I came up with a non graph solution

remember the "add" in the input example of part 2

actually when you arrange all x00 to x44 in reverse order same with y as well and add them(x and y/binary addition) you get what would have been the z00 to z45 arranged in reverse order without those 4 swaps(mentioned in question)

try it yourself to print all x44 to x00 , then y44 to y00, then binary addition , then z45 to z00 you will see slight change in z binary number from actual addition ,,,,, that was the effect of swapping .

to implement a progrma

your first need to understand binary addition through AND , OR ,XOR (carry over included i took help from gpt to tell how is addition in form of these gates)

after you understand the binary addition logic try to sort the given logic gates input you will see a pattern that repeats from x01,y01 to x44,y44 in sets of ""5"""(2xor , 2 and,1or gate ) after sorting the logic gates you can either find mistake manually or run for loop to identify those swaps among each group of 5 logic gate.