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    use std::collections::VecDeque;
    use std::cmp;
    use std::fmt;
    use std::mem::size_of;

    use ahocorasick::MatchKind;
    use automaton::Automaton;
    use classes::{ByteClasses, ByteClassBuilder};
    use error::Result;
    use prefilter::{self, Prefilter, PrefilterObj};
    use state_id::{StateID, dead_id, fail_id, usize_to_state_id};
    use Match;

    /// The identifier for a pattern, which is simply the position of the pattern
    /// in the sequence of patterns given by the caller.
    pub type PatternID = usize;

    /// The length of a pattern, in bytes.
    pub type PatternLength = usize;

    /// An Aho-Corasick automaton, represented as an NFA.
    ///
    /// This is the classical formulation of Aho-Corasick, which involves building
    /// up a prefix trie of a given set of patterns, and then wiring up failure
    /// transitions between states in order to guarantee linear time matching. The
    /// standard formulation is, technically, an NFA because of these failure
    /// transitions. That is, one can see them as enabling the automaton to be in
    /// multiple states at once. Indeed, during search, it is possible to check
    /// the transitions on multiple states for a single input byte.
    ///
    /// This particular implementation not only supports the standard style of
    /// matching, but also provides a mode for choosing leftmost-first or
    /// leftmost-longest match semantics. When a leftmost mode is chosen, some
    /// failure transitions that would otherwise be added are elided. See
    /// the documentation of `MatchKind` for more details and examples on how the
    /// match semantics may differ.
    ///
    /// If one wants a DFA, then it is necessary to first build an NFA and convert
    /// it into a DFA. Note, however, that because we've constrained ourselves to
    /// matching literal patterns, this does not need to use subset construction
    /// for determinization. Instead, the DFA has at most a number of states
    /// equivalent to the number of NFA states. The only real difference between
    /// them is that all failure transitions are followed and pre-computed. This
    /// uses much more memory, but also executes searches more quickly.
    #[derive(Clone)]
    pub struct NFA<S> {
        /// The match semantics built into this NFA.
        match_kind: MatchKind,
        /// The start state id as an index into `states`.
        start_id: S,
        /// The length, in bytes, of the longest pattern in this automaton. This
        /// information is useful for keeping correct buffer sizes when searching
        /// on streams.
        max_pattern_len: usize,
        /// The total number of patterns added to this automaton, including
        /// patterns that may never be matched.
        pattern_count: usize,
        /// The number of bytes of heap used by this NFA's transition table.
        heap_bytes: usize,
        /// A prefilter for quickly skipping to candidate matches, if pertinent.
        prefilter: Option<PrefilterObj>,
        /// A set of equivalence classes in terms of bytes. We compute this while
        /// building the NFA, but don't use it in the NFA's states. Instead, we
        /// use this for building the DFA. We store it on the NFA since it's easy
        /// to compute while visiting the the patterns.
        byte_classes: ByteClasses,
        /// A set of states. Each state defines its own transitions, a fail
        /// transition and a set of indices corresponding to matches.
        ///
        /// The first state is always the fail state, which is used only as a
        /// sentinel. Namely, in the final NFA, no transition into the fail state
        /// exists. (Well, they do, but they aren't followed. Instead, the state's
        /// failure transition is followed.)
        ///
        /// The second state (index 1) is always the dead state. Dead states are
        /// in every automaton, but only used when leftmost-{first,longest} match
        /// semantics are enabled. Specifically, they instruct search to stop
        /// at specific points in order to report the correct match location. In
        /// the standard Aho-Corasick construction, there are no transitions to
        /// the dead state.
        ///
        /// The third state (index 2) is generally intended to be the starting or
        /// "root" state.
        states: Vec<State<S>>,
    }

    impl<S: StateID> NFA<S> {
        /// Returns the equivalence classes of bytes found while constructing
        /// this NFA.
        ///
        /// Note that the NFA doesn't actually make use of these equivalence
        /// classes. Instead, these are useful for building the DFA when desired.
        pub fn byte_classes(&self) -> &ByteClasses {
            &self.byte_classes
        }

        /// Returns a start byte prefilter, if one exists.
        pub fn prefilter_obj(&self) -> Option<&PrefilterObj> {
            self.prefilter.as_ref()
        }

        /// Returns the total number of heap bytes used by this NFA's transition
        /// table.
        pub fn heap_bytes(&self) -> usize {
            self.heap_bytes
        }

        /// Return the length of the longest pattern in this automaton.
        pub fn max_pattern_len(&self) -> usize {
            self.max_pattern_len
        }

        /// Return the total number of patterns added to this automaton.
        pub fn pattern_count(&self) -> usize {
            self.pattern_count
        }

        /// Returns the total number of states in this NFA.
        pub fn state_len(&self) -> usize {
            self.states.len()
        }

        /// Returns the matches for the given state.
        pub fn matches(&self, id: S) -> &[(PatternID, PatternLength)] {
            &self.states[id.to_usize()].matches
        }

        /// Returns an iterator over all transitions in the given state according
        /// to the given equivalence classes, including transitions to `fail_id()`.
        /// The number of transitions returned is always equivalent to the number
        /// of equivalence classes.
        pub fn iter_all_transitions<F: FnMut(u8, S)>(
            &self,
            byte_classes: &ByteClasses,
            id: S,
            f: F,
        ) {
            self.states[id.to_usize()].trans.iter_all(byte_classes, f);
        }

        /// Returns the failure transition for the given state.
        pub fn failure_transition(&self, id: S) -> S {
            self.states[id.to_usize()].fail
        }

