Verify permutation in-place and implement fast power

Q: Verify permutation in-place and implement fast power

This is a Coding & Algorithms interview question from Tesla for Software Engineer roles. View the full question and solution on PracHub.

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Question

Given an integer list A of length n, determine whether A is a permutation of [0, 1, ..., n-1]. Do it in-place with O(
extra space (no auxiliary boolean arrays, hash sets, or sorting). Aim for an idiomatic Python solution; prefer expressions like all/any and comprehensions where appropriate. Provide an O(n)-time approach (e.g., XOR-based or index-placement) that detects out-of-range values and duplicates, and justify correctness and edge cases.
Implement a function power(base: float, exp: int) -> float that computes base^exp without using library exponentiation. Achieve O(log |exp|) time via exponentiation by squaring, handle negative exponents, exp = 0, base = 0, and the minimum 32-bit integer exponent. Use constant extra space (iterative solution preferred) and discuss numerical stability/overflow considerations.

Verify permutation in-place and implement fast power

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