|
| 1 | +use std::{fmt::Debug, time::Instant}; |
| 2 | + |
| 3 | +use itertools::Itertools; |
| 4 | +use rand::{thread_rng, Rng}; |
| 5 | + |
| 6 | +struct BitField { |
| 7 | + data: Vec<u64>, |
| 8 | + bits: usize, |
| 9 | + rank: Vec<u32>, |
| 10 | +} |
| 11 | + |
| 12 | +impl BitField { |
| 13 | + fn new() -> Self { |
| 14 | + Self { |
| 15 | + data: vec![], |
| 16 | + bits: 0, |
| 17 | + rank: vec![], |
| 18 | + } |
| 19 | + } |
| 20 | + |
| 21 | + fn push(&mut self, value: bool) { |
| 22 | + if self.data.len() * 64 <= self.bits { |
| 23 | + self.rank.push( |
| 24 | + self.rank.last().copied().unwrap_or_default() |
| 25 | + + self.data.last().copied().unwrap_or_default().count_ones(), |
| 26 | + ); |
| 27 | + self.data.push(0); |
| 28 | + } |
| 29 | + if value { |
| 30 | + self.data[self.bits / 64] |= 1 << (self.bits & 63); |
| 31 | + } |
| 32 | + self.bits += 1; |
| 33 | + } |
| 34 | + |
| 35 | + fn get(&self, index: usize) -> bool { |
| 36 | + self.data[index / 64] & (1 << (index & 63)) != 0 |
| 37 | + } |
| 38 | + |
| 39 | + fn get2(&self, index: usize) -> u32 { |
| 40 | + (self.data[index / 32] >> ((2 * index) & 63)) as u32 & 3 |
| 41 | + } |
| 42 | + |
| 43 | + fn rank(&self, index: usize) -> usize { |
| 44 | + let r = self.rank[index / 64]; |
| 45 | + (r + (self.data[index / 64] & !(u64::MAX << (index & 63))).count_ones()) as usize |
| 46 | + } |
| 47 | +} |
| 48 | + |
| 49 | +impl Debug for BitField { |
| 50 | + fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { |
| 51 | + f.debug_struct("BitField") |
| 52 | + .field("data", &self.data) |
| 53 | + .field("bits", &self.bits) |
| 54 | + .finish() |
| 55 | + } |
| 56 | +} |
| 57 | + |
| 58 | +struct BinaryPrefixTree { |
| 59 | + data: BitField, |
| 60 | +} |
| 61 | + |
| 62 | +const MAX_LEVEL: usize = 30; |
| 63 | + |
| 64 | +impl BinaryPrefixTree { |
| 65 | + fn new(values: &[u32]) -> Self { |
| 66 | + let mut data = BitField::new(); |
| 67 | + for level in (0..MAX_LEVEL).rev() { |
| 68 | + let mut previous_prefix = None; |
| 69 | + let mut occurrences = 0; |
| 70 | + for value in values { |
| 71 | + let prefix = *value >> level; |
| 72 | + if let Some(prev) = previous_prefix { |
| 73 | + if prefix >> 1 != prev { |
| 74 | + data.push(occurrences & 1 != 0); |
| 75 | + data.push(occurrences & 2 != 0); |
| 76 | + occurrences = 0; |
| 77 | + } |
| 78 | + } |
| 79 | + if prefix & 1 == 1 { |
| 80 | + occurrences |= 2; |
| 81 | + } else { |
| 82 | + occurrences |= 1; |
| 83 | + } |
| 84 | + previous_prefix = Some(prefix >> 1); |
| 85 | + } |
| 86 | + data.push(occurrences & 1 != 0); |
| 87 | + data.push(occurrences & 2 != 0); |
| 88 | + } |
| 89 | + println!("encoded size: {}", data.bits as f32 / values.len() as f32); |
| 90 | + Self { data } |
| 91 | + } |
| 92 | + |
| 93 | + fn check(&self, value: u32) -> bool { |
| 94 | + let mut i = 0; |
| 95 | + for level in (0..MAX_LEVEL).rev() { |
