|
| 1 | +use std::array; |
| 2 | +use utils::parser::{ParseError, ParseResult}; |
| 3 | +use utils::prelude::*; |
| 4 | + |
| 5 | +/// Iteratively applying pixel transformations. |
| 6 | +/// |
| 7 | +/// The key optimization is that every three iterations a 3x3 square splits into nine independent |
| 8 | +/// 3x3 squares. Therefore, we can store counts for each of the 512 unique 3x3 squares and simulate |
| 9 | +/// three iterations at a time for each square to find the counts for the following three iterations |
| 10 | +#[derive(Clone, Debug)] |
| 11 | +pub struct Day21 { |
| 12 | + part1: u32, |
| 13 | + part2: u32, |
| 14 | +} |
| 15 | + |
| 16 | +#[derive(Clone, Debug)] |
| 17 | +enum Rule { |
| 18 | + TwoToThree(usize, usize), |
| 19 | + ThreeToFour(usize, usize), |
| 20 | +} |
| 21 | + |
| 22 | +const START_3X3: usize = 0b010_001_111; |
| 23 | + |
| 24 | +impl Day21 { |
| 25 | + pub fn new(input: &str, _: InputType) -> Result<Self, InputError> { |
| 26 | + let parse_iterator = parser::one_of(( |
| 27 | + Self::parse_square::<3> |
| 28 | + .with_suffix(" => ") |
| 29 | + .then(Self::parse_square::<4>) |
| 30 | + .map(|(a, b)| Rule::ThreeToFour(a, b)), |
| 31 | + Self::parse_square::<2> |
| 32 | + .with_suffix(" => ") |
| 33 | + .then(Self::parse_square::<3>) |
| 34 | + .map(|(a, b)| Rule::TwoToThree(a, b)), |
| 35 | + )) |
| 36 | + .with_suffix(parser::eol()) |
| 37 | + .parse_iterator(input); |
| 38 | + |
| 39 | + let mut rules_2x2_to_3x3 = [0usize; 16]; |
| 40 | + let mut rules_3x3_to_4x4 = [0usize; 512]; |
| 41 | + for item in parse_iterator { |
| 42 | + match item? { |
| 43 | + Rule::TwoToThree(two, three) => { |
| 44 | + for transformed in Self::transformations_2x2(two) { |
| 45 | + rules_2x2_to_3x3[transformed] = three; |
| 46 | + } |
| 47 | + } |
| 48 | + Rule::ThreeToFour(three, four) => { |
| 49 | + for transformed in Self::transformations_3x3(three) { |
| 50 | + rules_3x3_to_4x4[transformed] = four; |
| 51 | + } |
| 52 | + } |
| 53 | + } |
| 54 | + } |
| 55 | + |
| 56 | + let (mut three_counts, mut three_counts_next) = ([0; 512], [0; 512]); |
| 57 | + three_counts[START_3X3] = 1; |
| 58 | + |
| 59 | + let mut on_pixels = [0; 21]; |
| 60 | + for i in (0..=18).step_by(3) { |
| 61 | + for (three, &count) in three_counts.iter().enumerate().filter(|(_, &c)| c > 0) { |
| 62 | + on_pixels[i] += three.count_ones() * count; |
| 63 | + |
| 64 | + let four = rules_3x3_to_4x4[three]; |
| 65 | + on_pixels[i + 1] += four.count_ones() * count; |
| 66 | + |
| 67 | + let six = Self::combine_3x3_into_6x6( |
| 68 | + Self::split_4x4_into_2x2(four).map(|two| rules_2x2_to_3x3[two]), |
| 69 | + ); |
