Year 2017 Day 16

Author: maneatingape

README.md

@@ -251,6 +251,7 @@ Performance is reasonable even on older hardware, for example a 2011 MacBook Pro
 | 13 | [Packet Scanners](https://adventofcode.com/2017/day/13) | [Source](src/year2017/day13.rs) | 2 |
 | 14 | [Disk Defragmentation](https://adventofcode.com/2017/day/14) | [Source](src/year2017/day14.rs) | 422 |
 | 15 | [Dueling Generators](https://adventofcode.com/2017/day/15) | [Source](src/year2017/day15.rs) | 425000 |
+| 16 | [Permutation Promenade](https://adventofcode.com/2017/day/16) | [Source](src/year2017/day16.rs) | 66 |
 
 ## 2016
 

benches/benchmark.rs

@@ -116,6 +116,7 @@ mod year2017 {
     benchmark!(year2017, day13);
     benchmark!(year2017, day14);
     benchmark!(year2017, day15);
+    benchmark!(year2017, day16);
 }
 
 mod year2019 {

src/lib.rs

@@ -98,6 +98,7 @@ pub mod year2017 {
     pub mod day13;
     pub mod day14;
     pub mod day15;
+    pub mod day16;
 }
 
 /// # Rescue Santa from deep space with a solar system adventure.

src/main.rs

@@ -163,6 +163,7 @@ fn year2017() -> Vec<Solution> {
         solution!(year2017, day13),
         solution!(year2017, day14),
         solution!(year2017, day15),
+        solution!(year2017, day16),
     ]
 }
 

src/year2017/day16.rs

@@ -0,0 +1,113 @@
+//! # Permutation Promenade
+//!
+//! The key insight is that a complete dance can be represented by just two transformations.
+//! The spin and exchange moves compose into a single transformation and the partner swaps compose
+//! into a second independent transformation.
+//!
+//! Each transformation can then be applied to itself to double the effect. For example a single
+//! complete dance turns into two dances, then doubles to four dances and so on.
+//!
+//! This allows us to compute part two with a similar approach to
+//! [exponentiation by squaring](https://en.wikipedia.org/wiki/Exponentiation_by_squaring).
+use crate::util::parse::*;
+use std::array::from_fn;
+
+#[derive(Copy, Clone)]
+pub struct Dance {
+    /// The letter in each position from left to right
+    /// with `a` represented by 0, `b` by 1 and so on.
+    position: [usize; 16],
+    /// A map of initial letter to final letter taking into account all partner swaps.
+    /// `a` is at index 0, `b` at index 1. For convenience letters are represented by 0..15.
+    exchange: [usize; 16],
+}
+
+impl Dance {
+    /// Creates a new Dance that represents the identity transformation.
+    fn new() -> Dance {
+        Dance { position: from_fn(|i| i), exchange: from_fn(|i| i) }
+    }
+
+    /// Converts a Dance into a string representation.
+    fn apply(self) -> String {
+        self.position.iter().map(|&i| to_char(self.exchange[i])).collect()
+    }
+
+    /// Combines two Dances into a new Dance.
+    fn compose(self, other: Dance) -> Dance {
+        let position = self.position.map(|i| other.position[i]);
+        let exchange = self.exchange.map(|i| other.exchange[i]);
+        Dance { position, exchange }
+    }
+}
+
+/// Reduces all 10,000 individual dance moves into just two independent transformations.
+pub fn parse(input: &str) -> Dance {
+    // Tokenize the input into two parallel iterators
+    let mut letters = input.bytes().filter(u8::is_ascii_lowercase);
+    let mut numbers = input.iter_unsigned::<usize>();
+
+    let mut offset = 0;
+    let mut lookup: [usize; 16] = from_fn(|i| i);
+    let Dance { mut position, mut exchange } = Dance::new();
+
+    while let Some(op) = letters.next() {
+        match op {
+            // Increasing the offset has the same effect as rotating elements to the right.
+            b's' => {
+                offset += 16 - numbers.next().unwrap();
+            }
+            // Swap two elements taking into account the offset when calculating indices.
+            b'x' => {
+                let first = numbers.next().unwrap();
+                let second = numbers.next().unwrap();
+                position.swap((first + offset) % 16, (second + offset) % 16);
+            }
+            // First lookup the index of each letter, then swap the mapping.
+            b'p' => {
+                let first = from_byte(letters.next().unwrap());
+                let second = from_byte(letters.next().unwrap());
+                lookup.swap(first, second);
+                exchange.swap(lookup[first], lookup[second]);
+            }
+            _ => unreachable!(),
+        }
+    }
+
+    // Rotate the array once to apply all spins.
+    position.rotate_left(offset % 16);
+
+    Dance { position, exchange }
+}
+
+/// Apply the transformation once.
+pub fn part1(input: &Dance) -> String {
+    input.apply()
+}
+
+/// If a bit is set in the binary representation of 1 billion apply the current transformation,
+/// then apply the transformation to itself to double the number of complete dances.
+pub fn part2(input: &Dance) -> String {
+    let mut e = 1_000_000_000;
+    let mut dance = *input;
+    let mut result = Dance::new();
+
+    while e > 0 {
+        if e & 1 == 1 {
+            result = result.compose(dance);
+        }
+
+        e >>= 1;
+        dance = dance.compose(dance);
+    }
+
+    result.apply()
+}
+
+fn from_byte(b: u8) -> usize {
+    (b - b'a') as usize
+}
+
+fn to_char(i: usize) -> char {
+    ((i as u8) + b'a') as char
+}

tests/test.rs

@@ -100,6 +100,7 @@ mod year2017 {
     mod day13_test;
     mod day14_test;
     mod day15_test;
+    mod day16_test;
 }
 
 mod year2019 {

tests/year2017/day16_test.rs

@@ -0,0 +1,9 @@
+#[test]
+fn part1_test() {
+    // No example data
+}
+
+#[test]
+fn part2_test() {
+    // No example data
+}