this post was submitted on 10 Dec 2025
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Advent Of Code
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An unofficial home for the advent of code community on programming.dev! Other challenges are also welcome!
Advent of Code is an annual Advent calendar of small programming puzzles for a variety of skill sets and skill levels that can be solved in any programming language you like.
Everybody Codes is another collection of programming puzzles with seasonal events.
EC 2025
AoC 2025
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Rust
Only took four days, but I made it, and without any maths libraries. I tried lots of unsuccessful searches (including A*) before realizing part 2 is a linear equation system. Then I tried to find all solutions by just going row by row, guessing all but one unknown variable and finding the smallest solution, but this was still way too slow due to the high amount of variables guessed.
By looking around on Wikipedia I found that the problem could be simplified by turning the matrix into Smith Normal Form or Hermitian Normal Form, but couldn't find any Rust library implementing these. Their algorithms looked just a bit too complicated to implement myself. Maybe I would have used Python, because sagemath has everything, but the problem of ultimately finding the smallest integer solution still remained, and I already had the search code in Rust without simplifying the matrix.
So put the matrix into echelon form by implementing Gaussian elimination, which wasn't too bad, and it significantly reduced the number of variables to guess. Now part 2 runs in 70ms.
View code on github
I'm still attempting to make "no lib" solution using matrices and Gaussian elimination. It definitely reduces my solution space, but I'm still struggling to find a good approach to search the space.
My next step is gonna be somehow extracting inequality boundaries, lock a variable at the boundary and solve that reduced equation system. Unfortunately I have no good way to get lower bounds like I do on paper (by default lower bounds for all variables are 0).
After looking at examples of graphical linear system solutions my hope is that optimal solutions will sit on these intersections between equations. The idea hinges on these equations being linear, meaning that without curves there should be no other optimum solutions.
On paper, looking at the inequality ranges, one variable maximum seems imply a minimum for another (in case there are two variables). Searching for solutions by solving smaller and smaller systems with these locked variables feels like a probable approach.
Congrats! I'll try not to peek at your code, but will definitely try to repeat your process. I want to remove z3 from my solution.
Nice job! I initially thought about using reduced-row echelon form, but the matrices all had infinitely many real solutions so I couldn't figure out how to proceed. Instead, I scanned Wikipedia for a bit, found the two-phase simplex algorithm, spent two days getting it to work on paper and another day implementing it.
And the reward?
I'm not even done because ~10% of the systems have non-integer optima, so I still need to use cutting planes to add extra constraints to get the integer optima.