use std::{collections::{HashMap, HashSet, VecDeque}, iter};

mod token;
pub use token::ParsingError;
use token::parse;

const START_NFA: usize = usize::MAX;
const START_DFA: usize = 0;

/// A regular expression implemented as a non-deterministic finite automaton.
#[derive(Debug)]
pub struct RegexpNFA {
	rules: HashMap<(usize, char), HashSet<usize>>,
	end_states: HashSet<usize>,
	alphabet: Vec<char>
}

impl RegexpNFA {
	pub fn new(pattern: &String) -> Result<RegexpNFA, ParsingError> {
		let r = parse(pattern, 0)?;
		let pattern_chars = Vec::from_iter(pattern.chars());
		let mut rules: HashMap<(usize, char), HashSet<usize>> = HashMap::new();
		let mut alphabet: HashSet<char> = HashSet::new();
		
		for i in r.list_first() {
			let c = pattern_chars[i];
			alphabet.insert(c);
			let key = (START_NFA, c);
			match rules.get_mut(&key) {
				Some(set) => {set.insert(i);},
				None => {rules.insert(key, HashSet::from([i]));}
			};
		}

		for (i, j) in r.list_neighbours() {
			let c = pattern_chars[j];
			alphabet.insert(c);
			let key = (i, c);
			match rules.get_mut(&key) {
				Some(set) => {set.insert(j);},
				None => {rules.insert(key, HashSet::from([j]));}
			};
		}

		let mut end_states = HashSet::from_iter(r.list_last().into_iter());
		if r.is_skippable() {
			end_states.insert(START_NFA);
		}

		let mut alphabet_vec = Vec::from_iter(alphabet.into_iter());
		alphabet_vec.sort();

		return Ok(RegexpNFA{rules, end_states, alphabet: alphabet_vec});
	}

	/// Decide if a string matches the regexp.
	pub fn eval(&self, s: String) -> bool {
		let mut multistate = HashSet::from([START_NFA]);

		for c in s.chars() {
			let mut new_multistate = HashSet::new();

			for state in multistate {
				if let Some(x) = self.rules.get(&(state, c)) {
					new_multistate = new_multistate.union(&x).map(|&y| y).collect();
				} else if let Some(x) = self.rules.get(&(state, '.')) {
					new_multistate = new_multistate.union(&x).map(|&y| y).collect();
				}
			}
			multistate = new_multistate;
		}

		return multistate.iter().any(|x| self.end_states.contains(x));
	}

	/// Convert the non-deterministic finite automaton into a deterministic one.
	pub fn determinize(&self) -> RegexpDFA {
		const FAIL: usize = usize::MAX;
		let alphabet_index: HashMap<char, usize> = self.alphabet.iter().enumerate().map(|(i, c)| (*c, i)).collect();
		let n = alphabet_index.len();
		let mut compact_rules = vec![FAIL; n];
		let mut end_states: HashSet<usize> = HashSet::new();
		if self.end_states.contains(&START_NFA) {end_states.insert(START_DFA);}

		// mapping the NFA state subsets -> DFA states
		let mut index = HashMap::from([(vec![START_NFA], START_DFA)]);
		let mut stack = vec![vec![START_NFA]];

		while !stack.is_empty() {
			let multistate = stack.pop().unwrap();
			let mut new_rules: HashMap<char, HashSet<usize>> = HashMap::new();

			// collect all possible destination states from the multistate
			for key in self.rules.keys().filter(|(st, _c)| multistate.binary_search(st).is_ok()) {
				let (_st, c) = key;
				if !new_rules.contains_key(c) {
					new_rules.insert(*c, HashSet::new());
				}
				for target in &self.rules[key] {
					new_rules.get_mut(c).unwrap().insert(*target);
				}
			}

			// build a row for the DFA transition function table
			for (c, target_set) in new_rules.into_iter() {
				let mut target_vec = Vec::from_iter(target_set.into_iter());
				target_vec.sort();
				let is_end = target_vec.iter().any(|st| self.end_states.contains(st));
				if !index.contains_key(&target_vec) {
					let target_new = index.len();
					index.insert(target_vec.clone(), target_new);
					compact_rules.extend(iter::repeat(FAIL).take(n));
					stack.push(target_vec.clone());
				}
				compact_rules[index[&multistate]*n + alphabet_index[&c]] = index[&target_vec];
				if is_end {
					end_states.insert(index[&target_vec]);
				}
			}
		}

