Year 2018 Day 18

Author: maneatingape

README.md

@@ -254,6 +254,7 @@ Performance is reasonable even on older hardware, for example a 2011 MacBook Pro
 | 15 | [Beverage Bandits](https://adventofcode.com/2018/day/15) | [Source](src/year2018/day15.rs) | 584 |
 | 16 | [Chronal Classification](https://adventofcode.com/2018/day/16) | [Source](src/year2018/day16.rs) | 36 |
 | 17 | [Reservoir Research ](https://adventofcode.com/2018/day/17) | [Source](src/year2018/day17.rs) | 145 |
+| 18 | [Settlers of The North Pole](https://adventofcode.com/2018/day/18) | [Source](src/year2018/day18.rs) | 387 |
 
 ## 2017
 

benches/benchmark.rs

@@ -141,6 +141,7 @@ mod year2018 {
     benchmark!(year2018, day15);
     benchmark!(year2018, day16);
     benchmark!(year2018, day17);
+    benchmark!(year2018, day18);
 }
 
 mod year2019 {

src/lib.rs

@@ -129,6 +129,7 @@ pub mod year2018 {
     pub mod day15;
     pub mod day16;
     pub mod day17;
+    pub mod day18;
 }
 
 /// # Rescue Santa from deep space with a solar system voyage.

src/main.rs

@@ -197,6 +197,7 @@ fn year2018() -> Vec<Solution> {
         solution!(year2018, day15),
         solution!(year2018, day16),
         solution!(year2018, day17),
+        solution!(year2018, day18),
     ]
 }
 

