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| 1 | +use std::cmp::Ordering; |
| 2 | +use std::collections::BinaryHeap; |
| 3 | +use utils::geometry::Vec3; |
| 4 | +use utils::prelude::*; |
| 5 | + |
| 6 | +/// Finding the point in range of the most nodes. |
| 7 | +#[derive(Clone, Debug)] |
| 8 | +pub struct Day23 { |
| 9 | + bots: Vec<Bot>, |
| 10 | +} |
| 11 | + |
| 12 | +#[derive(Clone, Debug)] |
| 13 | +struct Bot { |
| 14 | + pos: Vec3<i32>, |
| 15 | + r: u32, |
| 16 | +} |
| 17 | + |
| 18 | +// 2**29 seems to be the max range of the input, and 2**29 * 3 fits within i32 without overflow. |
| 19 | +const MAX_POW2: u32 = 29; |
| 20 | +const MIN: i32 = -(1 << MAX_POW2); |
| 21 | +const MAX: i32 = (1 << MAX_POW2) - 1; |
| 22 | + |
| 23 | +impl Day23 { |
| 24 | + pub fn new(input: &str, _: InputType) -> Result<Self, InputError> { |
| 25 | + Ok(Self { |
| 26 | + bots: parser::number_range(MIN..=MAX) |
| 27 | + .repeat_n(b',') |
| 28 | + .with_prefix("pos=<") |
| 29 | + .with_suffix(">, r=") |
| 30 | + .then(parser::u32()) |
| 31 | + .map(|(pos, r)| Bot { pos: pos.into(), r }) |
| 32 | + .parse_lines(input)?, |
| 33 | + }) |
| 34 | + } |
| 35 | + |
| 36 | + #[must_use] |
| 37 | + pub fn part1(&self) -> usize { |
| 38 | + let strongest = self.bots.iter().max_by_key(|b| b.r).unwrap(); |
| 39 | + |
| 40 | + self.bots |
| 41 | + .iter() |
| 42 | + .filter(|&b| b.pos.manhattan_distance_to(strongest.pos) <= strongest.r) |
| 43 | + .count() |
| 44 | + } |
| 45 | + |
| 46 | + #[must_use] |
| 47 | + pub fn part2(&self) -> u32 { |
| 48 | + let initial = Subcube::new(Vec3::splat(MIN), Vec3::splat(MAX), &self.bots); |
| 49 | + |
| 50 | + let mut heap = BinaryHeap::with_capacity(2048); |
| 51 | + heap.push(initial); |
| 52 | + |
| 53 | + while let Some(s) = heap.pop() { |
| 54 | + if s.size == 1 { |
| 55 | + return s.dist; |
| 56 | + } |
| 57 | + heap.extend(s.split(&self.bots)); |
| 58 | + } |
| 59 | + |
| 60 | + unreachable!() |
| 61 | + } |
| 62 | +} |
| 63 | + |
| 64 | +#[derive(Clone, Debug, Eq, PartialEq)] |
| 65 | +struct Subcube { |
| 66 | + min: Vec3<i32>, |
| 67 | + max: Vec3<i32>, |
| 68 | + bot_count: usize, |
| 69 | + dist: u32, |
| 70 | + size: u32, |
| 71 | +} |
| 72 | + |
| 73 | +impl Subcube { |
| 74 | + #[inline] |
| 75 | + fn new(min: Vec3<i32>, max: Vec3<i32>, bots: &[Bot]) -> Self { |
| 76 | + Self { |
| 77 | + min, |
| 78 | + max, |
| 79 | + bot_count: bots |
| 80 | + .iter() |
| 81 | + .filter(|&bot| bot.pos.manhattan_distance_to_aabb(min, max) <= bot.r) |
| 82 | + .count(), |
| 83 | + dist: Vec3::ORIGIN.manhattan_distance_to_aabb(min, max), |
| 84 | + size: max.x.abs_diff(min.x) + 1, |
| 85 | + } |
| 86 | + } |
| 87 | + |
| 88 | + #[inline] |
| 89 | + fn split(&self, bots: &[Bot]) -> [Self; 8] { |
| 90 | + let half = (self.size / 2) as i32; |
| 91 | + let xs = [ |
| 92 | + (self.min.x, self.min.x + half - 1), |
| 93 | + (self.min.x + half, self.max.x), |
| 94 | + ]; |
| 95 | + let ys = [ |
| 96 | + (self.min.y, self.min.y + half - 1), |
| 97 | + (self.min.y + half, self.max.y), |
| 98 | + ]; |
| 99 | + let zs = [ |
| 100 | + (self.min.z, self.min.z + half - 1), |
| 101 | + (self.min.z + half, self.max.z), |
| 102 | + ]; |
| 103 | + |
| 104 | + std::array::from_fn(|i| { |
| 105 | + let (min_x, max_x) = xs[i >> 2]; |
| 106 | + let (min_y, max_y) = ys[(i >> 1) & 1]; |
| 107 | + let (min_z, max_z) = zs[i & 1]; |
| 108 | + Self::new( |
| 109 | + Vec3::new(min_x, min_y, min_z), |
| 110 | + Vec3::new(max_x, max_y, max_z), |
| 111 | + bots, |
| 112 | + ) |
| 113 | + }) |
| 114 | + } |
| 115 | +} |
| 116 | + |
| 117 | +impl Ord for Subcube { |
| 118 | + #[inline] |
| 119 | + fn cmp(&self, other: &Self) -> Ordering { |
| 120 | + // Sort by bot count ascending, dist descending, size descending. |
| 121 | + // When used inside a MaxHeap this will order entries by the reverse (bot count descending, |
| 122 | + // dist ascending, size ascending), which ensures the first point visited is optimal. |
| 123 | + self.bot_count |
| 124 | + .cmp(&other.bot_count) |
| 125 | + .then(self.dist.cmp(&other.dist).reverse()) |
| 126 | + .then(self.size.cmp(&other.size).reverse()) |
| 127 | + } |
| 128 | +} |
| 129 | + |
| 130 | +impl PartialOrd for Subcube { |
| 131 | + #[inline] |
| 132 | + fn partial_cmp(&self, other: &Self) -> Option<Ordering> { |
| 133 | + Some(self.cmp(other)) |
| 134 | + } |
| 135 | +} |
| 136 | + |
| 137 | +examples!(Day23 -> (usize, u32) [ |
| 138 | + { |
| 139 | + input: "pos=<0,0,0>, r=4\n\ |
| 140 | + pos=<1,0,0>, r=1\n\ |
| 141 | + pos=<4,0,0>, r=3\n\ |
| 142 | + pos=<0,2,0>, r=1\n\ |
| 143 | + pos=<0,5,0>, r=3\n\ |
| 144 | + pos=<0,0,3>, r=1\n\ |
| 145 | + pos=<1,1,1>, r=1\n\ |
| 146 | + pos=<1,1,2>, r=1\n\ |
| 147 | + pos=<1,3,1>, r=1", |
| 148 | + part1: 7, |
| 149 | + }, |
| 150 | + { |
| 151 | + input: "pos=<10,12,12>, r=2\n\ |
| 152 | + pos=<12,14,12>, r=2\n\ |
| 153 | + pos=<16,12,12>, r=4\n\ |
| 154 | + pos=<14,14,14>, r=6\n\ |
| 155 | + pos=<50,50,50>, r=200\n\ |
| 156 | + pos=<10,10,10>, r=5", |
| 157 | + part2: 36, |
| 158 | + }, |
| 159 | +]); |
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