O(1) Range Queries: Are All Elements of a Subarray Distinct?

You are given an integer array `nums` and a range `[l, r]` of indices. Determine whether the elements `nums[l], nums[l + 1], ..., nums[r]` are all distinct, that is, whether no value appears twice in the range. The interviewer then extended the task: many different ranges will be queried against the same array, so precompute information about `nums` once, with the best preprocessing time you can achieve, such that every query is answered in O(1) time. Implement the extended version, which receives all the queries at once. ### Function Signature ```python def ranges_distinct(nums: list[int], queries: list[list[int]]) -> list[bool]: ``` ### Rules - Each query is `[l, r]` with 0-indexed, inclusive bounds. - The answer to a query is `True` if no value occurs more than once among `nums[l..r]`, and `False` otherwise. A range with one element is always `True`. - Return the answers in the order of `queries`. - The preprocessing may depend only on `nums`, and each query must then be answered in O(1) time. ### Constraints - `1 <= len(nums) <= 10^5` - `-10^9 <= nums[i] <= 10^9` - `1 <= len(queries) <= 10^5` - `0 <= l <= r < len(nums)` for every query ### Examples **Example 1** ```text Input: nums = [3, 1, 4, 1, 5, 9, 2, 6, 5] queries = [[0, 2], [0, 3], [4, 7], [2, 8], [5, 5]] Output: [True, False, True, False, True] ``` `nums[0..3]` contains `1` twice (indices 1 and 3), and `nums[2..8]` contains `5` twice (indices 4 and 8). The other three ranges have no repeated value. **Example 2** ```text Input: nums = [2, 2] queries = [[0, 0], [0, 1], [1, 1]] Output: [True, False, True] ``` Each single-element range is distinct, while the whole array repeats `2`.