers from 0 through 30.

Return the maximum value among all valid expressions. If an expression uses fewer than max_ops operations, it is still valid.

Constraints

2 <= max_ops <= 8
Exactly three literal 2 values must be used
Intermediate values have absolute value at most 10^8
Factorial inputs must be integers from 0 through 8
Exponents must be integers from 0 through 30
Division must be exact and cannot use zero as the divisor

Function Signature

def highest_three_twos(max_ops):

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Problem