        /// Returns the next state for the given state and input byte.
        ///
        /// Note that this does not follow failure transitions. As such, the id
        /// returned may be `fail_id`.
        pub fn next_state(&self, current: S, input: u8) -> S {
            self.states[current.to_usize()].next_state(input)
        }

        fn state(&self, id: S) -> &State<S> {
            &self.states[id.to_usize()]
        }

        fn state_mut(&mut self, id: S) -> &mut State<S> {
            &mut self.states[id.to_usize()]
        }

        fn start(&self) -> &State<S> {
            self.state(self.start_id)
        }

        fn start_mut(&mut self) -> &mut State<S> {
            let id = self.start_id;
            self.state_mut(id)
        }

        fn iter_transitions_mut(&mut self, id: S) -> IterTransitionsMut<S> {
            IterTransitionsMut::new(self, id)
        }

        fn copy_matches(&mut self, src: S, dst: S) {
            let (src, dst) = get_two_mut(
                &mut self.states, src.to_usize(), dst.to_usize(),
            );
            dst.matches.extend_from_slice(&src.matches);
        }

        fn copy_empty_matches(&mut self, dst: S) {
            let start_id = self.start_id;
            self.copy_matches(start_id, dst);
        }

        fn add_dense_state(&mut self, depth: usize) -> Result<S> {
            let trans = Transitions::Dense(vec![fail_id(); 256]);
            let id = usize_to_state_id(self.states.len())?;
            self.states.push(State {
                trans,
                fail: self.start_id,
                depth: depth,
                matches: vec![],
            });
            Ok(id)
        }

        fn add_sparse_state(&mut self, depth: usize) -> Result<S> {
            let trans = Transitions::Sparse(vec![]);
            let id = usize_to_state_id(self.states.len())?;
            self.states.push(State {
                trans,
                fail: self.start_id,
                depth: depth,
                matches: vec![],
            });
            Ok(id)
        }
    }

    impl<S: StateID> Automaton for NFA<S> {
        type ID = S;

        fn match_kind(&self) -> &MatchKind {
            &self.match_kind
        }

        fn prefilter(&self) -> Option<&Prefilter> {
            self.prefilter.as_ref().map(|p| p.as_ref())
        }

        fn start_state(&self) -> S {
            self.start_id
        }

        fn is_valid(&self, id: S) -> bool {
            id.to_usize() < self.states.len()
        }

        fn is_match_state(&self, id: S) -> bool {
            self.states[id.to_usize()].is_match()
        }

        fn get_match(
            &self,
            id: S,
            match_index: usize,
            end: usize,
        ) -> Option<Match> {
            let state = match self.states.get(id.to_usize()) {
                None => return None,
                Some(state) => state,
            };
            state.matches
                .get(match_index)
                .map(|&(id, len)| Match { pattern: id, len, end })
        }

        fn match_count(&self, id: S) -> usize {
            self.states[id.to_usize()].matches.len()
        }

        unsafe fn next_state_unchecked(&self, mut current: S, input: u8) -> S {
            // This terminates since:
            //
            // 1. `State.fail` never points to fail_id().
            // 2. All `State.fail` values point to a state closer to `start`.
            // 3. The start state has no transitions to fail_id().
            loop {
                let state = self.states.get_unchecked(current.to_usize());
                let next = state.next_state(input);
                if next != fail_id() {
                    return next;
                }
                current = state.fail;
            }
        }
    }

    /// A representation of an NFA state for an Aho-Corasick automaton.
    ///
    /// It contains the transitions to the next state, a failure transition for
    /// cases where there exists no other transition for the current input byte,
    /// the matches implied by visiting this state (if any) and the depth of this
    /// state. The depth of a state is simply the distance from it to the start
    /// state in the automaton, where the depth of the start state is 0.
    #[derive(Clone, Debug)]
    pub struct State<S> {
        trans: Transitions<S>,
        fail: S,
        matches: Vec<(PatternID, PatternLength)>,
        // TODO: Strictly speaking, this isn't needed for searching. It's only
        // used when building an NFA that supports leftmost match semantics. We
        // could drop this from the state and dynamically build a map only when
        // computing failure transitions, but it's not clear which is better.
        // Benchmark this.
        depth: usize,
    }

    impl<S: StateID> State<S> {
        fn heap_bytes(&self) -> usize {
            self.trans.heap_bytes()
            + (self.matches.len() * size_of::<(PatternID, PatternLength)>())
        }

        fn add_match(&mut self, i: PatternID, len: PatternLength) {
            self.matches.push((i, len));
        }

        fn is_match(&self) -> bool {
            !self.matches.is_empty()
        }

        fn get_longest_match_len(&self) -> Option<usize> {
            // Why is this true? Because the first match in any matching state
            // will always correspond to the match added to it during trie
            // construction (since when we copy matches due to failure transitions,
            // we always append them). Therefore, it follows that the first match
            // must always be longest since any subsequent match must be from a
            // failure transition, and a failure transition by construction points
            // to a proper suffix. A proper suffix is, by definition, smaller.
            self.matches.get(0).map(|&(_, len)| len)
        }

        fn next_state(&self, input: u8) -> S {
            self.trans.next_state(input)
        }

        fn set_next_state(&mut self, input: u8, next: S) {
            self.trans.set_next_state(input, next);
        }
    }