src/year2018/day18.rs

@@ -0,0 +1,176 @@
+//! # Settlers of The North Pole
+//!
+//! This problem is a cellular automaton similar to the well known
+//! [Game of Life](https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life). To solve part two
+//! we look for a [cycle](https://en.wikipedia.org/wiki/Cycle_detection) then
+//! extrapolate forward a billion generations.
+//!
+//! To efficiently compute the next generation a [SWAR](https://en.wikipedia.org/wiki/SWAR)
+//! approach is used. The count of trees and lumberyards is packed into a `u64` so that we can
+//! process 8 acres at a time. Lumberyards are stored in the high nibble of each byte
+//! and trees in the low nibble. For example:
+//!
+//! ```none
+//!     .#.#...|
+//!     .....#|# => 11 11 21 11 21 02 21 02 => 0x1111211121022102
+//!     .|..|...
+//! ```
+//!
+//! The total number of adjacent trees or lumberyards is then calculated in two passes.
+//! First the horizontal sum of each row is computed by bit shifting left and right by 8.
+//! Then the vertical sum of 3 horizontal sums gives the total.
+//!
+//! Bitwise logic then computes the next generation in batches of 8 acres at a time.
+use crate::util::hash::*;
+use std::hash::{Hash, Hasher};
+
+/// Bitwise logic galore.
+const OPEN: u64 = 0x00;
+const TREE: u64 = 0x01;
+const LUMBERYARD: u64 = 0x10;
+const EDGE: u64 = 0xffff000000000000;
+const LOWER: u64 = 0x0f0f0f0f0f0f0f0f;
+const UPPER: u64 = 0xf0f0f0f0f0f0f0f0;
+const THIRTEENS: u64 = 0x0d0d0d0d0d0d0d0d;
+const FIFTEENS: u64 = 0x0f0f0f0f0f0f0f0f;
+
+/// New type wrapper so that we can use a custom hash function.
+#[derive(PartialEq, Eq)]
+pub struct Key {
+    area: [u64; 350],
+}
+
+/// Hash only two cells as a reasonable tradeoff between speed and collision resistance.
+impl Hash for Key {
+    fn hash<H: Hasher>(&self, state: &mut H) {
+        self.area[100].hash(state);
+        self.area[200].hash(state);
+    }
+}
+
+/// Pack the input into an array of `u64`.
+/// The input is 50 acres wide, so requires `ceil(50 / 8) = 7` elements for each row.
+pub fn parse(input: &str) -> Key {
+    let mut area = [0; 350];
+
+    for (y, line) in input.lines().map(str::as_bytes).enumerate() {
+        for (x, byte) in line.iter().enumerate() {
+            let acre = match byte {
+                b'|' => TREE,
+                b'#' => LUMBERYARD,
+                _ => OPEN,
+            };
+            let index = (y * 7) + (x / 8);
+            let offset = 56 - 8 * (x % 8);
+            area[index] |= acre << offset;
+        }
+    }
+
+    Key { area }
+}
+
+/// Compute 10 generations.
+pub fn part1(input: &Key) -> u32 {
+    let mut area = input.area;
+    let mut rows = [0; 364];
+
+    for _ in 0..10 {
+        step(&mut area, &mut rows);
+    }
+
+    resource_value(&area)
+}
+
+/// Compute generations until a cycle is detected.
+pub fn part2(input: &Key) -> u32 {
+    let mut area = input.area;
+    let mut rows = [0; 364];
+    let mut seen = FastMap::with_capacity(1_000);
+
+    for minute in 1.. {
+        step(&mut area, &mut rows);
+
+        if let Some(previous) = seen.insert(Key { area }, minute) {
+            // Find the index of the state after 1 billion repetitions.
+            let offset = 1_000_000_000 - previous;
+            let cycle_width = minute - previous;
+            let remainder = offset % cycle_width;
+            let target = previous + remainder;
+
+            let (result, _) = seen.iter().find(|(_, &i)| i == target).unwrap();
+            return resource_value(&result.area);
+        }
+    }
+
+    unreachable!()
+}
+
+fn step(area: &mut [u64], rows: &mut [u64]) {
+    // Compute the horizontal sum of each column with its immediate neighbors.
+    for y in 0..50 {
+        // Shadow slices at correct starting offset for convenience. We pad `rows` on the top and
+        // bottom then shift index by 7 to avoid having to check for edge conditions.
+        let area = &area[7 * y..];
+        let rows = &mut rows[7 * (y + 1)..];
+
+        rows[0] = horizontal_sum(0, area[0], area[1]);
+        rows[1] = horizontal_sum(area[0], area[1], area[2]);
+        rows[2] = horizontal_sum(area[1], area[2], area[3]);
+        rows[3] = horizontal_sum(area[2], area[3], area[4]);
+        rows[4] = horizontal_sum(area[3], area[4], area[5]);
+        rows[5] = horizontal_sum(area[4], area[5], area[6]);
+        rows[6] = horizontal_sum(area[5], area[6], 0);
+
+        // The grid is 50 wide so the last 6 bytes in each row are unused and must be set to zero.
+        rows[6] &= EDGE;
+    }
+
+    for i in 0..350 {
+        // Sum of all adjacent trees and lumberyards, not including center acre.
+        let acre = area[i];
+        let sum = rows[i] + rows[i + 7] + rows[i + 14] - acre;
+
+        // Add 13 so that any values 3 and higher overflow into high nibble.
+        let mut to_tree = (sum & LOWER) + THIRTEENS;
+        // Clear low nibble as this is irrelevant.
+        to_tree &= UPPER;
+        // To become a tree, we must be open space.
+        to_tree &= !(acre | (acre << 4));
+        // Shift result back to low nibble.
+        to_tree >>= 4;
+
+        // Check for any values 3 or higher.
+        let mut to_lumberyard = ((sum >> 4) & LOWER) + THIRTEENS;
+        // Clear low nibble.
+        to_lumberyard &= UPPER;
+        // To become a lumberyard, we must already be a tree.
+        to_lumberyard &= acre << 4;
+        // Spread result to both high and low nibble. We will later XOR this to flip correct bits.
+        to_lumberyard |= to_lumberyard >> 4;
+
+        // We must be a lumberyard.
+        let mut to_open = acre & UPPER;
+        // Check for at least one adjacent tree.
+        to_open &= (sum & LOWER) + FIFTEENS;
+        // Check for at least one adjacent lumberyard.
+        to_open &= ((sum >> 4) & LOWER) + FIFTEENS;
+        // Flip bit as we will later XOR.
+        to_open ^= acre & UPPER;
+
+        // Flip relevant bits to transition to next state.
+        area[i] = acre ^ (to_tree | to_lumberyard | to_open);
+    }
+}
+
+/// Convenience method that also takes correct byte from left and right neighbors.
+#[inline]
+fn horizontal_sum(left: u64, middle: u64, right: u64) -> u64 {
+    (left << 56) + (middle >> 8) + middle + (middle << 8) + (right >> 56)
+}
+
+/// Each tree or lumberyard is represented by a single bit.
+fn resource_value(area: &[u64]) -> u32 {
+    let trees: u32 = area.iter().map(|n| (n & LOWER).count_ones()).sum();
+    let lumberyards: u32 = area.iter().map(|n| (n & UPPER).count_ones()).sum();
+    trees * lumberyards
+}

tests/test.rs

@@ -130,6 +130,7 @@ mod year2018 {
     mod day15_test;
     mod day16_test;
     mod day17_test;
+    mod day18_test;
 }
 
 mod year2019 {

tests/year2018/day18_test.rs

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