		// add a fail state, so the transition function is complete
		let fail = index.len();
		compact_rules = compact_rules.into_iter().map(|st| if st != FAIL {st} else {fail}).collect();
		compact_rules.extend(iter::repeat(fail).take(n));
		
		return RegexpDFA::new(compact_rules, end_states, alphabet_index);
	}
}

/// A regular expression implemented as a deterministic finite automaton.
/// This simplifies support for more features compared to the NFA Regexp.
#[derive(Clone)]
pub struct RegexpDFA {
	rules: Vec<usize>,
	end_states: HashSet<usize>,
	alphabet_index: HashMap<char, usize>
}

impl RegexpDFA {
	/// Construct a DFA with the provided parameters, or a minimal DFA if the parameters are empty.
	pub fn new(rules: Vec<usize>, end_states: HashSet<usize>, alphabet_index: HashMap<char, usize>) -> RegexpDFA {
		if rules.len() > 0 {
			return RegexpDFA{rules, end_states, alphabet_index};
		} else {
			// this saves us checking for an empty `alphabet_index` in other methods.
			return RegexpDFA{
				rules: vec![1, 1],
				end_states,
				alphabet_index: HashMap::from([('\0', 0)])
			};
		}
	}

	/// Decide if a string matches the regexp.
	pub fn eval(&self, s: String) -> bool {
		let n = self.alphabet_index.len();
		let mut state = START_DFA;

		for c in s.chars() {
			if let Some(ci) = self.alphabet_index.get(&c) {
				state = self.rules[state*n + ci];
			} else {
				return false;
			}
		}

		return self.end_states.contains(&state);
	}

	/// Minimize the automaton by collapsing equivalent states.
	pub fn reduce(&self) -> RegexpDFA {
		let partition = self.find_equivalent_states();
		return self.collapse_states(partition);
	}

	/// Normalize the automaton by relabeling the states in a breadth first search walkthrough order and remove unreachable states.
	pub fn normalize(&self) -> RegexpDFA {
		let n = self.alphabet_index.len();
		let m = self.rules.len()/n;
		let fail = m;
		let mut index: Vec<usize> = vec![fail;m];
		index[0] = 0;
		let mut queue = VecDeque::from([START_DFA]);

		let mut rules = vec![];
		let mut k = 1;

		while !queue.is_empty() {
			let si = queue.pop_front().unwrap();
			let row = &self.rules[si*n..(si+1)*n];
			for &sj in row {
				if sj != fail && index[sj] == fail {
					index[sj] = k;
					k += 1;
					queue.push_back(sj);
				}
			}
			rules.extend(row.iter().map(|&st| index[st]));
		}

		let end_states = self.end_states.iter().map(|st| index[*st]).collect();
		
		return RegexpDFA{rules, end_states, alphabet_index: self.alphabet_index.clone()};
	}

	/// Find the shortest string that is accepted by self or `r`, but not both.
	/// It is expected that the automatons are already reduced and normalized.
	pub fn find_distinguishing_string(&self, other: &RegexpDFA) -> Option<String> {
		if self.rules == other.rules && self.end_states == other.end_states {
			return None;
		}

		let r1 = self.expand_alphabet(&other.alphabet_index);
		let r2 = other.expand_alphabet(&self.alphabet_index);
		let product = r1.build_product_automaton(&r2);
		let n = product.alphabet_index.len();
		// mapping letter keys -> letters
		let inverse_alphabet_index: HashMap<usize, char> = HashMap::from_iter(product.alphabet_index.iter().map(|(&k, &v)| (v, k)));

		// look for an accepting state with a BFS
		let mut queue = VecDeque::from([(0, "".to_string())]);
		let mut visited = HashSet::new();
		while !queue.is_empty() {
			let (state, acc) = queue.pop_front().unwrap();
			if product.end_states.contains(&state) {
				return Some(acc);
			}
			for (i, target) in product.rules[state*n..(state+1)*n].iter().enumerate() {
				if !visited.contains(target) {
					queue.push_back((*target, acc.clone()+&String::from(inverse_alphabet_index[&i])));
					visited.insert(target);
				}
			}
		}

		panic!("Failed to detect the Regexps as equivalent and failed to find a distinguishing string.");
	}

	/// Partition states into their equivalence classes with Hopcroft's algorithm.
	fn find_equivalent_states(&self) -> Vec<HashSet<usize>> {
		let n = self.alphabet_index.len();
		let m = self.rules.len() / n;
		let mut inverse_rules = vec![HashSet::<usize>::new();m*n];

		for i in 0..m {
			for j in 0..n {
				let target = self.rules[i*n + j];
				inverse_rules[target*n + j].insert(i);
			}
		}