    /// A representation of transitions in an NFA.
    ///
    /// Transitions have either a sparse representation, which is slower for
    /// lookups but uses less memory, or a dense representation, which is faster
    /// for lookups but uses more memory. In the sparse representation, the absence
    /// of a state implies a transition to `fail_id()`. Transitions to `dead_id()`
    /// are still explicitly represented.
    ///
    /// For the NFA, by default, we use a dense representation for transitions for
    /// states close to the start state because it's likely these are the states
    /// that will be most frequently visited.
    #[derive(Clone, Debug)]
    enum Transitions<S> {
        Sparse(Vec<(u8, S)>),
        Dense(Vec<S>),
    }

    impl<S: StateID> Transitions<S> {
        fn heap_bytes(&self) -> usize {
            match *self {
                Transitions::Sparse(ref sparse) => {
                    sparse.len() * size_of::<(u8, S)>()
                }
                Transitions::Dense(ref dense) => {
                    dense.len() * size_of::<S>()
                }
            }
        }

        fn next_state(&self, input: u8) -> S {
            match *self {
                Transitions::Sparse(ref sparse) => {
                    for &(b, id) in sparse {
                        if b == input {
                            return id;
                        }
                    }
                    fail_id()
                }
                Transitions::Dense(ref dense) => {
                    // SAFETY: This is safe because all dense transitions have
                    // exactly 256 elements, so all u8 values are valid indices.
                    unsafe { *dense.get_unchecked(input as usize) }
                }
            }
        }

        fn set_next_state(&mut self, input: u8, next: S) {
            match *self {
                Transitions::Sparse(ref mut sparse) => {
                    match sparse.binary_search_by_key(&input, |&(b, _)| b) {
                        Ok(i) => sparse[i] = (input, next),
                        Err(i) => sparse.insert(i, (input, next)),
                    }
                }
                Transitions::Dense(ref mut dense) => {
                    dense[input as usize] = next;
                }
            }
        }

        /// Iterate over transitions in this state while skipping over transitions
        /// to `fail_id()`.
        fn iter<F: FnMut(u8, S)>(&self, mut f: F) {
            match *self {
                Transitions::Sparse(ref sparse) => {
                    for &(b, id) in sparse {
                        f(b, id);
                    }
                }
                Transitions::Dense(ref dense) => {
                    for b in AllBytesIter::new() {
                        let id = dense[b as usize];
                        if id != fail_id() {
                            f(b, id);
                        }
                    }
                }
            }
        }

        /// Iterate over all transitions in this state according to the given
        /// equivalence classes, including transitions to `fail_id()`.
        fn iter_all<F: FnMut(u8, S)>(&self, classes: &ByteClasses, mut f: F) {
            if classes.is_singleton() {
                match *self {
                    Transitions::Sparse(ref sparse) => {
                        sparse_iter(sparse, f);
                    }
                    Transitions::Dense(ref dense) => {
                        for b in AllBytesIter::new() {
                            f(b, dense[b as usize]);
                        }
                    }
                }
            } else {
                // In this case, we only want to yield a single byte for each
                // equivalence class.
                match *self {
                    Transitions::Sparse(ref sparse) => {
                        let mut last_class = None;
                        sparse_iter(sparse, |b, next| {
                            let class = classes.get(b);
                            if last_class != Some(class) {
                                last_class = Some(class);
                                f(b, next);
                            }
                        })
                    }
                    Transitions::Dense(ref dense) => {
                        for b in classes.representatives() {
                            f(b, dense[b as usize]);
                        }
                    }
                }
            }
        }
    }

    /// Iterator over transitions in a state, skipping transitions to `fail_id()`.
    ///
    /// This abstracts over the representation of NFA transitions, which may be
    /// either in a sparse or dense representation.
    ///
    /// This somewhat idiosyncratically borrows the NFA mutably, so that when one
    /// is iterating over transitions, the caller can still mutate the NFA. This
    /// is useful when creating failure transitions.
    #[derive(Debug)]
    struct IterTransitionsMut<'a, S: StateID + 'a> {
        nfa: &'a mut NFA<S>,
        state_id: S,
        cur: usize,
    }

    impl<'a, S: StateID> IterTransitionsMut<'a, S> {
        fn new(nfa: &'a mut NFA<S>, state_id: S) -> IterTransitionsMut<'a, S> {
            IterTransitionsMut { nfa, state_id, cur: 0 }
        }

        fn nfa(&mut self) -> &mut NFA<S> {
            self.nfa
        }
    }

    impl<'a, S: StateID> Iterator for IterTransitionsMut<'a, S> {
        type Item = (u8, S);

        fn next(&mut self) -> Option<(u8, S)> {
            match self.nfa.states[self.state_id.to_usize()].trans {
                Transitions::Sparse(ref sparse) => {
                    if self.cur >= sparse.len() {
                        return None;
                    }
                    let i = self.cur;
                    self.cur += 1;
                    Some(sparse[i])
                }
                Transitions::Dense(ref dense) => {
                    while self.cur < dense.len() {
                        // There are always exactly 255 transitions in dense repr.
                        debug_assert!(self.cur < 256);

                        let b = self.cur as u8;
                        let id = dense[self.cur];
                        self.cur += 1;
                        if id != fail_id() {
                            return Some((b, id));
                        }
                    }
                    None
                }
            }
        }
    }

