1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503
//! Diving deeper into mathematics, huh? In here you'll find mathematical sets - Sometimes pretty handy!
/// Brings mathematical sets into Rust.
#[derive(Debug, Clone)]
pub struct VecSet<'a, T> {
elements: Vec<T>,
parent: Option<&'a VecSet<'a, T>>,
}
// Main impl
impl<'a, T: Copy + Ord> VecSet<'a, T> {
/// Creates a new `VecSet`.
/// # Arguments
/// * `values` - The values for the `VecSet`.
/// # Returns
/// A new `VecSet`.
///
/// # Examples
/// ```
/// use lib_rapid::math::sets::vec_sets::VecSet;
///
/// let set = VecSet::new(&vec![0, 1, 2, 3, 4, 5]);
/// assert_eq!(set.elements(), &vec![0, 1, 2, 3, 4, 5]);
/// ```
#[inline]
#[must_use]
pub fn new(values: &[T]) -> VecSet<'a, T> {
let mut res: VecSet<T> = VecSet { elements: values.to_vec(),
parent: None };
res.elements.sort_unstable();
res.elements.dedup();
res
}
/// Get the empty set, ∅.
/// # Returns
/// A `VecSet<T>` with no elements.
/// # Examples
/// ```
/// use lib_rapid::math::sets::vec_sets::{VecSet, set};
/// let v: Vec<u8> = Vec::new();
///
/// assert_eq!(v, VecSet::empty_set().elements());
/// ```
#[inline]
#[must_use]
pub fn empty_set() -> VecSet<'a, T> {
VecSet { elements: Vec::new(), parent: None }
}
/// Creates a new `VecSet` using a parent-`VecSet` to which it applies a closure.
/// # Arguments
/// * `parent` - The `VecSet` from which the new `VecSet` emerges.
/// * `f` - The closure after which the new `VecSet` is created.
/// # Returns
/// A child `VecSet`.
/// # Examples
/// ```
/// use lib_rapid::math::sets::vec_sets::VecSet;
/// let test1: VecSet<u8> = VecSet::new(&vec![0,1,2,3,4]);
/// let from_parent: VecSet<u8> = VecSet::<u8>::new_subset(&test1, |x| x % 2 == 0);
/// assert_eq!(from_parent, VecSet::new(&vec![0,2,4]));
/// assert_eq!(test1.elements(), &vec![0,1,2,3,4])
/// ```
#[must_use]
pub fn new_subset<F: Fn(T) -> bool>(parent: &'a VecSet<T>, f: F) -> VecSet<'a, T> {
let mut res: VecSet<T> = VecSet { elements: Vec::with_capacity(parent.cardinality()),
parent: Some(parent) };
for elem in parent {
if f(elem) {
res.elements.push(elem);
}
}
res
}
/// Does a mathematical union on two VecSets.
/// `self ∪ other`.
/// # Arguments
/// * `self` - The first set.
/// * `other` - The second set.
/// # Returns
/// A new `VecSet<T>`: `self ∪ other`.
/// # Examples
/// ```
/// use lib_rapid::math::sets::vec_sets::VecSet;
/// use lib_rapid::math::sets::vec_sets::set;
/// use lib_rapid::compsci::general::BinaryInsert;
/// let s: VecSet<i32> = VecSet::new(&vec![0,1,2,3,4,5,6,7,8,9,10]);
/// let s1: VecSet<i32> = VecSet::new(&vec![11,12,13,13,11,0,0,0]);
///
/// let c: VecSet<i32> = s.union(&s1);
/// assert_eq!(c, set!(0,1,2,3,4,5,6,7,8,9,10,11,12,13));
/// ```
#[must_use]
pub fn union(&self, other: &VecSet<T>) -> VecSet<T> {
let mut res: VecSet<T> = VecSet {elements: Vec::with_capacity(self.cardinality() +
other.cardinality()),
parent: None };
res.elements.extend_from_slice(&self.elements);
res.elements.extend_from_slice(&other.elements);
res.elements.sort_unstable();
res.elements.dedup();
res
}
/// Does a mathematical intersection on two sets.
/// # Arguments
/// * `self` - The first set.
/// * `other` - The second set.
/// # Returns
/// A new `VecSet<T>`: `self ∩ other`.
/// # Examples
/// ```
/// use lib_rapid::math::sets::vec_sets::VecSet;
/// use lib_rapid::math::sets::vec_sets::set;
/// use lib_rapid::compsci::general::BinaryInsert; // Used for "set!"
