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//! Contains functions and data structures for partitioning items into groups.
//!
//! The symbols in this module is part of visioncortex's public API, but are generally
//! only useful for internal implementations.
use std::{hash::Hash, collections::HashMap};
/// Groups items with a key extraction function and a equivalence testing function on the keys.
/// See the documentation of `group_by` for the requirements of the testing function.
///
/// During grouping, the key function is called only once per element.
///
/// For simple key functions, `group_by` is likely to be faster.
///
/// # Example
/// ```
/// use visioncortex::disjoint_sets::group_by_cached_key;
/// let points = vec![1,1,7,9,24,1,4,7,3,8];
/// let groups = group_by_cached_key(points, |&x| x, |&x, &y| {
/// (x - y) * (x - y) < 2
/// });
/// // should be grouped as below:
/// // {1, 1, 1}, {3, 4}, {7, 7, 8, 9}, {24}
/// for mut group in groups {
/// println!("{:?}", group);
/// group.sort();
/// if group.len() == 4 {
/// assert_eq!(group, [7, 7, 8, 9]);
/// } else if group.len() == 3 {
/// assert_eq!(group, [1, 1, 1]);
/// } else if group.len() == 2 {
/// assert_eq!(group, [3, 4]);
/// } else {
/// assert_eq!(group, [24]);
/// }
/// }
/// ```
pub fn group_by_cached_key<T, Key, Extract, Group> (
items: Vec<T>,
extract_key: Extract,
should_group: Group
) -> Vec<Vec<T>>
where
Extract: Fn(&T) -> Key,
Group: Fn(&Key, &Key) -> bool,
{
let items_with_keys = items
.into_iter()
.map(|item| {
let k = extract_key(&item);
(item, k)
})
.collect();
group_by(items_with_keys, |(_, key1), (_, key2)| should_group(key1, key2))
.into_iter()
.map(|group| group.into_iter().map(|(item, _)| item).collect())
.collect()
}
/// Groups items with a equivalence testing function.
///
/// The testing function should define a equivalence relation `~` on the set of elements
/// and return true for elements `a` and `b` if-and-only-if `a ~ b`.
/// This implies that the function is commutative, i.e. `should_group(a, b) == should_group(b, a).
///
/// # Example
/// ```
/// use visioncortex::disjoint_sets::group_by;
/// let points = vec![1,1,7,9,24,1,4,7,3,8];
/// let groups = group_by(points, |&x, &y| {
/// (x - y) * (x - y) < 2
/// });
/// // should be grouped as below:
/// // {1, 1, 1}, {3, 4}, {7, 7, 8, 9}, {24}
/// for mut group in groups {
/// println!("{:?}", group);
/// group.sort();
/// if group.len() == 4 {
/// assert_eq!(group, [7, 7, 8, 9]);
/// } else if group.len() == 3 {
/// assert_eq!(group, [1, 1, 1]);
/// } else if group.len() == 2 {
/// assert_eq!(group, [3, 4]);
/// } else {
/// assert_eq!(group, [24]);
/// }
/// }
/// ```
pub fn group_by<T, F>(mut items: Vec<T>, should_group: F) -> Vec<Vec<T>>
where
F: Fn(&T, &T) -> bool,
{
let mut forests = Forests::new();
for i in 0..items.len() {
forests.make_set(i);
}
for (i, item1) in items.iter().enumerate() {
for (j, item2) in items.iter().enumerate().skip(i + 1) {
if should_group(item1, item2) {
forests.union(&i, &j);
}
}
}
let mut group_index = HashMap::new();
let mut groups = Vec::new();
while let Some(item) = items.pop() {
let index = items.len();
let label = forests.find_set(&index).unwrap(); // safe because we already made sets 0..n
if let Some(&i) = group_index.get(&label) {
let group: &mut Vec<T> = &mut groups[i]; // to bypass 'type annotation needed'
group.push(item);
} else {
group_index.insert(label, groups.len());
groups.push(vec![item]);
}
}
groups
}
#[derive(Debug, Hash, Copy, Clone, PartialOrd, Ord, PartialEq, Eq)]
#[repr(transparent)]
pub struct Label(u32);
#[derive(Copy, Clone, PartialOrd, Ord, PartialEq, Eq)]
#[repr(transparent)]
struct Rank(u8);
/// Data structure for building disjoint sets
pub struct Forests<T>
where
T: Eq + Hash,
{
parents: Vec<Label>,
ranks: Vec<Rank>,
labels: HashMap<T, Label>,
}
impl<T> Default for Forests<T>
where
T: Eq + Hash,
{
fn default() -> Self {
Self {
parents: vec![],
ranks: vec![],
labels: HashMap::new(),
}
}
}
impl<T> Forests<T>
where
T: Eq + Hash,
{
pub fn new() -> Self {
Self::default()
}
/// Counts the number of unique disjoint sets.
pub fn count_sets(&mut self) -> usize {
use std::collections::HashSet;
let mut roots = HashSet::new();
for i in 0..self.parents.len() {
let root = self.find_and_compress_path(Label::from(i));
roots.insert(root);
}
roots.len()
}
/// Groups `items` by their containing sets. The result is the indices of items in the provided `items`
/// that belongs to different disjoint sets. The order of groups is arbitrary.