    /// A simple builder for configuring the NFA construction of Aho-Corasick.
    #[derive(Clone, Debug)]
    pub struct Builder {
        dense_depth: usize,
        match_kind: MatchKind,
        prefilter: bool,
        ascii_case_insensitive: bool,
    }

    impl Default for Builder {
        fn default() -> Builder {
            Builder {
                dense_depth: 2,
                match_kind: MatchKind::default(),
                prefilter: true,
                ascii_case_insensitive: false,
            }
        }
    }

    impl Builder {
        pub fn new() -> Builder {
            Builder::default()
        }

        pub fn build<I, P, S: StateID>(
            &self,
            patterns: I,
        ) -> Result<NFA<S>>
        where I: IntoIterator<Item=P>,
              P: AsRef<[u8]>
        {
            Compiler::new(self)?.compile(patterns)
        }

        pub fn match_kind(&mut self, kind: MatchKind) -> &mut Builder {
            self.match_kind = kind;
            self
        }

        pub fn dense_depth(&mut self, depth: usize) -> &mut Builder {
            self.dense_depth = depth;
            self
        }

        pub fn prefilter(&mut self, yes: bool) -> &mut Builder {
            self.prefilter = yes;
            self
        }

        pub fn ascii_case_insensitive(&mut self, yes: bool) -> &mut Builder {
            self.ascii_case_insensitive = yes;
            self
        }
    }

    /// A compiler uses a builder configuration and builds up the NFA formulation
    /// of an Aho-Corasick automaton. This roughly corresponds to the standard
    /// formulation described in textbooks.
    #[derive(Debug)]
    struct Compiler<'a, S: StateID> {
        builder: &'a Builder,
        nfa: NFA<S>,
        byte_classes: ByteClassBuilder,
    }

    impl<'a, S: StateID> Compiler<'a, S> {
        fn new(builder: &'a Builder) -> Result<Compiler<'a, S>> {
            Ok(Compiler {
                builder: builder,
                nfa: NFA {
                    match_kind: builder.match_kind,
                    start_id: usize_to_state_id(2)?,
                    max_pattern_len: 0,
                    pattern_count: 0,
                    heap_bytes: 0,
                    prefilter: None,
                    byte_classes: ByteClasses::singletons(),
                    states: vec![],
                },
                byte_classes: ByteClassBuilder::new(),
            })
        }

        fn compile<I, P>(
            mut self,
            patterns: I,
        ) -> Result<NFA<S>>
        where I: IntoIterator<Item=P>,
              P: AsRef<[u8]>
        {
            self.add_state(0)?; // the fail state, which is never entered
            self.add_state(0)?; // the dead state, only used for leftmost
            self.add_state(0)?; // the start state
            self.build_trie(patterns)?;
            self.add_start_state_loop();
            self.add_dead_state_loop();
            if self.match_kind().is_leftmost() {
                self.fill_failure_transitions_leftmost();
            } else {
                self.fill_failure_transitions_standard();
            }
            self.close_start_state_loop();
            self.nfa.byte_classes = self.byte_classes.build();
            self.build_prefilters();
            self.calculate_size();
            Ok(self.nfa)
        }

        /// This sets up the initial prefix trie that makes up the Aho-Corasick
        /// automaton. Effectively, it creates the basic structure of the
        /// automaton, where every pattern given has a path from the start state to
        /// the end of the pattern.
        fn build_trie<I, P>(
            &mut self,
            patterns: I,
        ) -> Result<()>
        where I: IntoIterator<Item=P>,
              P: AsRef<[u8]>
        {
        'PATTERNS:
            for (pati, pat) in patterns.into_iter().enumerate() {
                let pat = pat.as_ref();
                self.nfa.max_pattern_len = cmp::max(
                    self.nfa.max_pattern_len, pat.len(),
                );
                self.nfa.pattern_count += 1;

                let mut prev = self.nfa.start_id;
                let mut saw_match = false;
                for (depth, &b) in pat.iter().enumerate() {
                    // When leftmost-first match semantics are requested, we
                    // specifically stop adding patterns when a previously added
                    // pattern is a prefix of it. We avoid adding it because
                    // leftmost-first semantics imply that the pattern can never
                    // match. This is not just an optimization to save space! It
                    // is necessary for correctness. In fact, this is the only
                    // difference in the automaton between the implementations for
                    // leftmost-first and leftmost-longest.
                    saw_match = saw_match || self.nfa.state(prev).is_match();
                    if self.builder.match_kind.is_leftmost_first() && saw_match {
                        // Skip to the next pattern immediately. This avoids
                        // incorrectly adding a match after this loop terminates.
                        continue 'PATTERNS;
                    }

                    // Add this byte to our equivalence classes. We don't use these
                    // for NFA construction. These are instead used only if we're
                    // building a DFA. They would technically be useful for the
                    // NFA, but it would require a second pass over the patterns.
                    self.byte_classes.set_range(b, b);

                    // If the transition from prev using the current byte already
                    // exists, then just move through it. Otherwise, add a new
                    // state. We track the depth here so that we can determine
                    // how to represent transitions. States near the start state
                    // use a dense representation that uses more memory but is
                    // faster. Other states use a sparse representation that uses
                    // less memory but is slower.
                    let next = self.nfa.state(prev).next_state(b);
                    if next != fail_id() {
                        prev = next;
                    } else {
                        let next = self.add_state(depth + 1)?;
                        self.nfa.state_mut(prev).set_next_state(b, next);
                        if self.builder.ascii_case_insensitive {
                            if b'A' <= b && b <= b'Z' {
                                let b = b.to_ascii_lowercase();
                                self.nfa.state_mut(prev).set_next_state(b, next);
                            } else if b'a' <= b && b <= b'z' {
                                let b = b.to_ascii_uppercase();
                                self.nfa.state_mut(prev).set_next_state(b, next);
                            }
                        }
                        prev = next;
                    }
                }
                // Once the pattern has been added, log the match in the final
                // state that it reached.
                self.nfa.state_mut(prev).add_match(pati, pat.len());
            }
            Ok(())
        }

