//! Varified
//! borrow from petgraph
use std::fmt;
use std::hash::Hash;
/// The default integer type for graph indices.
/// `u32` is the default to reduce the size of the graph's data and improve
/// performance in the common case.
///
/// Used for node and edge indices in `Graph` and `StableGraph`, used
/// for node indices in `Csr`.
pub type DefaultIx = u32;
/// Trait for the unsigned integer type used for node and edge indices.
///
/// Marked `unsafe` because: the trait must faithfully preserve
/// and convert index values.
pub unsafe trait IndexType: Copy + Default + Hash + Ord + fmt::Debug + 'static {
fn new(x: usize) -> Self;
fn index(&self) -> usize;
fn max() -> Self;
}
unsafe impl IndexType for usize {
#[inline(always)]
fn new(x: usize) -> Self {
x
}
#[inline(always)]
fn index(&self) -> Self {
*self
}
#[inline(always)]
fn max() -> Self {
::std::usize::MAX
}
}
unsafe impl IndexType for u32 {
#[inline(always)]
fn new(x: usize) -> Self {
x as u32
}
#[inline(always)]
fn index(&self) -> usize {
*self as usize
}
#[inline(always)]
fn max() -> Self {
::std::u32::MAX
}
}
unsafe impl IndexType for u16 {
#[inline(always)]
fn new(x: usize) -> Self {
x as u16
}
#[inline(always)]
fn index(&self) -> usize {
*self as usize
}
#[inline(always)]
fn max() -> Self {
::std::u16::MAX
}
}
unsafe impl IndexType for u8 {
#[inline(always)]
fn new(x: usize) -> Self {
x as u8
}
#[inline(always)]
fn index(&self) -> usize {
*self as usize
}
#[inline(always)]
fn max() -> Self {
::std::u8::MAX
}
}
// `UnionFind<K>` is a disjoint-set data structure.
use std::cmp::Ordering;
/// `UnionFind<K>` is a disjoint-set data structure. It tracks set membership of *n* elements
/// indexed from *0* to *n - 1*. The scalar type is `K` which must be an unsigned integer type.
///
/// <http://en.wikipedia.org/wiki/Disjoint-set_data_structure>
///
/// Too awesome not to quote:
///
/// “The amortized time per operation is **O(α(n))** where **α(n)** is the
/// inverse of **f(x) = A(x, x)** with **A** being the extremely fast-growing Ackermann function.”
#[derive(Debug, Clone)]
pub struct UnionFind<K> {
// For element at index *i*, store the index of its parent; the representative itself
// stores its own index. This forms equivalence classes which are the disjoint sets, each
// with a unique representative.
parent: Vec<K>,
// It is a balancing tree structure,
// so the ranks are logarithmic in the size of the container -- a byte is more than enough.
//
// Rank is separated out both to save space and to save cache in when searching in the parent
// vector.
rank: Vec<u8>,
}
#[inline]
unsafe fn get_unchecked<K>(xs: &[K], index: usize) -> &K {
debug_assert!(index < xs.len());
xs.get_unchecked(index)
}
#[inline]
unsafe fn get_unchecked_mut<K>(xs: &mut [K], index: usize) -> &mut K {
debug_assert!(index < xs.len());
xs.get_unchecked_mut(index)
}
impl<K> UnionFind<K>
where
K: IndexType,
{
/// Create a new `UnionFind` of `n` disjoint sets.
pub fn new(n: usize) -> Self {
let rank = vec![0; n];
let parent = (0..n).map(K::new).collect::<Vec<K>>();
UnionFind { parent, rank }
}
/// Return the representative for `x`.
///
/// **Panics** if `x` is out of bounds.
pub fn find(&self, x: K) -> K {
assert!(x.index() < self.parent.len());
unsafe {
let mut x = x;
loop {
// Use unchecked indexing because we can trust the internal set ids.
let xparent = *get_unchecked(&self.parent, x.index());
if xparent == x {
break;
}
x = xparent;
}
x
}
}
/// Return the representative for `x`.
///
/// Write back the found representative, flattening the internal
/// datastructure in the process and quicken future lookups.
///
/// **Panics** if `x` is out of bounds.
pub fn find_mut(&mut self, x: K) -> K {
assert!(x.index() < self.parent.len());
unsafe { self.find_mut_recursive(x) }
}
unsafe fn find_mut_recursive(&mut self, mut x: K) -> K {
let mut parent = *get_unchecked(&self.parent, x.index());
while parent != x {
let grandparent = *get_unchecked(&self.parent, parent.index());
*get_unchecked_mut(&mut self.parent, x.index()) = grandparent;
x = parent;
parent = grandparent;
}
x
}
/// Returns `true` if the given elements belong to the same set, and returns
/// `false` otherwise.
pub fn equiv(&self, x: K, y: K) -> bool {
self.find(x) == self.find(y)
}
/// Unify the two sets containing `x` and `y`.
///
/// Return `false` if the sets were already the same, `true` if they were unified.
///
/// **Panics** if `x` or `y` is out of bounds.
pub fn union(&mut self, x: K, y: K) -> bool {
if x == y {
return false;
}
let xrep = self.find_mut(x);
let yrep = self.find_mut(y);
if xrep == yrep {
return false;
}
let xrepu = xrep.index();
let yrepu = yrep.index();
let xrank = self.rank[xrepu];
let yrank = self.rank[yrepu];
// The rank corresponds roughly to the depth of the treeset, so put the
// smaller set below the larger
match xrank.cmp(&yrank) {
Ordering::Less => self.parent[xrepu] = yrep,
Ordering::Greater => self.parent[yrepu] = xrep,
Ordering::Equal => {
self.parent[yrepu] = xrep;
self.rank[xrepu] += 1;
}
}
true
}
/// Return a vector mapping each element to its representative.
pub fn into_labeling(mut self) -> Vec<K> {
// write in the labeling of each element
unsafe {
for ix in 0..self.parent.len() {
let k = *get_unchecked(&self.parent, ix);
let xrep = self.find_mut_recursive(k);
*self.parent.get_unchecked_mut(ix) = xrep;
}
}
self.parent
}
}