Using itertools for arbitrary number of nested loops of different ranges with dependencies?

Question

Given a list of upperbounds: B1, B2, .. BN;
Dependency Functions: f1, ..., fN-1,

I'm wondering if there's a recipe using itertools or other classes in python for:

for i1 in range(0, B1):  
    for i2 in range(f1(i1), B2): ...
         for iN in range(fN-1(iN-1), BN)
             dostuff(i1, i2, ... iN)

Where there are N levels of nesting?
I want to use this helper function like this:
dependentProducts(Bs, fs, dostuff),
which returns a list or iterable

Ideally, the implementation would be iterative instead of recursive.

Answer 1

An iterative solution using @LaurentLAPORTE's setup. Put this code right under his and it should work. My args is a stack of the arguments fed into dostuff whenever it's full. The actual solution is the middle part, top and bottom parts are just testing.

stefan = []
def dostuff(*args):
    stefan.append(list(args))

args = [-1]
while args:
    n = len(args)
    args[-1] += 1
    if args[-1] >= B[n-1]:
        args.pop()
    elif n == len(B):
        dostuff(*args)
    else:
        args.append(F[n](args[-1]) - 1)

assert expected == stefan