How does reduce function work?

Question

As far as I understand, the reduce function takes a list l and a function f. Then, it calls the function f on first two elements of the list and then repeatedly calls the function f with the next list element and the previous result.

So, I define the following functions:

The following function computes the factorial.

def fact(n):
    if n == 0 or n == 1:
        return 1
    return fact(n-1) * n


def reduce_func(x,y):
    return fact(x) * fact(y)

lst = [1, 3, 1]
print reduce(reduce_func, lst)

Now, shouldn't this give me ((1! * 3!) * 1!) = 6? But, instead it gives 720. Why 720? It seems to take the factorial of 6 too. But, I need to understand why.

Can someone explains why this happens and a work-around?

I basically want to compute the product of factorials of all the entries in the list. The backup plan is to run a loop and compute it. But, I would prefer using reduce.

Answer 1

Ok, got it:

I need to map the numbers to their factorials first and then call reduce with multiply operator.

So, this would work:

lst_fact = map(fact, lst)
reduce(operator.mul, lst_fact)