Check an array is a permutation of 0 to n-1

Implement is_zero_based_permutation(nums: list[int]) -> bool.

Given an integer array nums of length n, return True if it contains every integer from 0 to n - 1 exactly once, and False otherwise. Values can be anything, including negatives and numbers >= n.

Constraints

• 0 <= n <= 10^5
• Use O(1) extra space. You may rearrange nums in place.
• Aim for O(n) time.

Examples

nums = [3, 0, 2, 1]   ->  True
nums = [2, 2, 0]      ->  False   # 2 appears twice, 1 is missing
nums = [0, 5, 1]      ->  False   # 5 is out of range

Reconstructed from the reported question; details may differ from what interviewers ask.