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Here is an optimized version of your program.
- Since Python's `str.join` and `map` are already quite fast, the biggest improvement is to avoid unnecessary object and function creation.
- The original code creates a new `range` and map object on every call, but there is little to optimize further without changing behavior.
- But since `str(n)` is a simple type conversion, a slight gain may be obtained by using a generator expression instead of `map`, as it avoids creating a separate `map` object (very slight, but `map` will be slightly faster than a generator in CPython).
- However, the main speed up is to move the `lru_cache` `maxsize` to the actual number of possible inputs used (up to 1000, so we keep `1001`).
- But the real boost is to use a precomputed tuple cache (since ranges and their string representations are effectively static and deterministic). We build the cache only once, and access is O(1).
using a precomputed tuple.
This solution is considerably faster than the original for repeated calls with `0 <= n <= 1000` (because it avoids *all* repeated computation and object creation for lru_cache hits), and only falls back to on-demand computation for cases not precomputed.
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