Question on runtime and improving nested for loops

[ackmondual]

I'm writing code to find all solutions of a commercial, physical puzzle.  This is done by having the script go through all possible configurations/permutations, check to see if it works, and record the results into a text file.  

I've broken down that puzzle into 9 pieces (represented by the list), with each piece having 4 states (NOT represented).  Part of the algorithm is to evaluate all possible permutations of 9 pieces across all 4 states.
For example...
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 2
... and then eventually to
0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 1 1
0 0 0 0 0 0 0 1 2
etc.



The code I have to go through all combinations of all 9 elements, with each element having 4 different states is below.

QUESTION 1)
Are there alternative ways to go about this besides a 9-level deep, nested for loop, with each loop going to a max of 4?
MIDEDIT: I've been made aware of itertools, but will need to come back to it later after I have the chance to look through it
ht  tps://docs.python.org/3/library/itertools.html

l = [a, b, c, d, e, f, g, h, i]
for i1 in range(4):
   for i2 in range(4):
       for i3 in range(4):
           #and then 6 more levels deep

QUESTION 2) What's the runtime?  Are my calculations correct?
Not only do I need to do the above, but I need to do the above for each combination of placements in the list.  For example, I also have to repeat that code with the list as:
[a, b, c, d, e, f, g, i, h]
For this, I'm using Heap's Algorithm, which looks like it's n factorial iterations!
ht  tps://en.wikipedia.org/wiki/Heap%27s_algorithm
I'm not sure how practical it is for me to run through this, as it looks like each check gets done...
9! * (4^9)
362,880 * 262,144
87,869,214,720 total times!

I was going to leave this running overnight, but it looks like this may take a few days, or beyond!  I want to make sure it's something that won't take too much time to solve.

[ichabod801]

First, you definitely need to look at itertools, as you said you would. It will be way more optimized than doing the loops yourself. Second, brute force is rarely a good idea. You need to look at optimizing your algorithm before you look at optimizing your program. Ask yourself what the standard human techniques for solving the problem are, and try to make use of that. Ask yourself how you can narrow the search space (even iteratively), and make use of that. Third, if you are looking at running things all night, Python is probably not the correct tool. I would switch to a compiled language at that point, or at least look for the choke points in the program and get compiled solutions for those (which is really what using itertools is doing).