In particular the OP mentioned being grade 11, and I think “what is going on here” is an excellent question.įaced with a function like x! -which is defined for positive integers- which we want to extend to other numbers, the most important question we can ask is:Ī factorial is pretty simple. For a function, it means that if its arguments are compile-time constants, the function can be evaluated at compile time to produce a compile-time constant.An answer was never accepted so I’d like to take a stab at it. For data, this means that it is also const. Both the function and the table are qualified with constexpr, which means they can be evaluated at compile time. The working involves the separation of an actual function to calculate the factorial from the table of entries that hold the values. Here, the working has been placed out of the way in a namespace of its own, factorials, leaving the function of interest, factorial, as before. The type, the domain and the dependency mean we can replace the dictionary-based approach with a list-based approach: factorials = def factorial(n): while len(factorials) > for n in range(22): print(f' ![]() Any call to factorial(n) either will rely on an existing cached value for n or will populate all the entries from the highest cached value up to n. Different invocations of a function can be calculated in terms of previous invocations - they are not independent. Our function takes a single argument that is a non-negative integer. Because, by definition, a general-purpose cache is not specific to our situation, it is inevitably less optimal than one that takes advantage of the particular contours of our problem and solution spaces. It’s not that software development is stuck on repeat but… when I looked up the link for cache I noticed the example in the documentation was factorial. Let’s cache in on the previous calls: def factorial(n): return 1 if n = 0 else n * factorial(n - 1)Ī thin wrapper around a dictionary lookup for the function arguments. To store the result of a computation so that it can be subsequently retrieved without repeating the computation. ![]() Rather than recalculate the values, we can memoize them. Each call of factorial will recalculate many or all of the factorial values previously visited. Let’s start by revisiting a recursive Python implementation: def factorial(n): return 1 if n = 0 else n * factorial(n - 1)Įxcept for the base case of 0, each call will involve multiple invocations of factorial, executing and multiplying all the factorials from n down to 0. Continuing that journey, this time we unask the question of iteration versus recursion. In the case of factorial, the real lesson is seeing how something as seemingly simple as factorial - and therefore any code - can manifest in so many different ways, inviting so many considerations and techniques, to show what the limits and styles of languages can show us about data structures, control flow and paradigms. Simplicity, elegance and commodity are as much a function of context as they are a context of function. Defining something in terms of itself is profound and important, but that doesn’t mean it’s always either necessary or appropriate. Divinity, if there can be such a thing in code, is a more subtle quality achieved by many different paths. L Peter Deutsch felt thatĬool as it sounds, it’s not obvious this is always true. Another way of writing this is 52!, which is the factorial of 52.įactorial often finds itself as recursion’s poster child. ![]() The number of permutations of a 52-card deck is 52×51×50×…×2×1, which we can write more briefly as Π⁵² i. The probability that the particular arrangement of cards has ever existed before is vanishingly small. It has been said that if you want to create something unique, something likely never seen in the universe, shuffle a pack of cards.
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