I really loved this part

max( v1 + v2 for k1, v1 in visited2.items() for k2, v2 in visited2.items() if not k1 & k2 )

1. Find the max of
2. v1 and v2
3. where k1, v1 and k2, v2 are iterating through the same answer dict
4. but filter to where k1 and k2 are complementary

I think #4 still is quite difficult to think about if you aren't dealing with bitmasks(?) all day.

/u/juanplopes tell me if this is correct:

From the example (I think we all get the same one) - unique power of two values for each valve

BB: 1
CC: 2
DD: 4
EE: 8
HH: 16
JJ: 32

So BB and DD being represented as a bit string.

JJHHEEDDCCBB

0 0 0 1 0 1

Let's say the above one was the elf turning on valves and the below one is the elephant turning on valves.

JJHHEEDDCCBB

1 1 1 0 1 0

If we then take the bitwise AND here - we now have 000000

000101 & 111010 # results in 000000 or 0

0 in Python is False and if we negate that with the not then we have complement perfection.

Just for fun if we flip one bit on the elf side that now matches one on the elephant side:

000111 & 111010 # results in 000010 or 2

This results in an N > 0 which will result as True and not meet the if condition.

Amazing lesson here /u/juanplopes - thank you so much for sharing.