        /// This routine creates failure transitions according to the standard
        /// textbook formulation of the Aho-Corasick algorithm.
        ///
        /// Building failure transitions is the most interesting part of building
        /// the Aho-Corasick automaton, because they are what allow searches to
        /// be performed in linear time. Specifically, a failure transition is
        /// a single transition associated with each state that points back to
        /// the longest proper suffix of the pattern being searched. The failure
        /// transition is followed whenever there exists no transition on the
        /// current state for the current input byte. If there is no other proper
        /// suffix, then the failure transition points back to the starting state.
        ///
        /// For example, let's say we built an Aho-Corasick automaton with the
        /// following patterns: 'abcd' and 'cef'. The trie looks like this:
        ///
        /// ```ignore
        ///          a - S1 - b - S2 - c - S3 - d - S4*
        ///         /
        ///     S0 - c - S5 - e - S6 - f - S7*
        /// ```
        ///
        /// At this point, it should be fairly straight-forward to see how this
        /// trie can be used in a simplistic way. At any given position in the
        /// text we're searching (called the "subject" string), all we need to do
        /// is follow the transitions in the trie by consuming one transition for
        /// each byte in the subject string. If we reach a match state, then we can
        /// report that location as a match.
        ///
        /// The trick comes when searching a subject string like 'abcef'. We'll
        /// initially follow the transition from S0 to S1 and wind up in S3 after
        /// observng the 'c' byte. At this point, the next byte is 'e' but state
        /// S3 has no transition for 'e', so the search fails. We then would need
        /// to restart the search at the next position in 'abcef', which
        /// corresponds to 'b'. The match would fail, but the next search starting
        /// at 'c' would finally succeed. The problem with this approach is that
        /// we wind up searching the subject string potentially many times. In
        /// effect, this makes the algorithm have worst case `O(n * m)` complexity,
        /// where `n ~ len(subject)` and `m ~ len(all patterns)`. We would instead
        /// like to achieve a `O(n + m)` worst case complexity.
        ///
        /// This is where failure transitions come in. Instead of dying at S3 in
        /// the first search, the automaton can instruct the search to move to
        /// another part of the automaton that corresponds to a suffix of what
        /// we've seen so far. Recall that we've seen 'abc' in the subject string,
        /// and the automaton does indeed have a non-empty suffix, 'c', that could
        /// potentially lead to another match. Thus, the actual Aho-Corasick
        /// automaton for our patterns in this case looks like this:
        ///
        /// ```ignore
        ///          a - S1 - b - S2 - c - S3 - d - S4*
        ///         /                      /
        ///        /       ----------------
        ///       /       /
        ///     S0 - c - S5 - e - S6 - f - S7*
        /// ```
        ///
        /// That is, we have a failure transition from S3 to S5, which is followed
        /// exactly in cases when we are in state S3 but see any byte other than
        /// 'd' (that is, we've "failed" to find a match in this portion of our
        /// trie). We know we can transition back to S5 because we've already seen
        /// a 'c' byte, so we don't need to re-scan it. We can then pick back up
        /// with the search starting at S5 and complete our match.
        ///
        /// Adding failure transitions to a trie is fairly simple, but subtle. The
        /// key issue is that you might have multiple failure transition that you
        /// need to follow. For example, look at the trie for the patterns
        /// 'abcd', 'b', 'bcd' and 'cd':
        ///
        /// ```ignore
        ///        - a - S1 - b - S2 - c - S3 - d - S4*
        ///       /
        ///     S0 - b - S5* - c - S6 - d - S7*
        ///       \
        ///        - c - S8 - d - S9*
        /// ```
        ///
        /// The failure transitions for this trie are defined from S2 to S5,
        /// S3 to S6 and S6 to S8. Moreover, state S2 needs to track that it
        /// corresponds to a match, since its failure transition to S5 is itself
        /// a match state.
        ///
        /// Perhaps simplest way to think about adding these failure transitions
        /// is recursively. That is, if you know the failure transitions for every
        /// possible previous state that could be visited (e.g., when computing the
        /// failure transition for S3, you already know the failure transitions
        /// for S0, S1 and S2), then you can simply follow the failure transition
        /// of the previous state and check whether the incoming transition is
        /// defined after following the failure transition.
        ///
        /// For example, when determining the failure state for S3, by our
        /// assumptions, we already know that there is a failure transition from
        /// S2 (the previous state) to S5. So we follow that transition and check
        /// whether the transition connecting S2 to S3 is defined. Indeed, it is,
        /// as there is a transition from S5 to S6 for the byte 'c'. If no such
        /// transition existed, we could keep following the failure transitions
        /// until we reach the start state, which is the failure transition for
        /// every state that has no corresponding proper suffix.
        ///
        /// We don't actually use recursion to implement this, but instead, use a
        /// breadth first search of the automaton. Our base case is the start
        /// state, whose failure transition is just a transition to itself.
        fn fill_failure_transitions_standard(&mut self) {
            // Initialize the queue for breadth first search with all transitions
            // out of the start state. We handle the start state specially because
            // we only want to follow non-self transitions. If we followed self
            // transitions, then this would never terminate.
            let mut queue = VecDeque::new();
            for b in AllBytesIter::new() {
                let next = self.nfa.start().next_state(b);
                if next != self.nfa.start_id {
                    queue.push_back(next);
                }
            }
            while let Some(id) = queue.pop_front() {
                let mut it = self.nfa.iter_transitions_mut(id);
                while let Some((b, next)) = it.next() {
                    queue.push_back(next);

