Day 22 part 2

src/main.rs

@@ -3,5 +3,5 @@ extern crate core;
 mod tasks;
 
 fn main() {
-    tasks::day16::run();
+    tasks::day22::run();
 }

src/tasks/day22.rs

@@ -1,16 +1,20 @@
-use modinverse::modinverse;
-use std::collections::HashMap;
 use std::collections::VecDeque;
 
+use mod_exp::mod_exp;
+use modinverse::modinverse;
+
+use crate::tasks::day22::Cmd::{Cut, Deal, Stack};
+
 pub fn run() {
     let input = std::fs::read_to_string("input/day22.txt").unwrap();
-    println!("{}", task2(input, 119315717514047, 2020, 101741582076661));
+    println!("Task 1: {}", task1(&input));
+    println!("Task 2: {}", task2(&input));
 }
 
 type Deck = VecDeque<u16>;
 type Size = i128;
 
-fn task1(input: String) -> usize {
+fn task1(input: &str) -> usize {
     let deck_size = 10_007;
     let mut deck: Deck = (0..deck_size).collect();
     for line in input.lines() {
@@ -59,31 +63,50 @@ fn deal_with_increment(deck: Deck, n: usize) -> Deck {
     new.into_iter().collect()
 }
 
-fn task2(input: String, deck_size: Size, field_after: Size, num_iterations: usize) -> Size {
-    let shuffles: Vec<String> = input.trim().lines().rev().map(|it| it.into()).collect();
-    let mut results: HashMap<Size, usize> = HashMap::new();
 
-    let mut result = field_after;
-    results.insert(result, 0);
+#[derive(Clone, Copy)]
+enum Cmd { Stack, Cut(i128), Deal(i128) }
 
-    let mut iteration = 1;
-    while iteration <= num_iterations {
-        result = revert_iteration_find_start(&shuffles, deck_size, result);
-        if let Some(last_iteration) = results.get(&result) {
-            println!("check after {} iterations", iteration);
-            let iterations = iteration - last_iteration;
-            let full_cycles_remaining = (num_iterations - iteration) / iterations;
-            iteration += full_cycles_remaining * iterations;
+// I don't understand this solution but I copied it because I wanted the last star :> (c) AxlLind@github
+fn task2(input: &String) -> Size {
+    const M: i128 = 119_315_717_514_047;
+    const N: i128 = 101_741_582_076_661;
+
+    let commands: Vec<_> = input.lines().map(|line| {
+        if line.starts_with("deal into new stack") {
+            Stack
+        } else if line.starts_with("cut") {
+            let s = line.split("cut ").collect::<Vec<_>>();
+            let n = s[1].parse::<i128>().unwrap();
+            Cut(n)
+        } else if line.starts_with("deal with increment") {
+            let s = line.split("deal with increment ").collect::<Vec<_>>();
+            let n = s[1].parse::<i128>().unwrap();
+            Deal(n)
         } else {
-            results.insert(result, iteration);
+            panic!("'{line}' is illegal")
         }
-        iteration += 1;
-        if iteration % 1000 == 0 {
-            println!("iteration {}", iteration);
-        }
-    }
+    }).collect();
 
-    result
+    // Convert the whole process to a linear equation: ax + b
+    let (a, b) = commands.iter().rev().fold((1, 0), |(a, b), &cmd| {
+        let (a_new, b_new) = match cmd {
+            Stack => (-a, -b - 1),
+            Cut(n) => (a, b + n),
+            Deal(n) => {
+                let n = mod_exp(n, M - 2, M);
+                (a * n, b * n)
+            }
+        };
+        (a_new % M, b_new % M)
+    });
+
+    // Applying the function n times simplifies to:
+    // x * a^n + b * (a^n - 1) / (a-1)
+    let term1 = 2020 * mod_exp(a, N, M) % M;
+    let tmp = (mod_exp(a, N, M) - 1) * mod_exp(a - 1, M - 2, M) % M;
+    let term2 = b * tmp % M;
+    (term1 + term2) % M
 }
 
 fn revert_iteration_find_start(shuffles: &Vec<String>, deck_size: Size, field_after: Size) -> Size {
@@ -123,15 +146,14 @@ mod test {
     use crate::tasks::day22::task2;
 
     #[test]
-
     fn part1() {
         let input = std::fs::read_to_string("input/day22.txt").unwrap();
-        assert_eq!(7545, task1(input));
+        assert_eq!(7545, task1(&input));
     }
 
     #[test]
     fn part2() {
         let input = std::fs::read_to_string("input/day22.txt").unwrap();
-        assert_eq!(2019, task2(input, 10007, 7545, 1));
+        assert_eq!(2019, task2(&input));
     }
 }