- By Vasudev Ram - Online Python training / SQL training / Linux training
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Hi, readers,
The factorial function (Wikipedia article) is often implemented in programming languages as either an iterative or a recursive function. Both are fairly simple to implement.
For the iterative version, to find the value of n factorial (written n! in mathematics), you set a variable called, say, product, equal to 1, then multiply it in a loop by each value of a variable i that ranges from 1 to n.
For the recursive version, you define the base case as 0! = 1, and then for all higher values of n factorial, you compute them recursively as the product of n with (n - 1) factorial.
[ Wikipedia article about Iteration. ]
[ Wikipedia article about Recursion in computer_science. ]
Here is another way of doing it, which is also iterative, but uses no explicit loop; instead it uses Python's built-in reduce() function, which is part of the functional programming paradigm or style:
In [179]: for fact_num in range(1, 11):
...: print reduce(mul, range(1, fact_num + 1))
...:
1
2
6
24
120
720
5040
40320
362880
3628800
The above snippet (run in IPython - command-line version), loops over the values 1 to 10, and computes the factorial of each of those values, using reduce with operator.mul (which is a functional version of the multiplication operator). In more detail: the function call range(1, 11) returns a list with the values 1 to 10, and the for statement iterates over those values, passing each to the expression involving reduce and mul, which together compute each value's factorial, using the iterable returned by the second range call, which produces all the numbers that have to be multiplied together to get the factorial of fact_num.The Python docstring for reduce:
reduce.__doc__: reduce(function, sequence[, initial]) -> value Apply a function of two arguments cumulatively to the items of a sequence, from left to right, so as to reduce the sequence to a single value. For example, reduce(lambda x, y: x+y, [1, 2, 3, 4, 5]) calculates ((((1+2)+3)+4)+5). If initial is present, it is placed before the items of the sequence in the calculation, and serves as a default when the sequence is empty.Did you know that there are many different kinds of factorials? To learn more, check out this post:
Permutation facts
- Enjoy.
- Vasudev Ram - Online Python training and consulting
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3 comments:
Range in 3.6 doesn't return a list. Type(range(1,10)) -> range.
@digital-camera-links:
Right, thanks. I did know that range() in Python 3.x returns a range value, not a list, and that is why I had deliberately used the term "iterable" in the last part of the blog post (see excerpt below - "using the iterable"). But I forgot to change "list" to "iterable" in "returns a list" earlier in the post, because I was thinking about Python 2 at that time. And the code was run on Python 2, as you can see from the print statement used.
>In more detail: the function call range(1, 11) returns a list with the values 1 to 10, and the for statement iterates over those values, passing each to the expression involving reduce and mul, which together compute each value's factorial, using the iterable returned by the second range call
I should also mention that in the code snippet in the post above, I only showed the code for computing factorials of positive numbers (by the reduce / mul approach), not for 0 (0! = 1) and did no check for negative numbers (for which factorial is not defined). Both those should be there in a production implementation.
Another interesting point is whether the reduce / mul approach may crash for a very large value of fact_num, due to some limitation in the implementation of reduce, like what can happen with a recursive implementation running out of stack space? Not sure. Would have to look at the reduce source code in the Python interpreter's source code to figure it out.
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