		// store state subsets here so we can just pass around their indices
		let mut set_bag = vec![
			self.end_states.clone(),
			HashSet::from_iter(0..m).difference(&self.end_states).copied().collect()
		];
		let mut res = HashSet::<usize>::from([0, 1]);
		let mut work = HashSet::<usize>::from([0, 1]);

		while !work.is_empty() {
			let key = *work.iter().next().unwrap();
			work.remove(&key);
			let target_set = set_bag[key].clone();
			for j in 0..n {
				let source_set = HashSet::<usize>::from_iter(target_set.iter().flat_map(|&t| inverse_rules[t*n+j].iter()).copied());
				for k in res.clone().into_iter() {
					let part = &set_bag[k];
					let intersection = part.intersection(&source_set).copied().collect::<HashSet<usize>>();
					let diff = part.difference(&source_set).copied().collect::<HashSet<usize>>();
					if intersection.is_empty() || diff.is_empty() {
						continue;
					}
					res.remove(&k);
					let ki = set_bag.len();
					set_bag.push(intersection);
					res.insert(ki);
					let kd = set_bag.len();
					set_bag.push(diff);
					res.insert(kd);
					if work.contains(&k) {
						work.remove(&k);
						work.insert(ki);
						work.insert(kd);
					} else if set_bag[ki].len() < set_bag[kd].len() {
						work.insert(ki);
					} else {
						work.insert(kd);
					}
				}
			}
		}

		return Vec::from_iter(res.into_iter().map(|k| std::mem::take(&mut set_bag[k])));
	}

	/// Collapse equivalent states from each partition class into a single state.
	fn collapse_states(&self, partition: Vec<HashSet<usize>>) -> RegexpDFA {
		let n = self.alphabet_index.len();
		let m = self.rules.len()/n;
		let mut rules = vec![];

		// states mapping due to the equivalents collapse
		let mut eq_mapping: Vec<usize> = ((0..m)).collect();
		for eq_set in partition.into_iter() {
			let mut eq_vec = Vec::from_iter(eq_set.into_iter());
			eq_vec.sort();
			let label = eq_vec[0];
			for st in eq_vec.into_iter() {
				eq_mapping[st] = label;
			}
		}

		// states mapping to keep the rules list compact after the equivalents collapse
		let mut discard_mapping: Vec<usize> = ((0..m)).collect();
		let mut discard_count = 0;

		for si in 0..m {
			if eq_mapping[si] != si {
				discard_count += 1;
				continue;
			}
			discard_mapping[si] = si-discard_count;
			rules.extend(self.rules[si*n..(si+1)*n].iter().map(|&st| eq_mapping[st]));
		}

		rules = rules.into_iter().map(|st| discard_mapping[st]).collect();
		let end_states = self.end_states.iter().map(|st| discard_mapping[eq_mapping[*st]]).collect();

		return RegexpDFA{rules, end_states, alphabet_index: self.alphabet_index.clone()};
	}

	/// Expand the automaton to accommodate union of `self.alphabet_index` and the provided `alphabet_index`.
	fn expand_alphabet(&self, alphabet_index: &HashMap<char, usize>) -> RegexpDFA {
		if *alphabet_index == self.alphabet_index {
			return self.clone();
		}

		let n1 = self.alphabet_index.len();
		let m = self.rules.len() / n1;

		let combined_alphabet: HashSet<char> = HashSet::from_iter(self.alphabet_index.keys().chain(alphabet_index.keys()).copied());
		let mut combined_vec = Vec::from_iter(combined_alphabet.into_iter());
		combined_vec.sort();
		// a new alphabet_index
		let combined_index = HashMap::from_iter(combined_vec.iter().enumerate().map(|(i, c)| (*c, i)));
		// a new letter key -> the old letter key
		let conversion_index: HashMap<usize, usize> = HashMap::from_iter(self.alphabet_index.iter().map(|(k, v)| (combined_index[k], *v)));
		let n2 = combined_vec.len();

		// rewrite the rules into a new table, filling blanks with a new fail state
		let rules: Vec<usize> = (0..m*n2).map(
			|i| {
				let (j, k) = (i/n2, i%n2);
				return if conversion_index.contains_key(&k) {
					self.rules[j*n1 + conversion_index[&k]]
				} else {m};
			}
		).chain(std::iter::repeat(m).take(n2)).collect();

		return RegexpDFA{rules, end_states: self.end_states.clone(), alphabet_index: combined_index}.reduce().normalize();
	}

	/// Create a new automaton, with a carthesian product of the arguments' states and corresponding transition rules.
	fn build_product_automaton(&self, other: &RegexpDFA) -> RegexpDFA {
		let n = self.alphabet_index.len();
		let m = other.rules.len() / n;
		let k = self.rules.len() / n;

		let mut rules = vec![];
		let mut end_states = HashSet::new();

		// expand each self state into m new states, one for each of the `other` states
		for s1 in 0..k {
			let row1 = &self.rules[s1*n..(s1+1)*n];
			for s2 in 0..m {
				let row2 = &other.rules[s2*n..(s2+1)*n];
				rules.extend(row1.iter().zip(row2.iter()).map(|(x, y)| x*m + y));
				if (self.end_states.contains(&s1)) ^ (other.end_states.contains(&s2)) {
					end_states.insert(s1*m + s2);
				}
			}
		}

		return RegexpDFA{rules, end_states, alphabet_index: self.alphabet_index.clone()}.reduce().normalize();
	}
}