| 96 | + if value & (1 << level) != 0 { |
| 97 | + i += 1; |
| 98 | + } |
| 99 | + if !self.data.get(i) { |
| 100 | + return false; |
| 101 | + } |
| 102 | + i = self.data.rank(i + 1) * 2; |
| 103 | + } |
| 104 | + true |
| 105 | + } |
| 106 | + |
| 107 | + fn as_iter(&self) -> BinaryPrefixTreeIterator<'_> { |
| 108 | + BinaryPrefixTreeIterator::new(self) |
| 109 | + } |
| 110 | + |
| 111 | + #[inline(always)] |
| 112 | + fn recurse(&self, node: usize, level: usize, value: u32, results: &mut Vec<u32>) { |
| 113 | + if level == 1 { |
| 114 | + self.recurse1(node, value, results); |
| 115 | + } else { |
| 116 | + let n = self.data.get2(node); |
| 117 | + let value = value * 2; |
| 118 | + let mut r = self.data.rank(node * 2); |
| 119 | + if n & 1 != 0 { |
| 120 | + r += 1; |
| 121 | + self.recurse(r, level - 1, value, results); |
| 122 | + } |
| 123 | + if n & 2 != 0 { |
| 124 | + r += 1; |
| 125 | + self.recurse(r, level - 1, value + 1, results); |
| 126 | + } |
| 127 | + } |
| 128 | + } |
| 129 | + |
| 130 | + #[inline(always)] |
| 131 | + fn recurse1(&self, node: usize, value: u32, results: &mut Vec<u32>) { |
| 132 | + let n = self.data.get2(node); |
| 133 | + let value = value * 2; |
| 134 | + let mut r = self.data.rank(node * 2); |
| 135 | + if n & 1 != 0 { |
| 136 | + r += 1; |
| 137 | + self.recurse0(r, value, results); |
| 138 | + } |
| 139 | + if n & 2 != 0 { |
| 140 | + r += 1; |
| 141 | + self.recurse0(r, value + 1, results); |
| 142 | + } |
| 143 | + } |
| 144 | + |
| 145 | + #[inline(always)] |
| 146 | + fn recurse0(&self, node: usize, value: u32, results: &mut Vec<u32>) { |
| 147 | + let n = self.data.get2(node); |
| 148 | + let value = value * 2; |
| 149 | + if n & 1 != 0 { |
| 150 | + results.push(value); |
| 151 | + } |
| 152 | + if n & 2 != 0 { |
| 153 | + results.push(value + 1); |
| 154 | + } |
| 155 | + } |
| 156 | +} |
| 157 | + |
| 158 | +trait TreeIterator { |
| 159 | + fn get(&self, level: usize) -> u32; |
| 160 | + fn down(&mut self, level: usize, value: bool); |
| 161 | +} |
| 162 | + |
| 163 | +struct BinaryPrefixTreeIterator<'a> { |
| 164 | + bpt: &'a BinaryPrefixTree, |
| 165 | + pos: [u32; MAX_LEVEL], |
| 166 | +} |
| 167 | + |
| 168 | +impl<'a> BinaryPrefixTreeIterator<'a> { |
| 169 | + fn new(bpt: &'a BinaryPrefixTree) -> Self { |
| 170 | + Self { |
| 171 | + bpt, |
| 172 | + pos: [0; MAX_LEVEL], |
| 173 | + } |
| 174 | + } |
| 175 | + |
| 176 | + fn into_iter(self) -> RustIterator<'a> { |
| 177 | + RustIterator::new(self) |
| 178 | + } |
| 179 | + |
| 180 | + fn into_vec(mut self) -> Vec<u32> { |
| 181 | + let mut res = vec![]; |
| 182 | + // init positions |
| 183 | + for level in (1..MAX_LEVEL).rev() { |
| 184 | + let index = self.pos[level]; |
| 185 | + let new_index = self.bpt.data.rank(index as usize) as u32 + 1; |
| 186 | + self.pos[level - 1] = new_index * 2; |
| 187 | + } |
| 188 | + let mut level = MAX_LEVEL - 1; |
