use core::{cell::RefCell, fmt, mem};
use alloc::{collections::BTreeMap, rc::Rc, vec, vec::Vec};
use crate::{
dfa::{automaton::Automaton, dense, DEAD},
util::{
alphabet,
primitives::{PatternID, StateID},
},
};
/// An implementation of Hopcroft's algorithm for minimizing DFAs.
///
/// The algorithm implemented here is mostly taken from Wikipedia:
/// https://en.wikipedia.org/wiki/DFA_minimization#Hopcroft's_algorithm
///
/// This code has had some light optimization attention paid to it,
/// particularly in the form of reducing allocation as much as possible.
/// However, it is still generally slow. Future optimization work should
/// probably focus on the bigger picture rather than micro-optimizations. For
/// example:
///
/// 1. Figure out how to more intelligently create initial partitions. That is,
/// Hopcroft's algorithm starts by creating two partitions of DFA states
/// that are known to NOT be equivalent: match states and non-match states.
/// The algorithm proceeds by progressively refining these partitions into
/// smaller partitions. If we could start with more partitions, then we
/// could reduce the amount of work that Hopcroft's algorithm needs to do.
/// 2. For every partition that we visit, we find all incoming transitions to
/// every state in the partition for *every* element in the alphabet. (This
/// is why using byte classes can significantly decrease minimization times,
/// since byte classes shrink the alphabet.) This is quite costly and there
/// is perhaps some redundant work being performed depending on the specific
/// states in the set. For example, we might be able to only visit some
/// elements of the alphabet based on the transitions.
/// 3. Move parts of minimization into determinization. If minimization has
/// fewer states to deal with, then it should run faster. A prime example
/// of this might be large Unicode classes, which are generated in way that
/// can create a lot of redundant states. (Some work has been done on this
/// point during NFA compilation via the algorithm described in the
/// "Incremental Construction of MinimalAcyclic Finite-State Automata"
/// paper.)
pub(crate) struct Minimizer<'a> {
dfa: &'a mut dense::OwnedDFA,
in_transitions: Vec<Vec<Vec<StateID>>>,
partitions: Vec<StateSet>,
waiting: Vec<StateSet>,
}
impl<'a> fmt::Debug for Minimizer<'a> {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
f.debug_struct("Minimizer")
.field("dfa", &self.dfa)
.field("in_transitions", &self.in_transitions)
.field("partitions", &self.partitions)
.field("waiting", &self.waiting)
.finish()
}
}
/// A set of states. A state set makes up a single partition in Hopcroft's
/// algorithm.
///
/// It is represented by an ordered set of state identifiers. We use shared
/// ownership so that a single state set can be in both the set of partitions
/// and in the set of waiting sets simultaneously without an additional
/// allocation. Generally, once a state set is built, it becomes immutable.
///
/// We use this representation because it avoids the overhead of more
/// traditional set data structures (HashSet/BTreeSet), and also because
/// computing intersection/subtraction on this representation is especially
/// fast.
#[derive(Clone, Debug, Eq, PartialEq, PartialOrd, Ord)]
struct StateSet {
ids: Rc<RefCell<Vec<StateID>>>,
}
impl<'a> Minimizer<'a> {
pub fn new(dfa: &'a mut dense::OwnedDFA) -> Minimizer<'a> {
let in_transitions = Minimizer::incoming_transitions(dfa);
let partitions = Minimizer::initial_partitions(dfa);
let waiting = partitions.clone();
Minimizer { dfa, in_transitions, partitions, waiting }
}
pub fn run(mut self) {
let stride2 = self.dfa.stride2();
let as_state_id = |index: usize| -> StateID {
StateID::new(index << stride2).unwrap()
};
let as_index = |id: StateID| -> usize { id.as_usize() >> stride2 };
let mut incoming = StateSet::empty();
let mut scratch1 = StateSet::empty();
let mut scratch2 = StateSet::empty();
let mut newparts = vec![];
// This loop is basically Hopcroft's algorithm. Everything else is just
// shuffling data around to fit our representation.
while let Some(set) = self.waiting.pop() {
for b in self.dfa.byte_classes().iter() {
self.find_incoming_to(b, &set, &mut incoming);
// If incoming is empty, then the intersection with any other
// set must also be empty. So 'newparts' just ends up being
// 'self.partitions'. So there's no need to go through the loop
// below.
