Advent of Code 2024 Week 2: this time it's all grids, all the time
Advent of Code 2024 Week 2: this time it's all grids, all the time
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Day 13, day 13 of shirking other responsibilities.
p1
Ok. So, I overthought this a little. Ultimately, this problem boils down to solving a system of 2 linear equations aka inverting a matrix.
Of course, anyone who has done undergraduate linear algebra knows to look to the determinant in case some shit goes down. For the general problem space, a zero determinant means that one equation is just a multiple of the other. A solution could still exist in this case. Consider:
a => x+1, y+1 b => x+2, y+2 x = 4, y = 4 (answer: 2 tokens)The following has no solution:
a => x+2, y+2 b => x+4, y+4 x = 3, y = 3I thought of all this, and instead of coding the solution, I just checked if any such cases were in my input. There weren't, and I was home free.
p2
No real changes to the solution to p1 aside from the new targets. I wasn't sure if 64 bit ints were big enough to fit the numbers so I changed my code to use big ints.
I'm looking at my code again and I'm pretty sure that was all unnecessary.
13 commentary
Solved p1 by graph search before looking a bit closer on the examples and going, oh...
In pt2 I had some floating point weirdness when solving for keypress count, I was checking if the key presses where integers (can't press button A five and half times after all) by checking if A = floor(A) and sometimes A would drop to the number below when floored, i.e. it was in reality (A-1).999999999999999999999999999999999999999999999. Whatever, I rounded it away but I did spend a stupid amount of time on it because it didn't happen in the example set.
I liked day 13, a bit easy but in the right way.
Edit:
Spoilers
Although saying "minimum" was a bit evil when all of the systems had exactly 1 solution (not necessarily in ℕ^2), I wonder if it's puzzle trickiness, anti-LLM (and unfortunate non comp-sci souls) trickiness or if the puzzle was maybe scaled down from a version where there are more solutions.
spoiler
Given the lack of edge cases, I feel the latter possibility is strong. I'm just glad it was easy!