                    let mut fail = it.nfa().state(id).fail;
                    while it.nfa().state(fail).next_state(b) == fail_id() {
                        fail = it.nfa().state(fail).fail;
                    }
                    fail = it.nfa().state(fail).next_state(b);
                    it.nfa().state_mut(next).fail = fail;
                    it.nfa().copy_matches(fail, next);
                }
                // If the start state is a match state, then this automaton can
                // match the empty string. This implies all states are match states
                // since every position matches the empty string, so copy the
                // matches from the start state to every state. Strictly speaking,
                // this is only necessary for overlapping matches since each
                // non-empty non-start match state needs to report empty matches
                // in addition to its own. For the non-overlapping case, such
                // states only report the first match, which is never empty since
                // it isn't a start state.
                it.nfa().copy_empty_matches(id);
            }
        }

        /// This routine is just like fill_failure_transitions_standard, except
        /// it adds failure transitions in a way that preserves leftmost match
        /// semantics (for both leftmost-first and leftmost-longest).
        ///
        /// The algorithms are so similar that it would be possible to write it
        /// generically. But doing so without overhead would require a bit of
        /// ceremony, so we just copy it and add in the extra leftmost logic.
        /// Moreover, the standard algorithm above is so simple that it feels like
        /// a crime to disturb it.
        ///
        /// In effect, this proceeds just like the standard approach, but we
        /// specifically add only a subset of all failure transitions. Namely, we
        /// only add failure transitions that either do not occur after a match
        /// or failure transitions that do occur after a match but preserve the
        /// match. The comments in the implementation below should help.
        ///
        /// N.B. The only differences in the automaton between leftmost-first and
        /// leftmost-longest are in trie construction. Otherwise, both have exactly
        /// the same set of failure transitions. leftmost-longest adds everything
        /// to the trie, where as leftmost-first skips any patterns for which there
        /// exists a prefix of it that was added earlier.
        ///
        /// N.B. I came up with this algorithm on my own, and after scouring all of
        /// the other AC implementations I know of (Perl, Snort, many on GitHub).
        /// I couldn't find any that implement leftmost semantics like this.
        /// Perl of course needs leftmost-first semantics, but they implement it
        /// with a seeming hack at *search* time instead of encoding it into the
        /// automaton. There are also a couple Java libraries that support leftmost
        /// longest semantics, but they do it by building a queue of matches at
        /// search time, which is even worse than what Perl is doing. ---AG
        fn fill_failure_transitions_leftmost(&mut self) {
            /// Represents an item in our queue of states to process.
            ///
            /// Fundamentally, this queue serves the same purpose as the queue
            /// for filling failure transitions using the standard formulation.
            /// In the leftmost case, though, we need to track a bit more
            /// information. See comments below.
            #[derive(Clone, Copy, Debug)]
            struct QueuedState<S> {
                /// The id of the state to visit.
                id: S,
                /// The depth at which the first match was observed in the path
                /// to this state. Note that this corresponds to the depth at
                /// which the beginning of the match was detected. If no match
                /// has been seen, then this is None.
                match_at_depth: Option<usize>,
            }

            impl<S: StateID> QueuedState<S> {
                /// Create a queued state corresponding to the given NFA's start
                /// state.
                fn start(nfa: &NFA<S>) -> QueuedState<S> {
                    let match_at_depth =
                        if nfa.start().is_match() {
                            Some(0)
                        } else {
                            None
                        };
                    QueuedState { id: nfa.start_id, match_at_depth }
                }

                /// Return the next state to queue up. The given id must be a state
                /// corresponding to a single transition from this queued state.
                fn next_queued_state(
                    &self,
                    nfa: &NFA<S>,
                    id: S,
                ) -> QueuedState<S> {
                    let match_at_depth = self.next_match_at_depth(nfa, id);
                    QueuedState { id, match_at_depth }
                }

                /// Return the earliest depth at which a match has occurred for
                /// the given state. The given state must correspond to a single
                /// transition from this queued state.
                fn next_match_at_depth(
                    &self,
                    nfa: &NFA<S>,
                    next: S,
                ) -> Option<usize> {
                    // This is a little tricky. If the previous state has already
                    // seen a match or if `next` isn't a match state, then nothing
                    // needs to change since a later state cannot find an earlier
                    // match.
                    match self.match_at_depth {
                        Some(x) => return Some(x),
                        None if nfa.state(next).is_match() => {}
                        None => return None,
                    }
                    let depth =
                        nfa.state(next).depth
                        - nfa.state(next).get_longest_match_len().unwrap()
                        + 1;
                    Some(depth)
                }
            }

            // Initialize the queue for breadth first search with all transitions
            // out of the start state. We handle the start state specially because
            // we only want to follow non-self transitions. If we followed self
            // transitions, then this would never terminate.
            let mut queue: VecDeque<QueuedState<S>> = VecDeque::new();
            let start = QueuedState::start(&self.nfa);
            for b in AllBytesIter::new() {
                let next_id = self.nfa.start().next_state(b);
                if next_id != start.id {
                    let next = start.next_queued_state(&self.nfa, next_id);
                    queue.push_back(next);
                    // If a state immediately following the start state is a match
                    // state, then we never want to follow its failure transition
                    // since the failure transition necessarily leads back to the
                    // start state, which we never want to do for leftmost matching
                    // after a match has been found.
                    //
                    // N.B. This is a special case of the more general handling
                    // found below.
                    if self.nfa.state(next_id).is_match() {
                        self.nfa.state_mut(next_id).fail = dead_id();
                    }
                }
            }
            while let Some(item) = queue.pop_front() {
                let mut any_trans = false;
                let mut it = self.nfa.iter_transitions_mut(item.id);
                while let Some((b, next_id)) = it.next() {
                    any_trans = true;

