Python 2.7代码，需要说明

Question

def fact( n ):
    """fact( number ) -> number

    Returns the number of permutations of n things."""
    if n == 0:
        return 1L
    return n*fact(n-1L)

Anyone can explain me what this code does? I am confused about the return statement ... n*fact(n-1L)! This seems Infinite for me :/

Thanks.

Answer 1

This is a recursive function.

Line by line

Line 1: if n == 0:

This is pretty self explanatory. In this if statement, we check to see if n is equal to 0 .

Line 2: return 1L

If n is indeed equal to 0 , we return 1L (1 Long , or essentially 1 in this case.) Note, that if we get to this return , we do not go on to the 3 ^rd line because a return is like a break .

Line 3: return n*fact(n-1L)

We multiply n times n-1 and pass it back into the recursive function because it is checking for factorials, and we want to go all the way until n is 0 ( 6! shouldn't yield 6*5 , it should yield 6*5*4*3*2*1 .)

Answer 2

Not infinite. It is, in fact, a classic example of inductive definition, which in programming translates into recursion. For it to work, there need to be two parts:

• Terminating condition, that describes when the problem is simple enough that we know the answer. In this case, what to do for fact(0) .
• Non-terminating condition, that describes how to break down a complex problem into simpler ones. In this case, look up fact(n - 1) and multiply by n .

So... let's say you have fact(3) . It is not terminating, so it is 3 * fact(2) . Still not terminating, so it is 3 * (2 * fact(1)) . Still going! 3 * (2 * (1 * fact(0))) . And there's our terminating condition, which does not call fact any more: 3 * (2 * (1 * (1))) . So... not so infinite :)