| 189 | + let mut value = 0u32; |
| 190 | + while level < MAX_LEVEL { |
| 191 | + let v = self.bpt.data.get(self.pos[level] as usize); |
| 192 | + // println!("{value} {level} {} {v}", self.pos[level]); |
| 193 | + self.pos[level] += 1; |
| 194 | + if v { |
| 195 | + if level == 0 { |
| 196 | + res.push(value); |
| 197 | + value += 1 << level; |
| 198 | + level = value.trailing_zeros() as usize; |
| 199 | + } else { |
| 200 | + level -= 1; |
| 201 | + } |
| 202 | + } else { |
| 203 | + value += 1 << level; |
| 204 | + level = value.trailing_zeros() as usize; |
| 205 | + } |
| 206 | + } |
| 207 | + res |
| 208 | + } |
| 209 | +} |
| 210 | + |
| 211 | +impl<'a> TreeIterator for BinaryPrefixTreeIterator<'a> { |
| 212 | + fn get(&self, level: usize) -> u32 { |
| 213 | + self.bpt.data.get2(self.pos[level] as usize) |
| 214 | + } |
| 215 | + |
| 216 | + fn down(&mut self, level: usize, value: bool) { |
| 217 | + let index = self.pos[level] * 2 + value as u32; |
| 218 | + let new_index = self.bpt.data.rank(index as usize + 1); |
| 219 | + self.pos[level - 1] = new_index as u32; |
| 220 | + } |
| 221 | +} |
| 222 | + |
| 223 | +struct RustIterator<'a> { |
| 224 | + inner: BinaryPrefixTreeIterator<'a>, |
| 225 | + level: usize, |
| 226 | + item: u32, |
| 227 | +} |
| 228 | + |
| 229 | +impl<'a> RustIterator<'a> { |
| 230 | + fn new(inner: BinaryPrefixTreeIterator<'a>) -> Self { |
| 231 | + Self { |
| 232 | + inner, |
| 233 | + level: MAX_LEVEL - 1, |
| 234 | + item: 0, |
| 235 | + } |
| 236 | + } |
| 237 | +} |
| 238 | + |
| 239 | +impl<'a> Iterator for RustIterator<'a> { |
| 240 | + type Item = u32; |
| 241 | + |
| 242 | + fn next(&mut self) -> Option<u32> { |
| 243 | + while self.level < MAX_LEVEL { |
| 244 | + let bitmask = self.inner.get(self.level); |
| 245 | + let curr = self.item & (1 << self.level); |
| 246 | + if curr == 0 && bitmask & 1 != 0 { |
| 247 | + if self.level == 0 { |
| 248 | + let res = self.item; |
| 249 | + self.item += 1; |
| 250 | + return Some(res); |
| 251 | + } |
| 252 | + self.inner.down(self.level, false); |
| 253 | + self.level -= 1; |
| 254 | + } else if bitmask & 2 != 0 { |
| 255 | + if curr == 0 { |
| 256 | + self.item += 1 << self.level; |
| 257 | + } |
| 258 | + if self.level == 0 { |
| 259 | + let res = self.item; |
| 260 | + self.item += 1; |
| 261 | + self.level = self.item.trailing_zeros() as usize + 1; |
| 262 | + return Some(res); |
| 263 | + } |
| 264 | + self.inner.down(self.level, true); |
| 265 | + self.level -= 1; |
| 266 | + } else { |
| 267 | + self.item += 1 << self.level; |
| 268 | + self.level = self.item.trailing_zeros() as usize; |
| 269 | + } |
| 270 | + } |
| 271 | + None |
| 272 | + } |
| 273 | +} |
| 274 | + |
| 275 | +#[test] |
| 276 | +fn test_bpt() { |
| 277 | + let values = &[3, 6, 7, 10]; |
| 278 | + let bpt = BinaryPrefixTree::new(values); |
| 279 | + println!("{:x?} {:?}", bpt.data.data, bpt.data.rank); |