| 70 | + on_pixels[i + 2] += six.count_ones() * count; |
| 71 | + |
| 72 | + for two in Self::split_6x6_into_2x2(six) { |
| 73 | + let next = rules_2x2_to_3x3[two]; |
| 74 | + three_counts_next[next] += count; |
| 75 | + } |
| 76 | + } |
| 77 | + |
| 78 | + three_counts = three_counts_next; |
| 79 | + three_counts_next.fill(0); |
| 80 | + } |
| 81 | + |
| 82 | + Ok(Self { |
| 83 | + part1: on_pixels[5], |
| 84 | + part2: on_pixels[18], |
| 85 | + }) |
| 86 | + } |
| 87 | + |
| 88 | + #[must_use] |
| 89 | + pub fn part1(&self) -> u32 { |
| 90 | + self.part1 |
| 91 | + } |
| 92 | + |
| 93 | + #[must_use] |
| 94 | + pub fn part2(&self) -> u32 { |
| 95 | + self.part2 |
| 96 | + } |
| 97 | + |
| 98 | + #[inline] |
| 99 | + fn parse_square<const N: usize>(mut input: &[u8]) -> ParseResult<usize> { |
| 100 | + let mut result = 0; |
| 101 | + for row in 0..N { |
| 102 | + for col in 0..N { |
| 103 | + match input.first() { |
| 104 | + Some(b'.') => {} |
| 105 | + Some(b'#') => result |= 1 << (col + N * row), |
| 106 | + _ => return Err((ParseError::Custom("expected '.' or '#'"), input)), |
| 107 | + } |
| 108 | + input = &input[1..]; |
| 109 | + } |
| 110 | + |
| 111 | + if row < N - 1 { |
| 112 | + if input.first().copied() != Some(b'/') { |
| 113 | + return Err((ParseError::Custom("expected '/'"), input)); |
| 114 | + } |
| 115 | + input = &input[1..]; |
| 116 | + } |
| 117 | + } |
| 118 | + |
| 119 | + Ok((result, input)) |
| 120 | + } |
| 121 | + |
| 122 | + #[inline] |
| 123 | + #[expect(clippy::identity_op)] |
| 124 | + fn transformations_2x2(square: usize) -> [usize; 4] { |
| 125 | + let b: [_; 4] = array::from_fn(|i| (square >> i) & 1); |
| 126 | + |
| 127 | + [ |
| 128 | + // | Original | 90° rotation | 180° rotation | 270° rotation | |
| 129 | + // | 01 | 20 | 32 | 13 | |
| 130 | + // | 23 | 31 | 10 | 02 | |
| 131 | + square, |
| 132 | + b[2] << 0 | b[0] << 1 | b[3] << 2 | b[1] << 3, |
| 133 | + b[3] << 0 | b[2] << 1 | b[1] << 2 | b[0] << 3, |
| 134 | + b[1] << 0 | b[3] << 1 | b[0] << 2 | b[2] << 3, |
| 135 | + ] |
| 136 | + } |
| 137 | + |
| 138 | + #[inline] |
| 139 | + #[rustfmt::skip] |
| 140 | + #[expect(clippy::identity_op)] |
| 141 | + fn transformations_3x3(square: usize) -> [usize; 8] { |
| 142 | + let b: [_; 9] = array::from_fn(|i| (square >> i) & 1); |
| 143 | + |
| 144 | + [ |
| 145 | + // | Original | 90° rotation | 180° rotation | 270° rotation | |
| 146 | + // | 012 | 630 | 876 | 258 | |
| 147 | + // | 345 | 741 | 543 | 147 | |
| 148 | + // | 678 | 852 | 210 | 036 | |
| 149 | + square, |
| 150 | + b[6] << 0 | b[3] << 1 | b[0] << 2 | b[7] << 3 | b[4] << 4 | b[1] << 5 | b[8] << 6 | b[5] << 7 | b[2] << 8, |
