# Advent of Code - 2019 - Day 21-22

The twenty-first problem was about writing a little bit of assembly-like code to solve a puzzle. Nothing algorithmic but instead a straight-forward puzzle. Part 1 was quite easy. The twist for part 2 made it a bit harder but not overly so. Run-time in Sophia was a few seconds for part 1 and a minute and a half for part 2. The Sophia `Intcode` interpreter isn’t super-fast…

``````43> aefa_sophia_test:run_file("/Users/hans/Personal/Repos/AoC2019/21/sol_21.aes", "solve_1", []).
0 steps / 173980099 gas / 0 reductions / 4115.54ms
19354083
44> aefa_sophia_test:run_file("/Users/hans/Personal/Repos/AoC2019/21/sol_21.aes", "solve_2", []).
0 steps / 86713494597 gas / 0 reductions / 96768.97ms
1143499964
``````
1 Like

The twenty-second problem was about shuffling a (huge) deck of cards. For part 1 you could get away with a naive implementation that actually did handle the deck of cards. But the run-time was not impressive (minutes in Sophia). To optimize you should figure out that the solution only asks for a single card (and hence a single index) in the deck. So we can transform the problem to only track one index at a time.

For part 2 where the deck isn’t huge but enormous (containing around 10^14 cards) this is crucial, and we should also perform the shuffling no less than 101741582076661 times. I.e. no naive solution will cut it. The key observation to make is that all different shuffle techniques are linear, i.e. we turn the sequence of shuffle-steps into a single function `ax + b = y`. So the problem reduces to finding `a` and `b` and then apply it to `101741582076661`. And all of this should be done modulo the deck size (a large prime). Lots of things to get wrong, but once the bits fall into place the code turns out nicely and it
runs quickly.

``````53> aefa_sophia_test:run_file("/Users/hans/Personal/Repos/AoC2019/22/sol_22.aes", "solve_1", []).
0 steps / 22218 gas / 0 reductions / 7.65ms
7860
54> aefa_sophia_test:run_file("/Users/hans/Personal/Repos/AoC2019/22/sol_22.aes", "solve_2", []).
0 steps / 205431 gas / 0 reductions / 43.75ms
61256063148970
``````
2 Likes

Impressive again. Very impressive.