/// Items that do not exist in the forest belongs to the same group that does not consist of other contained items.
pub fn group_items(&mut self, items: &[T]) -> Vec<Vec<usize>> {
let mut groups = HashMap::new();
let mut not_exists = vec![];
for (i, item) in items.iter().enumerate() {
if let Some(root) = self.find_set(item) {
let group = groups.entry(root).or_insert_with(Vec::new);
group.push(i);
} else {
not_exists.push(i);
}
}
let mut groups: Vec<_> = groups.into_iter().map(|(_, v)| v).collect();
if !not_exists.is_empty() {
groups.push(not_exists);
}
groups
}
/// Makes a new singleton set with exactly one element `item`.
pub fn make_set(&mut self, item: T) {
if self.labels.contains_key(&item) {
return;
}
// The new label of `item` should be the next available index.
let label = Label::from(self.ranks.len());
self.labels.insert(item, label);
self.parents.push(label); // parent points to item itself
self.ranks.push(Rank::zero());
}
/// Find the label of the set `item` belongs to.
pub fn find_set(&mut self, item: &T) -> Option<Label> {
self.labels.get(item).copied().map(|label| self.find_and_compress_path(label))
}
/// Finds the root label of `label`, compressing the path along the traversal towards root as a side effect.
fn find_and_compress_path(&mut self, label: Label) -> Label {
let mut path_visited = vec![];
let mut cur = label;
loop {
// traverse towards parent until parent == itself
let parent = self.parents[cur.as_usize()];
if parent == cur {
break;
}
path_visited.push(cur);
cur = parent;
}
// compress path
for visited in path_visited {
self.parents[visited.as_usize()] = cur;
}
cur
}
/// Unions the two sets containing `item1` and `item2`.
/// No-op if either `item1` or `item2` is not present (i.e. no `make_set` has been made).
pub fn union(&mut self, item1: &T, item2: &T) {
if let (Some(root1), Some(root2)) = (self.find_set(item1), self.find_set(item2)) {
self.link(root1, root2);
}
}
/// Implements union by rank.
fn link(&mut self, x: Label, y: Label) {
match self.ranks[x.as_usize()].cmp(&self.ranks[y.as_usize()]) {
std::cmp::Ordering::Greater => self.parents[y.as_usize()] = x,
std::cmp::Ordering::Less => self.parents[x.as_usize()] = y,
std::cmp::Ordering::Equal => {
// break ties arbitrarily
self.parents[x.as_usize()] = y;
self.ranks[y.as_usize()].inc();
}
}
}
}
impl Label {
fn as_usize(&self) -> usize {
self.0 as usize
}
}
impl Rank {
pub const fn zero() -> Self {
Self(0)
}
fn inc(&mut self) {
self.0 += 1;
}
}
impl From<usize> for Label {
fn from(i: usize) -> Self {
Self(i as u32)
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn union_find() {
let mut forests = Forests::new();
for i in 1..11 {
forests.make_set(i);
}
forests.union(&2, &4);
forests.union(&5, &7);
forests.union(&1, &3);
forests.union(&8, &9);
forests.union(&1, &2);
forests.union(&5, &6);
forests.union(&2, &3);
assert_eq!(forests.find_set(&1), forests.find_set(&2));
assert_eq!(forests.find_set(&2), forests.find_set(&3));
assert_eq!(forests.find_set(&3), forests.find_set(&4));
assert_eq!(forests.find_set(&5), forests.find_set(&6));
assert_eq!(forests.find_set(&6), forests.find_set(&7));
assert_eq!(forests.find_set(&8), forests.find_set(&9));
assert_ne!(forests.find_set(&10), forests.find_set(&1));
assert_ne!(forests.find_set(&1), forests.find_set(&5));
assert_ne!(forests.find_set(&6), forests.find_set(&8));
assert_eq!(forests.count_sets(), 4);
let items: Vec<_> = (1..11).collect();
let groups = forests.group_items(&items);
for group in groups {
if group.len() == 4 {
assert_eq!(group, [0, 1, 2, 3]);
} else if group.len() == 3 {
assert_eq!(group, [4, 5, 6]);
} else if group.len() == 2 {
assert_eq!(group, [7, 8]);
} else {
assert_eq!(group, [9]);
}
}
}
#[test]
fn group_items() {
let points = vec![1,1,7,9,24,1,4,7,3,8];
let groups = group_by(points, |&x, &y| {
(x - y) * (x - y) < 2
});
// should be grouped as below:
// {1, 1, 1}, {3, 4}, {7, 7, 8, 9}, {24}
for mut group in groups {
println!("{:?}", group);
group.sort_unstable();
if group.len() == 4 {
assert_eq!(group, [7, 7, 8, 9]);
} else if group.len() == 3 {
assert_eq!(group, [1, 1, 1]);
} else if group.len() == 2 {
assert_eq!(group, [3, 4]);
} else {
assert_eq!(group, [24]);
}
}
}
#[test]
fn group_cached() {
let points = vec![1,1,7,9,24,1,4,7,3,8];
let groups = group_by_cached_key(points, |&x| x, |&x, &y| {
(x - y) * (x - y) < 2
});
// should be grouped as below:
// {1, 1, 1}, {3, 4}, {7, 7, 8, 9}, {24}
for mut group in groups {
println!("{:?}", group);
group.sort_unstable();
if group.len() == 4 {
assert_eq!(group, [7, 7, 8, 9]);
} else if group.len() == 3 {
assert_eq!(group, [1, 1, 1]);
} else if group.len() == 2 {
assert_eq!(group, [3, 4]);
} else {
assert_eq!(group, [24]);
}
}
}
}