                    // Queue up the next state.
                    let next = item.next_queued_state(it.nfa(), next_id);
                    queue.push_back(next);

                    // Find the failure state for next. Same as standard.
                    let mut fail = it.nfa().state(item.id).fail;
                    while it.nfa().state(fail).next_state(b) == fail_id() {
                        fail = it.nfa().state(fail).fail;
                    }
                    fail = it.nfa().state(fail).next_state(b);

                    // This is the key difference from the standard formulation.
                    // Namely, if we've seen a match, then we only want a failure
                    // transition if the failure transition preserves the match
                    // we've seen. In general, this is not true of all failure
                    // transitions since they can point back to any suffix of what
                    // we've seen so far. Instead, we only want to point back to
                    // suffixes that contain any match we've seen.
                    //
                    // We achieve this by comparing the depth of the failure
                    // transition with the number of states between this state
                    // and the beginning of the earliest match detected. If the
                    // depth of the failure state is smaller than this difference,
                    // then it cannot contain the match. If it's bigger or equal
                    // to the difference, then it necessarily includes the match
                    // we've seen since all failure transitions correspond to a
                    // suffix.
                    //
                    // If we've determined that we don't want the failure
                    // transition, then we set this state's failure transition to
                    // the dead state. In other words, when a search hits this
                    // state, it will not continue and correctly stop. (N.B. A
                    // dead state is different than a fail state. A dead state
                    // MUST be preceded by a match and acts as a sentinel to search
                    // routines to terminate.)
                    //
                    // Understanding this is tricky, and it took me several days
                    // to think through this and get it right. If you want to grok
                    // it, then I'd recommend: 1) switch the implementation to
                    // always use the standard algorithm for filling in failure
                    // transitions, 2) run the test suite and 3) examine the test
                    // failures. Write out the automatons for them and try to work
                    // backwards by figuring out which failure transitions should
                    // be removed. You should arrive at the same rule used below.
                    if let Some(match_depth) = next.match_at_depth {
                        let fail_depth = it.nfa().state(fail).depth;
                        let next_depth = it.nfa().state(next.id).depth;
                        if next_depth - match_depth + 1 > fail_depth {
                            it.nfa().state_mut(next.id).fail = dead_id();
                            continue;
                        }
                        assert_ne!(
                            start.id,
                            it.nfa().state(next.id).fail,
                            "states that are match states or follow match \
                             states should never have a failure transition \
                             back to the start state in leftmost searching",
                        );
                    }
                    it.nfa().state_mut(next.id).fail = fail;
                    it.nfa().copy_matches(fail, next.id);
                }
                // If there are no transitions for this state and if it's a match
                // state, then we must set its failure transition to the dead
                // state since we never want it to restart the search.
                if !any_trans && it.nfa().state(item.id).is_match() {
                    it.nfa().state_mut(item.id).fail = dead_id();
                }
                // We don't need to copy empty matches from the start state here
                // because that's only necessary for overlapping matches and
                // leftmost match kinds don't support overlapping matches.
            }
        }

        /// Construct prefilters from the automaton, if applicable.
        fn build_prefilters(&mut self) {
            if !self.builder.prefilter {
                return;
            }

            let mut builder = prefilter::StartBytesBuilder::new();
            for b in AllBytesIter::new() {
                if self.nfa.start().next_state(b) != self.nfa.start_id {
                    builder.add(b);
                }
            }
            self.nfa.prefilter = builder.build();
        }

        /// Set the failure transitions on the start state to loop back to the
        /// start state. This effectively permits the Aho-Corasick automaton to
        /// match at any position. This is also required for finding the next
        /// state to terminate, namely, finding the next state should never return
        /// a fail_id.
        ///
        /// This must be done after building the initial trie, since trie
        /// construction depends on transitions to `fail_id` to determine whether a
        /// state already exists or not.
        fn add_start_state_loop(&mut self) {
            let start_id = self.nfa.start_id;
            let start = self.nfa.start_mut();
            for b in AllBytesIter::new() {
                if start.next_state(b) == fail_id() {
                    start.set_next_state(b, start_id);
                }
            }
        }

        /// Remove the start state loop by rewriting any transitions on the start
        /// state back to the start state with transitions to the dead state.
        ///
        /// The loop is only closed when two conditions are met: the start state
        /// is a match state and the match kind is leftmost-first or
        /// leftmost-longest.
        ///
        /// The reason for this is that under leftmost semantics, a start state
        /// that is also a match implies that we should never restart the search
        /// process. We allow normal transitions out of the start state, but if
        /// none exist, we transition to the dead state, which signals that
        /// searching should stop.
        fn close_start_state_loop(&mut self) {
            if self.match_kind().is_leftmost() && self.nfa.start().is_match() {
                let start_id = self.nfa.start_id;
                let start = self.nfa.start_mut();
                for b in AllBytesIter::new() {
                    if start.next_state(b) == start_id {
                        start.set_next_state(b, dead_id());
                    }
                }
            }
        }