///
/// let s: VecSet<i32> = VecSet::new(&vec![0,1,2,3,4,5,6,7,8,9,10,11]);
/// let s2: VecSet<i32> = VecSet::new(&vec![0,1,2,3,11,0,0,0]);
///
/// let c: VecSet<i32> = s.intersection(&s2);
/// assert_eq!(c, set!(0, 1, 2, 3, 11));
/// ```
#[must_use]
pub fn intersection(&self, other: &VecSet<T>) -> VecSet<T> {
let mut res: VecSet<T> = self.clone();
res.elements.retain(|x| other.elements.binary_search(x).is_ok());
res
}
/// Checks for disjointness between `self` and `other`.
/// # Arguments
/// * `other` - The other set to be checked for disjointness.
/// # Returns
/// A `bool`
/// # Examples
///```
/// use lib_rapid::math::sets::vec_sets::VecSet;
/// use lib_rapid::math::sets::vec_sets::set;
///
/// let s1 = set!(0, 1, 2, 3, 4, 5, 6, 7, 8);
/// let s2 = set!(0, 1, 2, 3, 4, 5, 6);
/// let s3 = set!(8, 9, 10, 11, 12, 13, 14);
/// let s4 = set!(9, 10, 11, 12, 13, 14, 15);
///
/// assert_eq!(false, s1.is_disjoint_with(&s2));
/// assert_eq!(false, s1.is_disjoint_with(&s3));
/// assert_eq!(true, s1.is_disjoint_with(&s4));
/// ```
#[must_use]
pub fn is_disjoint_with(&self, other: &VecSet<T>) -> bool {
for i in self {
if other.has_element(i)
{ return false; }
}
true
}
/// Checks for mathematical difference between two sets - `A \ B`.
/// # Arguments
/// * `other` - The other set to be checked for.
/// # Returns
/// A `VecSet<T>`.
/// # Examples
///```
/// use lib_rapid::math::sets::vec_sets::VecSet;
/// use lib_rapid::math::sets::vec_sets::set;
///
/// let s1 = set!(1, 2, 3, 4, 5);
/// let s2 = set!(3, 4, 5);
///
/// assert_eq!(set!(1, 2), s1.difference_with(&s2));
///```
#[must_use]
pub fn difference_with(&self, other: &VecSet<T>) -> VecSet<T> {
let mut res_vec: Vec<T> = Vec::with_capacity(std::cmp::max(self.cardinality(), other.cardinality()));
for i in self {
if !other.has_element(i)
{ res_vec.push(i); }
}
VecSet { elements: res_vec,
parent: None }
}
/// Gets the cartesian product of two sets in `O(n·m)`.
/// # Arguments
/// * `other` - `&VecSet<T>`-
/// # Returns
/// A `VecSet<(T, T)>`.
///```
/// use lib_rapid::math::sets::vec_sets::VecSet;
/// use lib_rapid::math::sets::vec_sets::set;
///
/// let s1 = set!(1, 2, 3);
/// let s2 = set!(1, 2);
///
/// assert_eq!(set!((1, 1), (1, 2), (2, 1), (2, 2), (3, 1), (3, 2)), s1.cartesian_product(&s2));
///```
#[must_use]
pub fn cartesian_product(&self, other: &VecSet<T>) -> VecSet<(T, T)> {
let mut res_vec = Vec::with_capacity(self.cardinality() * other.cardinality());
for i in self {
for j in other {
res_vec.push((i, j));
}
}
VecSet { elements: res_vec, parent: None }
}
/// Gets the symmetric difference (Elements either in `self` or `other`, but not in both).
/// # Arguments
/// * `other` - A `&VecSet<T>`.
/// # Examples
///```
/// use lib_rapid::math::sets::vec_sets::VecSet;
/// use lib_rapid::math::sets::vec_sets::set;
///
/// let s1 = set!(1, 2, 3, 4, 5);
/// let s2 = set!(3, 4);
///
/// assert_eq!(set!(1, 2, 5), s1.symmetric_difference_with(&s2));
///```
#[must_use]
pub fn symmetric_difference_with(&self, other: &VecSet<T>) -> VecSet<T> {
let diff1 = self.difference_with(&other);
let diff2 = other.difference_with(&self).clone();
VecSet {elements: diff1.union(&diff2).elements,
parent: None }
}
/// Lets you check for an element in a set.
/// # Arguments
/// * `elem` - The element to check for.
/// # Returns
/// A boolean value which determines if `elem ∈ self`.