| 280 | + assert!(!bpt.check(0)); |
| 281 | + assert!(!bpt.check(1)); |
| 282 | + assert!(!bpt.check(2)); |
| 283 | + assert!(bpt.check(3)); |
| 284 | + assert!(!bpt.check(4)); |
| 285 | + assert!(!bpt.check(5)); |
| 286 | + assert!(bpt.check(6)); |
| 287 | + assert!(bpt.check(7)); |
| 288 | + assert!(!bpt.check(8)); |
| 289 | + assert!(!bpt.check(9)); |
| 290 | + assert!(bpt.check(10)); |
| 291 | + |
| 292 | + /* let mut iter = bpt.as_iter(); |
| 293 | + assert_eq!(iter.get(7), 1); |
| 294 | + iter.down(7, false); |
| 295 | + assert_eq!(iter.get(6), 1); |
| 296 | + iter.down(6, false); |
| 297 | + assert_eq!(iter.get(5), 1); |
| 298 | + iter.down(5, false); |
| 299 | + assert_eq!(iter.get(4), 1); |
| 300 | + iter.down(4, false); |
| 301 | + assert_eq!(iter.get(3), 3); |
| 302 | + iter.down(3, false); |
| 303 | + assert_eq!(iter.get(2), 3); |
| 304 | + iter.down(2, false); |
| 305 | + assert_eq!(iter.get(1), 2); |
| 306 | + iter.down(1, true); |
| 307 | + assert_eq!(iter.get(0), 2);*/ |
| 308 | + |
| 309 | + let iter = bpt.as_iter().into_iter(); |
| 310 | + assert_eq!(iter.collect_vec(), values.iter().copied().collect_vec()); |
| 311 | + |
| 312 | + assert_eq!( |
| 313 | + bpt.as_iter().into_vec(), |
| 314 | + values.iter().copied().collect_vec() |
| 315 | + ); |
| 316 | +} |
| 317 | + |
| 318 | +#[test] |
| 319 | +fn test_intersection() { |
| 320 | + let start = Instant::now(); |
| 321 | + // let mut values = (0..1) |
| 322 | + let mut values = (0..1000000) |
| 323 | + .map(|_| thread_rng().gen_range(0..100000000)) |
| 324 | + .collect_vec(); |
| 325 | + values.sort(); |
| 326 | + values.dedup(); |
| 327 | + println!("generation of values {:?}", start.elapsed()); |
| 328 | + |
| 329 | + let start = Instant::now(); |
| 330 | + let bpt = BinaryPrefixTree::new(&values); |
| 331 | + println!("construction of tree {:?}", start.elapsed()); |
| 332 | + |
| 333 | + let start = Instant::now(); |
| 334 | + assert_eq!(bpt.as_iter().into_iter().collect_vec(), values); |
| 335 | + println!("iteration {:?}", start.elapsed()); |
| 336 | + |
| 337 | + let start = Instant::now(); |
| 338 | + let mut v = Vec::with_capacity(values.len()); |
| 339 | + bpt.recurse(0, MAX_LEVEL - 1, 0, &mut v); |
| 340 | + assert_eq!(v, values); |
| 341 | + println!("recursive collect {:?}", start.elapsed()); |
| 342 | + |
| 343 | + let start = Instant::now(); |
| 344 | + let v = bpt.as_iter().into_vec(); |
| 345 | + println!("iteration {:?}", start.elapsed()); |
| 346 | + assert_eq!(bpt.as_iter().into_vec(), values); |
| 347 | + |
| 348 | + let start = Instant::now(); |
| 349 | + let mut v = Vec::with_capacity(values.len()); |
| 350 | + for i in values.iter() { |
| 351 | + v.push(*i); |
| 352 | + } |
| 353 | + println!("iteration {:?}", start.elapsed()); |
| 354 | + assert_eq!(v, values); |
| 355 | +} |
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