## Problem IDs are generated using lowercase letters `a-z` in lexicographic order, similar to how Excel names columns: `a, b, ..., z, aa, ab, ..., az, ba, ...`. Given an integer `n` (1-indexed), return the `n`-th ID string. ```python def nth_id(n: int) -> str: ``` ## Example ``` nth_id(1) -> "a" nth_id(26) -> "z" nth_id(27) -> "aa" nth_id(28) -> "ab" nth_id(702) -> "zz" nth_id(703) -> "aaa" ``` Note: This is analogous to base-26 but with no zero digit -- each "digit" is 1-indexed. ## Follow-ups 1. Write the inverse: given an ID string, return its 1-indexed position. 2. What changes if the alphabet is alphanumeric (a-z, 0-9, 36 chars)? 3. For very large `n` (e.g., 10^15), does your solution still work? What is its time complexity? 4. How would you extend IDs to support a prefix namespace, e.g., `"usr_a"`, `"usr_b"`, ...?

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Nth ID - Generate Lexicographically Nth Identifier

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Problem IDs are generated using lowercase letters a-z in lexicographic order, similar to how Excel names columns: a, b, ..., z, aa, ab, ..., az, ba, .... Given an integer n (1-indexed), return the n-th ID string. Example Note: This is analogous to ba…

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