///
/// # Examples
/// ```
/// use lib_rapid::math::sets::vec_sets::VecSet;
/// use lib_rapid::math::sets::vec_sets::set;
///
/// let set = set!(0, 1, 2, 3, 4, 5, 6);
///
/// assert_eq!(false, set.has_element(7));
/// assert_eq!(false, set.has_element(-1));
/// assert_eq!(true, set.has_element(1));
/// ```
#[inline]
#[must_use]
pub fn has_element(&self, elem: T) -> bool {
self.elements.binary_search(&elem).is_ok()
}
/// Lets you insert an element into a set. Does not insert already present values.
/// # Arguments
/// * `elem` - The element to insert.
/// # Returns
/// Nothing.
/// # Examples
/// ```
/// use lib_rapid::math::sets::vec_sets::VecSet;
/// use lib_rapid::math::sets::vec_sets::set;
/// let mut s: VecSet<i32> = VecSet::new(&vec![0,1,2,3,4,5,6,7,8,9,10]);
///
/// s.insert(5);
/// assert_eq!(s.elements(), &vec![0,1,2,3,4,5,6,7,8,9,10]);
/// ```
pub fn insert(&mut self, elem: T) {
self.elements.binary_insert_no_dup(elem)
}
/// Lets you check wether a set has a parent (emerged from another set) or not.
/// # Returns
/// A boolean value which determines if the set is a subset of any other set.
/// # Examples
/// ```
/// use lib_rapid::math::sets::vec_sets::VecSet;
/// use lib_rapid::math::sets::vec_sets::set;
///
/// let set = set!(0, 1, 2, 3, 4, 5, 6);
/// let subset = VecSet::new_subset(&set, |x| x % 2 == 0);
///
/// assert_eq!(true, subset.has_emerged());
/// assert_eq!(false, set.has_emerged());
/// ```
#[inline]
#[must_use]
pub fn has_emerged(&self) -> bool {
self.parent.is_some()
}
/// Gets you the optional superset from which the Set emerged.
/// # Returns
/// A `Option<&VecSet<T>>`.
/// # Examples
/// ```
/// use lib_rapid::math::sets::vec_sets::VecSet;
/// use lib_rapid::math::sets::vec_sets::set;
///
/// let set = set!(0, 1, 2, 3, 4, 5, 6);
/// let subset = VecSet::new_subset(&set, |x| x % 2 == 0);
///
/// assert_eq!(&set, subset.get_parent().unwrap());
/// ```
#[inline]
#[must_use]
pub fn get_parent(&self) -> Option<&VecSet<T>> {
self.parent
}
/// Determines whether `self` is a subset of `other`, unconditional from whether `self` emerged from `other`.
/// # Arguments
/// * `other` - A `VecSet<T>`.
/// # Returns
/// A `bool`
/// # Examples
/// ```
/// use lib_rapid::math::sets::vec_sets::VecSet;
/// use lib_rapid::math::sets::vec_sets::set;
///
/// let set = set!(0, 1, 2, 3, 4, 5, 6);
/// let set2 = set!(0, 1, 2, 3, 4);
///
/// assert_eq!(false, set.is_subset_of(&set2));
/// assert_eq!(true, set2.is_subset_of(&set));
/// ```
#[must_use]
pub fn is_subset_of(&self, other: &VecSet<T>) -> bool {
for i in self {
if !other.has_element(i)
{ return false; }
}
true
}
/// Gets the cardinality of a set.
/// # Returns
/// A `usize`: `|self|`.
/// # Examples
/// ```
/// use lib_rapid::math::sets::vec_sets::VecSet;
/// use lib_rapid::math::sets::vec_sets::set;
///
/// let set = set!(0, 1, 2, 3, 4, 5, 6);
///
/// assert_eq!(7, set.cardinality());
/// ```
#[inline]
#[must_use]
pub fn cardinality(&self) -> usize {
self.elements.len()
}
/// Lets you set the elements of a set.
/// # Arguments
/// * `vals` - The Vec to change the values to.
/// # Returns
/// Nothing.
/// # Examples
/// ```
/// use lib_rapid::math::sets::vec_sets::VecSet;
/// use lib_rapid::math::sets::vec_sets::set;
///
/// let mut set = set!(0, 1, 2, 3, 4, 5, 6);
/// set.set_elements(&vec![0, 2, 4, 6]);
///
/// assert_eq!(&vec![0, 2, 4, 6], set.elements());
/// ```
#[inline]
pub fn set_elements(&mut self, vals: &[T]) {
self.elements = vals.to_vec();
self.elements.sort_unstable();
}
/// Lets you get the elements of a set.
