Another way to implement memoization in Python is by using a dictionary to manually cache the results of a function. You can define a separate dictionary outside of the function and use the function's input parameters as keys to store and retrieve the results. At the beginning of the function, you can check if the result for a given set of input parameters exists in the dictionary. If it does, you can simply return the cached result instead of recomputing it. If it doesn't, you can compute the result and store it in the dictionary before returning it. While this method offers more control over the caching process, it requires manual management of the cache dictionary and can become cumbersome for complex functions with multiple input parameters.

Memoization is a way to optimize the execution time of a function by caching its results for a given set of input parameters. In Python, you can implement memoization using the `functools` module, specifically the `lru_cache` decorator. This decorator automatically caches the results of a function, eliminating the need to recompute them for the same input. You can simply apply `@functools.lru_cache` on top of your function definition and it will take care of caching the results. However, it's important to note that memoization is only effective for functions that are idempotent, meaning they always produce the same output for the same input. If your function has side effects or its output can change over time, memoization might not be suitable.

Apart from using `functools.lru_cache` and manual dictionary caching, there are other third-party libraries in Python that provide more advanced memoization techniques. One such library is `cachetools`, which offers a variety of ready-to-use memoization decorators with different caching strategies and expiration policies. The `cachetools` library can be especially useful when you need fine-grained control over the caching behavior or want to implement custom cache eviction strategies. You can install `cachetools` using pip and explore its documentation for more details and examples.