Year 2019 Day 12

README.md

@@ -204,6 +204,7 @@ pie
 | 9 | [Sensor Boost](https://adventofcode.com/2019/day/9) | [Source](src/year2019/day09.rs) | 1356 |
 | 10 | [Monitoring Station](https://adventofcode.com/2019/day/10) | [Source](src/year2019/day10.rs) | 1001 |
 | 11 | [Space Police](https://adventofcode.com/2019/day/11) | [Source](src/year2019/day11.rs) | 470 |
+| 12 | [The N-Body Problem](https://adventofcode.com/2019/day/12) | [Source](src/year2019/day12.rs) | 1024 |
 
 ## 2015
 

benches/benchmark.rs

@@ -60,6 +60,7 @@ mod year2019 {
     benchmark!(year2019, day09);
     benchmark!(year2019, day10);
     benchmark!(year2019, day11);
+    benchmark!(year2019, day12);
 }
 
 mod year2020 {

input/year2019/day12.txt

@@ -0,0 +1,4 @@
+<x=17, y=-12, z=13>
+<x=2, y=1, z=1>
+<x=-1, y=-17, z=7>
+<x=12, y=-14, z=18>

src/lib.rs

@@ -113,6 +113,7 @@ pub mod year2019 {
     pub mod day09;
     pub mod day10;
     pub mod day11;
+    pub mod day12;
 }
 
 /// # What could go wrong trying to enjoy a well deserved vacation?

src/main.rs

@@ -98,6 +98,7 @@ fn all_solutions() -> Vec<Solution> {
         solution!(year2019, day09),
         solution!(year2019, day10),
         solution!(year2019, day11),
+        solution!(year2019, day12),
         // 2020
         solution!(year2020, day01),
         solution!(year2020, day02),

src/year2019/day12.rs

@@ -0,0 +1,94 @@
+//! # The N-Body Problem
+//!
+//! There are two insights needed to solve part two:
+//!
+//! * Each axis is independent
+//! * Each axis is periodic somewhat like
+//!   [simple harmonic motion](https://en.wikipedia.org/wiki/Simple_harmonic_motion).
+//!   The velocity returns to zero twice per period.
+//!
+//! First find the period of each axis, then the answer is the
+//! [least common multiple](https://en.wikipedia.org/wiki/Least_common_multiple) of all three
+//! combined.
+//!
+//! The [`signum`] function comes in handy when updating the velocity.
+//!
+//! [`signum`]: i32::signum
+use crate::util::math::*;
+use crate::util::parse::*;
+
+type Axis = [i32; 8];
+type Input = [Axis; 3];
+
+/// Group each axis together
+pub fn parse(input: &str) -> Input {
+    let n: Vec<_> = input.iter_signed().collect();
+    [
+        [n[0], n[3], n[6], n[9], 0, 0, 0, 0],
+        [n[1], n[4], n[7], n[10], 0, 0, 0, 0],
+        [n[2], n[5], n[8], n[11], 0, 0, 0, 0],
+    ]
+}
+
+pub fn part1(input: &Input) -> i32 {
+    let [mut x, mut y, mut z] = *input;
+
+    for _ in 0..1000 {
+        x = step(x);
+        y = step(y);
+        z = step(z);
+    }
+
+    let e: Vec<_> = (0..8).map(|i| x[i].abs() + y[i].abs() + z[i].abs()).collect();
+    e[0] * e[4] + e[1] * e[5] + e[2] * e[6] + e[3] * e[7]
+}
+
+pub fn part2(input: &Input) -> usize {
+    let [mut x, mut y, mut z] = *input;
+    let [mut a, mut b, mut c] = [0, 0, 0];
+    let mut count = 0;
+
+    while a == 0 || b == 0 || c == 0 {
+        count += 1;
+
+        if a == 0 {
+            x = step(x);
+            if stopped(x) {
+                a = count;
+            }
+        }
+
+        if b == 0 {
+            y = step(y);
+            if stopped(y) {
+                b = count;
+            }
+        }
+
+        if c == 0 {
+            z = step(z);
+            if stopped(z) {
+                c = count;
+            }
+        }
+    }
+
+    // a, b and c are the half period, so multiply by 2 to get final result.
+    2 * a.lcm(b.lcm(c))
+}
+
+fn step(axis: Axis) -> Axis {
+    // "p" is position and "v" velocity
+    let [p0, p1, p2, p3, v0, v1, v2, v3] = axis;
+
+    let n0 = v0 + (p1 - p0).signum() + (p2 - p0).signum() + (p3 - p0).signum();
+    let n1 = v1 + (p0 - p1).signum() + (p2 - p1).signum() + (p3 - p1).signum();
+    let n2 = v2 + (p0 - p2).signum() + (p1 - p2).signum() + (p3 - p2).signum();
+    let n3 = v3 + (p0 - p3).signum() + (p1 - p3).signum() + (p2 - p3).signum();
+
+    [p0 + n0, p1 + n1, p2 + n2, p3 + n3, n0, n1, n2, n3]
+}
+
+fn stopped(axis: Axis) -> bool {
+    axis[4] == 0 && axis[5] == 0 && axis[6] == 0 && axis[7] == 0
+}

tests/test.rs

@@ -53,6 +53,7 @@ mod year2019 {
     mod day09_test;
     mod day10_test;
     mod day11_test;
+    mod day12_test;
 }
 
 mod year2020 {

tests/year2019/day12_test.rs

@@ -0,0 +1,19 @@
+use aoc::year2019::day12::*;
+
+const EXAMPLE: &str = "
+<x=-8, y=-10, z=0>
+<x=5, y=5, z=10>
+<x=2, y=-7, z=3>
+<x=9, y=-8, z=-3>";
+
+#[test]
+fn part1_test() {
+    let input = parse(EXAMPLE);
+    assert_eq!(part1(&input), 14645);
+}
+
+#[test]
+fn part2_test() {
+    let input = parse(EXAMPLE);
+    assert_eq!(part2(&input), 4686774924);
+}