Day 22 part 2

Cargo.lock

@@ -15,10 +15,11 @@ dependencies = [
 name = "aoc_2019"
 version = "0.1.0"
 dependencies = [
- "itertools",
- "modinverse",
- "num-integer",
- "regex",
+    "itertools",
+    "mod_exp",
+    "modinverse",
+    "num-integer",
+    "regex",
 ]
 
 [[package]]
@@ -39,7 +40,7 @@ version = "0.10.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "a9a9d19fa1e79b6215ff29b9d6880b706147f16e9b1dbb1e4e5947b5b02bc5e3"
 dependencies = [
- "either",
+    "either",
 ]
 
 [[package]]
@@ -48,13 +49,45 @@ version = "2.4.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "308cc39be01b73d0d18f82a0e7b2a3df85245f84af96fdddc5d202d27e47b86a"
 
+[[package]]
+name = "mod_exp"
+version = "1.0.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "bb4a3fad6af79fcf8d1417b2f6359d814a173fb413a1bd48ba04208b42b0d8b0"
+dependencies = [
+    "num",
+]
+
 [[package]]
 name = "modinverse"
 version = "0.1.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "2f62f577f148cc1a9466e7065a22e59466a7d537cceba5e77e57181d0f706633"
 dependencies = [
- "num-integer",
+    "num-integer",
+]
+
+[[package]]
+name = "num"
+version = "0.2.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "b8536030f9fea7127f841b45bb6243b27255787fb4eb83958aa1ef9d2fdc0c36"
+dependencies = [
+    "num-complex",
+    "num-integer",
+    "num-iter",
+    "num-rational",
+    "num-traits",
+]
+
+[[package]]
+name = "num-complex"
+version = "0.2.4"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "b6b19411a9719e753aff12e5187b74d60d3dc449ec3f4dc21e3989c3f554bc95"
+dependencies = [
+    "autocfg",
+    "num-traits",
 ]
 
 [[package]]
@@ -63,8 +96,30 @@ version = "0.1.44"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "d2cc698a63b549a70bc047073d2949cce27cd1c7b0a4a862d08a8031bc2801db"
 dependencies = [
- "autocfg",
- "num-traits",
+    "autocfg",
+    "num-traits",
+]
+
+[[package]]
+name = "num-iter"
+version = "0.1.43"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "7d03e6c028c5dc5cac6e2dec0efda81fc887605bb3d884578bb6d6bf7514e252"
+dependencies = [
+    "autocfg",
+    "num-integer",
+    "num-traits",
+]
+
+[[package]]
+name = "num-rational"
+version = "0.2.4"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "5c000134b5dbf44adc5cb772486d335293351644b801551abe8f75c84cfa4aef"
+dependencies = [
+    "autocfg",
+    "num-integer",
+    "num-traits",
 ]
 
 [[package]]
@@ -73,7 +128,7 @@ version = "0.2.14"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "9a64b1ec5cda2586e284722486d802acf1f7dbdc623e2bfc57e65ca1cd099290"
 dependencies = [
- "autocfg",
+    "autocfg",
 ]
 
 [[package]]

Cargo.toml

@@ -11,3 +11,4 @@ itertools = "0.10.3"
 regex = "1.5.5"
 num-integer = "0.1.44"
 modinverse = "0.1.1"
+mod_exp = "1.0.1"

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));
     }
 }