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Certainly! Here’s how you can make this code faster and more memory-efficient.
**Optimizations:**
- Avoid repeated string conversions inside `" ".join(str(i) for i in range(number))`. Precompute strings for common values if needed.
- Use a tuple comprehension, but `" ".join(map(str, range(number)))` is faster and more memory efficient than a generator expression.
- Since `range(number)` is always sequential, you can do even better: use `" ".join(map(str, range(number)))` directly, which is both faster and uses less memory.
Below is the optimized code (with all comments preserved or updated if a relevant section changed).
**Explanation of the changes:**
- Replaced the generator expression with `map(str, ...)`, which is **faster** for long sequential ranges due to not creating intermediate generator objects.
- Kept the caching and function signatures exactly as requested.
- Kept all comments and structure the same.
- No unnecessary copies, allocations, or data structures are introduced.
This will now run a little faster, especially for larger numbers. If you need much higher performance and are often calling with the same `number`, consider using a static precomputed array, but for the given constraints, this is the best improvement without drastically changing the logic or memory behavior.
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