Dojo Pythonic Coding Pair: Permutation Check and Pow

Requirements

• Task 1: Given a list containing n values, decide whether its contents are exactly a permutation of [0, 1, 2, ..., n - 1].
• A first solution that allocates a separate Boolean list may be rejected because of its additional memory usage.
• Task 1 follow-up: Can you perform the check in place or otherwise avoid auxiliary memory?
• Task 2: Write pow(a: float, b: int) to compute a raised to the integer power b.
• The interviewer might permit no memory beyond the stack frames used by recursion.
• Favor compact, idiomatic Python; clear use of built-ins, comprehensions, any / all, and clean expressions is valued.

Examples

Task 1

is_permutation([2, 0, 3, 1])  # True

The list contains every value from 0 through 3 exactly once.

is_permutation([1, 0, 1])  # False

For a list of length three, the required values are 0, 1, and 2; 2 is absent and 1 is repeated.

Task 2

pow(3.0, 4)  # 81.0

Raising 3.0 to the fourth power produces 81.0.

pow(5.0, -2)  # 0.04

A negative exponent takes the reciprocal, so the result is 1 / (5.0 ** 2).

pow(7.0, 0)  # 1.0

Any nonzero base raised to the zeroth power evaluates to 1.0.