//
// This actually turns out to be rather large optimization. On
// the order of making minimization 4-5x faster. It's likely
// that the vast majority of all states have very few incoming
// transitions.
if incoming.is_empty() {
continue;
}
for p in 0..self.partitions.len() {
self.partitions[p].intersection(&incoming, &mut scratch1);
if scratch1.is_empty() {
newparts.push(self.partitions[p].clone());
continue;
}
self.partitions[p].subtract(&incoming, &mut scratch2);
if scratch2.is_empty() {
newparts.push(self.partitions[p].clone());
continue;
}
let (x, y) =
(scratch1.deep_clone(), scratch2.deep_clone());
newparts.push(x.clone());
newparts.push(y.clone());
match self.find_waiting(&self.partitions[p]) {
Some(i) => {
self.waiting[i] = x;
self.waiting.push(y);
}
None => {
if x.len() <= y.len() {
self.waiting.push(x);
} else {
self.waiting.push(y);
}
}
}
}
newparts = mem::replace(&mut self.partitions, newparts);
newparts.clear();
}
}
// At this point, we now have a minimal partitioning of states, where
// each partition is an equivalence class of DFA states. Now we need to
// use this partitioning to update the DFA to only contain one state for
// each partition.
// Create a map from DFA state ID to the representative ID of the
// equivalence class to which it belongs. The representative ID of an
// equivalence class of states is the minimum ID in that class.
let mut state_to_part = vec![DEAD; self.dfa.state_len()];
for p in &self.partitions {
p.iter(|id| state_to_part[as_index(id)] = p.min());
}
// Generate a new contiguous sequence of IDs for minimal states, and
// create a map from equivalence IDs to the new IDs. Thus, the new
// minimal ID of *any* state in the unminimized DFA can be obtained
// with minimals_ids[state_to_part[old_id]].
let mut minimal_ids = vec![DEAD; self.dfa.state_len()];
let mut new_index = 0;
for state in self.dfa.states() {
if state_to_part[as_index(state.id())] == state.id() {
minimal_ids[as_index(state.id())] = as_state_id(new_index);
new_index += 1;
}
}
// The total number of states in the minimal DFA.
let minimal_count = new_index;
// Convenience function for remapping state IDs. This takes an old ID,
// looks up its Hopcroft partition and then maps that to the new ID
// range.
let remap = |old| minimal_ids[as_index(state_to_part[as_index(old)])];
// Re-map this DFA in place such that the only states remaining
// correspond to the representative states of every equivalence class.
for id in (0..self.dfa.state_len()).map(as_state_id) {
// If this state isn't a representative for an equivalence class,
// then we skip it since it won't appear in the minimal DFA.
if state_to_part[as_index(id)] != id {
continue;
}
self.dfa.remap_state(id, remap);
self.dfa.swap_states(id, minimal_ids[as_index(id)]);
}
// Trim off all unused states from the pre-minimized DFA. This
// represents all states that were merged into a non-singleton
// equivalence class of states, and appeared after the first state
// in each such class. (Because the state with the smallest ID in each
// equivalence class is its representative ID.)
self.dfa.truncate_states(minimal_count);
// Update the new start states, which is now just the minimal ID of
// whatever state the old start state was collapsed into. Also, we
// collect everything before-hand to work around the borrow checker.
// We're already allocating so much that this is probably fine. If this
// turns out to be costly, then I guess add a `starts_mut` iterator.
let starts: Vec<_> = self.dfa.starts().collect();
for (old_start_id, anchored, start_type) in starts {
self.dfa.set_start_state(
anchored,
start_type,
remap(old_start_id),
);
}
// Update the match state pattern ID list for multi-regexes. All we
// need to do is remap the match state IDs. The pattern ID lists are
// always the same as they were since match states with distinct
// pattern ID lists are always considered distinct states.
let mut pmap = BTreeMap::new();
for (match_id, pattern_ids) in self.dfa.pattern_map() {
let new_id = remap(match_id);
pmap.insert(new_id, pattern_ids);
}
// This unwrap is OK because minimization never increases the number of
// match states or patterns in those match states. Since minimization
// runs after the pattern map has already been set at least once, we
// know that our match states cannot error.
self.dfa.set_pattern_map(&pmap).unwrap();
// In order to update the ID of the maximum match state, we need to
// find the maximum ID among all of the match states in the minimized
// DFA. This is not necessarily the new ID of the unminimized maximum
// match state, since that could have been collapsed with a much
// earlier match state. Therefore, to find the new max match state,
// we iterate over all previous match states, find their corresponding
// new minimal ID, and take the maximum of those.
let old = self.dfa.special().clone();
let new = self.dfa.special_mut();
// ... but only remap if we had match states.
if old.matches() {
new.min_match = StateID::MAX;
new.max_match = StateID::ZERO;
for i in as_index(old.min_match)..=as_index(old.max_match) {
let new_id = remap(as_state_id(i));
if new_id < new.min_match {
new.min_match = new_id;
}
if new_id > new.max_match {
new.max_match = new_id;
}
}
}
// ... same, but for start states.