| 151 | + b[8] << 0 | b[7] << 1 | b[6] << 2 | b[5] << 3 | b[4] << 4 | b[3] << 5 | b[2] << 6 | b[1] << 7 | b[0] << 8, |
| 152 | + b[2] << 0 | b[5] << 1 | b[8] << 2 | b[1] << 3 | b[4] << 4 | b[7] << 5 | b[0] << 6 | b[3] << 7 | b[6] << 8, |
| 153 | + // | Flipped | 90° rotation | 180° rotation | 270° rotation | |
| 154 | + // | 678 | 036 | 210 | 852 | |
| 155 | + // | 345 | 147 | 543 | 741 | |
| 156 | + // | 012 | 258 | 876 | 630 | |
| 157 | + b[6] << 0 | b[7] << 1 | b[8] << 2 | b[3] << 3 | b[4] << 4 | b[5] << 5 | b[0] << 6 | b[1] << 7 | b[2] << 8, |
| 158 | + b[0] << 0 | b[3] << 1 | b[6] << 2 | b[1] << 3 | b[4] << 4 | b[7] << 5 | b[2] << 6 | b[5] << 7 | b[8] << 8, |
| 159 | + b[2] << 0 | b[1] << 1 | b[0] << 2 | b[5] << 3 | b[4] << 4 | b[3] << 5 | b[8] << 6 | b[7] << 7 | b[6] << 8, |
| 160 | + b[8] << 0 | b[5] << 1 | b[2] << 2 | b[7] << 3 | b[4] << 4 | b[1] << 5 | b[6] << 6 | b[3] << 7 | b[0] << 8, |
| 161 | + ] |
| 162 | + } |
| 163 | + |
| 164 | + #[inline] |
| 165 | + fn split_4x4_into_2x2(square: usize) -> [usize; 4] { |
| 166 | + // [ 0] 1 [ 2] 3 0 0 1 1 |
| 167 | + // 4 5 6 7 0 0 1 1 |
| 168 | + // [ 8] 9 [10] 11 2 2 3 3 |
| 169 | + // 12 13 14 15 2 2 3 3 |
| 170 | + [0, 2, 8, 10].map(|i| ((square >> i) & 0b11) | ((square >> (i + 4)) & 0b11) << 2) |
| 171 | + } |
| 172 | + |
| 173 | + #[inline] |
| 174 | + fn combine_3x3_into_6x6(squares: [usize; 4]) -> usize { |
| 175 | + // [ 0] 1 2 [ 3] 4 5 [0] 0-2 [1] 0-2 |
| 176 | + // 6 7 8 9 10 11 [0] 3-5 [1] 3-5 |
| 177 | + // 12 13 14 15 16 17 [0] 6-8 [1] 6-8 |
| 178 | + // [18] 19 20 [21] 22 23 [2] 0-2 [3] 0-2 |
| 179 | + // 24 25 26 27 28 29 [2] 3-5 [3] 3-5 |
| 180 | + // 30 31 32 33 34 35 [2] 6-8 [3] 6-8 |
| 181 | + let mut result = 0; |
| 182 | + for (&square, offset) in squares.iter().zip([0, 3, 18, 21]) { |
| 183 | + result |= (square & 0b111) << offset |
| 184 | + | ((square >> 3) & 0b111) << (offset + 6) |
| 185 | + | ((square >> 6) & 0b111) << (offset + 12); |
| 186 | + } |
| 187 | + result |
| 188 | + } |
| 189 | + |
| 190 | + #[inline] |
| 191 | + fn split_6x6_into_2x2(square: usize) -> [usize; 9] { |
| 192 | + // [ 0] 1 [ 2] 3 [ 4] 5 0 0 1 1 2 2 |
| 193 | + // 6 7 8 9 10 11 0 0 1 1 2 2 |
| 194 | + // [12] 13 [14] 15 [16] 17 3 3 4 4 5 5 |
| 195 | + // 18 19 20 21 22 23 3 3 4 4 5 5 |
| 196 | + // [24] 25 [26] 27 [28] 29 6 6 7 7 8 8 |
| 197 | + // 30 31 32 33 34 35 6 6 7 7 8 8 |
| 198 | + [0, 2, 4, 12, 14, 16, 24, 26, 28] |
| 199 | + .map(|i| ((square >> i) & 0b11) | ((square >> (i + 6)) & 0b11) << 2) |
| 200 | + } |
| 201 | +} |
| 202 | + |
| 203 | +examples!(Day21 -> (u32, u32) []); |
0 commit comments