/// # Arguments
/// * none
/// # Returns
/// A `&[T]` containing all elements.
/// # Examples
/// ```
/// use lib_rapid::math::sets::vec_sets::VecSet;
/// use lib_rapid::math::sets::vec_sets::set;
///
/// let mut set = set!(0, 1, 2, 3, 4, 5, 6);
///
/// assert_eq!(&vec![0, 1, 2, 3, 4, 5, 6], set.elements());
/// ```
#[inline]
#[must_use]
pub fn elements(&self) -> &[T] {
&self.elements
}
}
/// Creates a new `VecSet` more elegantly from values.
/// # Returns
/// A new `VecSet`.
/// # Examples
/// ```
/// use lib_rapid::set;
/// use lib_rapid::math::sets::vec_sets::VecSet;
///
/// let set: VecSet<i32> = set!(0,1,2,3,4,5,6,-1);
/// ```
#[macro_export]
#[must_use]
macro_rules! set {
( $( $a:expr ),* ) => {
{
use lib_rapid::compsci::general::BinaryInsert;
let mut res_vec = Vec::with_capacity(20);
$(
res_vec.binary_insert_no_dup($a);
)*
VecSet::new(&res_vec)
}
};
}
pub use set;
use crate::compsci::general::BinaryInsert;
impl<T: ToString + Copy + Ord> VecSet<'_, T> {
/// Lets you print a set with all its parents recursively.
/// # Returns
/// Nothing.
/// # Examples
/// ```
/// use lib_rapid::math::sets::vec_sets::VecSet;
/// let s: VecSet<i32> = VecSet::new(&vec![0,1,2,3,4,5,6,7,8,9,10]);
/// let s1: VecSet<i32> = VecSet::new_subset(&s, |x| x % 2 == 0);
/// let s2: VecSet<i32> = VecSet::new_subset(&s1, |x| x == 4);
///
/// s2.full_println(); // Prints this set and the superset, see to_full_string.
/// println!("{}", s2); // Only prints this set
/// ```
pub fn full_println(&self) {
println!("{}", self.rec_to_string(&mut String::new()));
}
/// Converts a set with all subsets to a string.
/// # Returns
/// A String containing the result.
/// # Examples
/// ```
/// use lib_rapid::math::sets::vec_sets::VecSet;
/// let s: VecSet<i32> = VecSet::new(&vec![0,1,2,3,4,5,6,7,8,9,10]);
/// let s1: VecSet<i32> = VecSet::new_subset(&s, |x| x % 2 == 0);
/// let s2: VecSet<i32> = VecSet::new_subset(&s1, |x| x == 4);
/// assert_eq!(s2.to_full_string(), "{ 4 } ⊆ { 0; 2; 4; 6; 8; 10 } ⊆ { 0; 1; 2; 3; 4; 5; 6; 7; 8; 9; 10 }".to_string());
/// ```
#[must_use]
pub fn to_full_string(&self) -> String {
self.rec_to_string(&mut String::new())
}
fn rec_to_string(&self, string: &mut String) -> String {
string.push_str(&self.to_string()); // The child-set at the bottom
if let Some(x) = self.parent { string.push_str(" ⊆ "); // Add subset-character
x.rec_to_string(string); } // Recursively append parent sets
string.to_string()
}
}
// Indexing for Sets
impl<T> std::ops::Index<usize> for VecSet<'_, T> {
type Output = T;
#[inline]
fn index(&self, index: usize) -> &Self::Output {
&self.elements[index]
}
}
// Implement Printing
impl<T: ToString + Copy + Ord> std::fmt::Display for VecSet<'_, T> {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
let mut res: String = String::from('{');
for elem in self.elements() {
res.push(' ');
res.push_str(&elem.to_string());
res.push(';');
}
res.pop();
write!(f, "{} }}", res)
}
}
// Implement Equality
impl<T: PartialEq> PartialEq for VecSet<'_, T> {
#[inline]
fn eq(&self, other: &Self) -> bool {
self.elements == other.elements
}
}
impl<T> IntoIterator for VecSet<'_, T> {
type Item = T;
type IntoIter = std::vec::IntoIter<Self::Item>;
#[inline]
fn into_iter(self) -> Self::IntoIter {
self.elements.into_iter()
}
}
impl<T: Copy + Clone + Ord> IntoIterator for &VecSet<'_, T> {
type Item = T;
type IntoIter = std::vec::IntoIter<Self::Item>;
fn into_iter(self) -> Self::IntoIter {
self.elements().to_owned().into_iter()
}
}