if old.starts() {
new.min_start = StateID::MAX;
new.max_start = StateID::ZERO;
for i in as_index(old.min_start)..=as_index(old.max_start) {
let new_id = remap(as_state_id(i));
if new_id == DEAD {
continue;
}
if new_id < new.min_start {
new.min_start = new_id;
}
if new_id > new.max_start {
new.max_start = new_id;
}
}
if new.max_start == DEAD {
new.min_start = DEAD;
}
}
new.quit_id = remap(new.quit_id);
new.set_max();
}
fn find_waiting(&self, set: &StateSet) -> Option<usize> {
self.waiting.iter().position(|s| s == set)
}
fn find_incoming_to(
&self,
b: alphabet::Unit,
set: &StateSet,
incoming: &mut StateSet,
) {
incoming.clear();
set.iter(|id| {
for &inid in
&self.in_transitions[self.dfa.to_index(id)][b.as_usize()]
{
incoming.add(inid);
}
});
incoming.canonicalize();
}
fn initial_partitions(dfa: &dense::OwnedDFA) -> Vec<StateSet> {
// For match states, we know that two match states with different
// pattern ID lists will *always* be distinct, so we can partition them
// initially based on that.
let mut matching: BTreeMap<Vec<PatternID>, StateSet> = BTreeMap::new();
let mut is_quit = StateSet::empty();
let mut no_match = StateSet::empty();
for state in dfa.states() {
if dfa.is_match_state(state.id()) {
let mut pids = vec![];
for i in 0..dfa.match_len(state.id()) {
pids.push(dfa.match_pattern(state.id(), i));
}
matching
.entry(pids)
.or_insert(StateSet::empty())
.add(state.id());
} else if dfa.is_quit_state(state.id()) {
is_quit.add(state.id());
} else {
no_match.add(state.id());
}
}
let mut sets: Vec<StateSet> =
matching.into_iter().map(|(_, set)| set).collect();
sets.push(no_match);
sets.push(is_quit);
sets
}
fn incoming_transitions(dfa: &dense::OwnedDFA) -> Vec<Vec<Vec<StateID>>> {
let mut incoming = vec![];
for _ in dfa.states() {
incoming.push(vec![vec![]; dfa.alphabet_len()]);
}
for state in dfa.states() {
for (b, next) in state.transitions() {
incoming[dfa.to_index(next)][b.as_usize()].push(state.id());
}
}
incoming
}
}
impl StateSet {
fn empty() -> StateSet {
StateSet { ids: Rc::new(RefCell::new(vec![])) }
}
fn add(&mut self, id: StateID) {
self.ids.borrow_mut().push(id);
}
fn min(&self) -> StateID {
self.ids.borrow()[0]
}
fn canonicalize(&mut self) {
self.ids.borrow_mut().sort();
self.ids.borrow_mut().dedup();
}
fn clear(&mut self) {
self.ids.borrow_mut().clear();
}
fn len(&self) -> usize {
self.ids.borrow().len()
}
fn is_empty(&self) -> bool {
self.len() == 0
}
fn deep_clone(&self) -> StateSet {
let ids = self.ids.borrow().iter().cloned().collect();
StateSet { ids: Rc::new(RefCell::new(ids)) }
}
fn iter<F: FnMut(StateID)>(&self, mut f: F) {
for &id in self.ids.borrow().iter() {
f(id);
}
}
fn intersection(&self, other: &StateSet, dest: &mut StateSet) {
dest.clear();
if self.is_empty() || other.is_empty() {
return;
}
let (seta, setb) = (self.ids.borrow(), other.ids.borrow());
let (mut ita, mut itb) = (seta.iter().cloned(), setb.iter().cloned());
let (mut a, mut b) = (ita.next().unwrap(), itb.next().unwrap());
loop {
if a == b {
dest.add(a);
a = match ita.next() {
None => break,
Some(a) => a,
};
b = match itb.next() {
None => break,
Some(b) => b,
};
} else if a < b {
a = match ita.next() {
None => break,
Some(a) => a,
};
} else {
b = match itb.next() {
None => break,
Some(b) => b,
};
}
}
}
fn subtract(&self, other: &StateSet, dest: &mut StateSet) {
dest.clear();
if self.is_empty() || other.is_empty() {
self.iter(|s| dest.add(s));
return;
}
let (seta, setb) = (self.ids.borrow(), other.ids.borrow());
let (mut ita, mut itb) = (seta.iter().cloned(), setb.iter().cloned());
let (mut a, mut b) = (ita.next().unwrap(), itb.next().unwrap());
loop {
if a == b {
a = match ita.next() {
None => break,
Some(a) => a,
};
b = match itb.next() {
None => {
dest.add(a);
break;
}
Some(b) => b,
};
} else if a < b {
dest.add(a);
a = match ita.next() {
None => break,
Some(a) => a,
};
} else {
b = match itb.next() {
None => {
dest.add(a);
break;
}
Some(b) => b,
};
}
}
for a in ita {
dest.add(a);
}
}
}
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