        /// Sets all transitions on the dead state to point back to the dead state.
        /// Normally, missing transitions map back to the failure state, but the
        /// point of the dead state is to act as a sink that can never be escaped.
        fn add_dead_state_loop(&mut self) {
            let dead = self.nfa.state_mut(dead_id());
            for b in AllBytesIter::new() {
                dead.set_next_state(b, dead_id());
            }
        }

        /// Computes the total amount of heap used by this NFA in bytes.
        fn calculate_size(&mut self) {
            let mut size = 0;
            for state in &self.nfa.states {
                size += state.heap_bytes();
            }
            self.nfa.heap_bytes = size;
        }

        /// Add a new state to the underlying NFA with the given depth. The depth
        /// is used to determine how to represent the transitions.
        ///
        /// If adding the new state would overflow the chosen state ID
        /// representation, then this returns an error.
        fn add_state(&mut self, depth: usize) -> Result<S> {
            if depth < self.builder.dense_depth {
                self.nfa.add_dense_state(depth)
            } else {
                self.nfa.add_sparse_state(depth)
            }
        }

        /// Returns the match kind configured on the underlying builder.
        fn match_kind(&self) -> MatchKind {
            self.builder.match_kind
        }
    }

    /// An iterator over every byte value.
    ///
    /// We use this instead of (0..256).map(|b| b as u8) because this optimizes
    /// better in debug builds.
    ///
    /// We also use this instead of 0..=255 because we're targeting Rust 1.24 and
    /// inclusive range syntax was stabilized in Rust 1.26. We can get rid of this
    /// once our MSRV is Rust 1.26 or newer.
    #[derive(Debug)]
    struct AllBytesIter(u16);

    impl AllBytesIter {
        fn new() -> AllBytesIter {
            AllBytesIter(0)
        }
    }

    impl Iterator for AllBytesIter {
        type Item = u8;

        fn next(&mut self) -> Option<Self::Item> {
            if self.0 >= 256 {
                None
            } else {
                let b = self.0 as u8;
                self.0 += 1;
                Some(b)
            }
        }
    }

    impl<S: StateID> fmt::Debug for NFA<S> {
        fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
            writeln!(f, "NFA(")?;
            writeln!(f, "match_kind: {:?}", self.match_kind)?;
            writeln!(f, "{}", "-".repeat(79))?;
            for (id, s) in self.states.iter().enumerate() {
                let mut trans = vec![];
                s.trans.iter(|byte, next| {
                    // The start state has a bunch of uninteresting transitions
                    // back into itself. It's questionable to hide them since they
                    // are critical to understanding the automaton, but they are
                    // very noisy without better formatting for contiugous ranges
                    // to the same state.
                    if id == self.start_id.to_usize() && next == self.start_id {
                        return;
                    }
                    // Similarly, the dead state has a bunch of uninteresting
                    // transitions too.
                    if id == dead_id() {
                        return;
                    }
                    trans.push(format!("{} => {}", escape(byte), next.to_usize()));
                });
                writeln!(f, "{:04}: {}", id, trans.join(", "))?;

                let matches: Vec<String> = s.matches
                    .iter()
                    .map(|&(pattern_id, _)| pattern_id.to_string())
                    .collect();
                writeln!(f, "  matches: {}", matches.join(", "))?;
                writeln!(f, "     fail: {}", s.fail.to_usize())?;
                writeln!(f, "    depth: {}", s.depth)?;
            }
            writeln!(f, "{}", "-".repeat(79))?;
            writeln!(f, ")")?;
            Ok(())
        }
    }

    /// Iterate over all possible byte transitions given a sparse set.
    fn sparse_iter<S: StateID, F: FnMut(u8, S)>(trans: &[(u8, S)], mut f: F) {
        let mut byte = 0u16;
        for &(b, id) in trans {
            while byte < (b as u16) {
                f(byte as u8, fail_id());
                byte += 1;
            }
            f(b, id);
            byte += 1;
        }
        for b in byte..256 {
            f(b as u8, fail_id());
        }
    }

    /// Safely return two mutable borrows to two different locations in the given
    /// slice.
    ///
    /// This panics if i == j.
    fn get_two_mut<T>(xs: &mut [T], i: usize, j: usize) -> (&mut T, &mut T) {
        assert!(i != j, "{} must not be equal to {}", i, j);
        if i < j {
            let (before, after) = xs.split_at_mut(j);
            (&mut before[i], &mut after[0])
        } else {
            let (before, after) = xs.split_at_mut(i);
            (&mut after[0], &mut before[j])
        }
    }

    /// Return the given byte as its escaped string form.
    fn escape(b: u8) -> String {
        use std::ascii;

        String::from_utf8(ascii::escape_default(b).collect::<Vec<_>>()).unwrap()
    }

    #[cfg(test)]
    mod tests {
        use super::*;

        #[test]
        fn scratch() {
            let nfa: NFA<usize> = Builder::new()
                .dense_depth(0)
                // .match_kind(MatchKind::LeftmostShortest)
                // .match_kind(MatchKind::LeftmostLongest)
                .match_kind(MatchKind::LeftmostFirst)
                // .build(&["abcd", "ce", "b"])
                // .build(&["ab", "bc"])
                // .build(&["b", "bcd", "ce"])
                // .build(&["abc", "bx"])
                // .build(&["abc", "bd", "ab"])
                // .build(&["abcdefghi", "hz", "abcdefgh"])
                // .build(&["abcd", "bce", "b"])
                .build(&["abcdefg", "bcde", "bcdef"])
                .unwrap();
            println!("{:?}", nfa);
        }
    }

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