From fdbbd934a491a03e970204b8b0693df0af6fed10 Mon Sep 17 00:00:00 2001
From: Jan-Bulthuis <git@bulthuis.dev>
Date: Sat, 14 Dec 2024 22:55:40 +0100
Subject: [PATCH] Rewrote part 2 using Chinese Remainder theorem

---
 aoc_2024/Cargo.lock   |  7 +++++
 aoc_2024/Cargo.toml   |  1 +
 aoc_2024/src/day14.rs | 63 +++++++++++++++++++++----------------------
 3 files changed, 39 insertions(+), 32 deletions(-)

diff --git a/aoc_2024/Cargo.lock b/aoc_2024/Cargo.lock
index 1eb54fe..17a4a9b 100644
--- a/aoc_2024/Cargo.lock
+++ b/aoc_2024/Cargo.lock
@@ -55,6 +55,7 @@ dependencies = [
  "hashbrown",
  "nom",
  "num",
+ "num-modular",
  "regex",
  "topological-sort",
 ]
@@ -169,6 +170,12 @@ dependencies = [
  "num-traits",
 ]
 
+[[package]]
+name = "num-modular"
+version = "0.6.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "17bb261bf36fa7d83f4c294f834e91256769097b3cb505d44831e0a179ac647f"
+
 [[package]]
 name = "num-rational"
 version = "0.4.2"
diff --git a/aoc_2024/Cargo.toml b/aoc_2024/Cargo.toml
index 72c8b23..5a4b35d 100644
--- a/aoc_2024/Cargo.toml
+++ b/aoc_2024/Cargo.toml
@@ -9,5 +9,6 @@ aoc-runner-derive = "0.3.0"
 hashbrown = "0.15.2"
 nom = "7.1.3"
 num = "0.4.3"
+num-modular = "0.6.1"
 regex = "1.11.1"
 topological-sort = "0.2.2"
diff --git a/aoc_2024/src/day14.rs b/aoc_2024/src/day14.rs
index eb5e3b8..9368665 100644
--- a/aoc_2024/src/day14.rs
+++ b/aoc_2024/src/day14.rs
@@ -1,5 +1,3 @@
-use std::sync::OnceLock;
-
 use aoc_runner_derive::{aoc, aoc_generator};
 
 use nom::{
@@ -10,6 +8,8 @@ use nom::{
     sequence::{preceded, separated_pair},
 };
 
+use num_modular::ModularPow;
+
 type Input = Vec<((i64, i64), (i64, i64))>;
 
 #[aoc_generator(day14)]
@@ -54,43 +54,42 @@ fn part1(input: &Input) -> i64 {
 }
 
 #[aoc(day14, part2)]
-fn part2(input: &Input) -> usize {
+fn part2(input: &Input) -> i64 {
     let (w, h) = (101, 103);
 
-    let mut input = input.clone();
-
-    let mut iter = 0;
-
-    loop {
-        iter += 1;
-
-        let mut total = (0f64, 0f64);
-        input = input
-            .into_iter()
-            .map(|((px, py), (vx, vy))| {
-                let (px, py) = ((px + vx + w) % w, (py + vy + h) % h);
-                total.0 += px as f64;
-                total.1 += py as f64;
-                ((px, py), (vx, vy))
-            })
-            .collect();
-        let mean = (total.0 / input.len() as f64, total.1 / input.len() as f64);
-        let variance = input
-            .iter()
-            .map(|((px, py), _)| {
-                let dx = *px as f64 - mean.0;
-                let dy = *py as f64 - mean.1;
-                dx * dx + dy * dy
-            })
+    let mut offset_x = 0;
+    let mut min_var = f64::INFINITY;
+    for t in 0..w {
+        let values = input.iter().map(|((p, _), (v, _))| (p + t * (v + w)) % w);
+        let mean = values.clone().sum::<i64>() as f64 / input.len() as f64;
+        let variance = values
+            .map(|v| (v as f64 - mean) * (v as f64 - mean))
             .sum::<f64>()
             / input.len() as f64;
-
-        if variance < 1000.0 {
-            break;
+        if variance < min_var {
+            min_var = variance;
+            offset_x = t;
         }
     }
 
-    iter
+    let mut offset_y = 0;
+    let mut min_var = f64::INFINITY;
+    for t in 0..h {
+        let values = input.iter().map(|((_, p), (_, v))| (p + t * (v + h)) % h);
+        let mean = values.clone().sum::<i64>() as f64 / input.len() as f64;
+        let variance = values
+            .map(|v| (v as f64 - mean) * (v as f64 - mean))
+            .sum::<f64>()
+            / input.len() as f64;
+        if variance < min_var {
+            min_var = variance;
+            offset_y = t;
+        }
+    }
+
+    let invmod_x = (w as u64).powm((h - 2) as u64, &(h as u64)) as i64;
+    let invmod_y = (h as u64).powm((w - 2) as u64, &(w as u64)) as i64;
+    (offset_x * h * invmod_x + offset_y * w * invmod_y) % (w * h)
 }
 
 #[cfg(test)]