// label_reachable.h

// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
// Copyright 2005-2010 Google, Inc.
// Author: riley@google.com (Michael Riley)
//
// \file
// Class to determine if a non-epsilon label can be read as the
// first non-epsilon symbol along some path from a given state.


#ifndef FST_LIB_LABEL_REACHABLE_H__
#define FST_LIB_LABEL_REACHABLE_H__

#include <unordered_map>
using std::tr1::unordered_map;
using std::tr1::unordered_multimap;
#include <vector>
using std::vector;

#include <fst/accumulator.h>
#include <fst/arcsort.h>
#include <fst/interval-set.h>
#include <fst/state-reachable.h>
#include <fst/vector-fst.h>


namespace fst {

// Stores shareable data for label reachable class copies.
template <typename L>
class LabelReachableData {
 public:
  typedef L Label;
  typedef typename IntervalSet<L>::Interval Interval;

  explicit LabelReachableData(bool reach_input, bool keep_relabel_data = true)
      : reach_input_(reach_input),
        keep_relabel_data_(keep_relabel_data),
        have_relabel_data_(true),
        final_label_(kNoLabel) {}

  ~LabelReachableData() {}

  bool ReachInput() const { return reach_input_; }

  vector< IntervalSet<L> > *IntervalSets() { return &isets_; }

  unordered_map<L, L> *Label2Index() {
    if (!have_relabel_data_)
      FSTERROR() << "LabelReachableData: no relabeling data";
    return &label2index_;
  }

  Label FinalLabel() {
    if (final_label_ == kNoLabel)
      final_label_ = label2index_[kNoLabel];
    return final_label_;
  }

  static LabelReachableData<L> *Read(istream &istrm) {
    LabelReachableData<L> *data = new LabelReachableData<L>();

    ReadType(istrm, &data->reach_input_);
    ReadType(istrm, &data->keep_relabel_data_);
    data->have_relabel_data_ = data->keep_relabel_data_;
    if (data->keep_relabel_data_)
      ReadType(istrm, &data->label2index_);
    ReadType(istrm, &data->final_label_);
    ReadType(istrm, &data->isets_);
    return data;
  }

  bool Write(ostream &ostrm) {
    WriteType(ostrm, reach_input_);
    WriteType(ostrm, keep_relabel_data_);
    if (keep_relabel_data_)
      WriteType(ostrm, label2index_);
    WriteType(ostrm, FinalLabel());
    WriteType(ostrm, isets_);
    return true;
  }

  int RefCount() const { return ref_count_.count(); }
  int IncrRefCount() { return ref_count_.Incr(); }
  int DecrRefCount() { return ref_count_.Decr(); }

 private:
  LabelReachableData() {}

  bool reach_input_;                  // Input or output labels considered?
  bool keep_relabel_data_;            // Save label2index_ to file?
  bool have_relabel_data_;            // Using label2index_?
  Label final_label_;                 // Final label
  RefCounter ref_count_;              // Reference count.
  unordered_map<L, L> label2index_;        // Finds index for a label.
  vector<IntervalSet <L> > isets_;    // Interval sets per state.

  DISALLOW_COPY_AND_ASSIGN(LabelReachableData);
};


// Tests reachability of labels from a given state. If reach_input =
// true, then input labels are considered, o.w. output labels are
// considered. To test for reachability from a state s, first do
// SetState(s). Then a label l can be reached from state s of FST f
// iff Reach(r) is true where r = Relabel(l). The relabeling is
// required to ensure a compact representation of the reachable
// labels.

// The whole FST can be relabeled instead with Relabel(&f,
// reach_input) so that the test Reach(r) applies directly to the
// labels of the transformed FST f. The relabeled FST will also be
// sorted appropriately for composition.
//
// Reachablity of a final state from state s (via an epsilon path)
// can be tested with ReachFinal();
//
// Reachability can also be tested on the set of labels specified by
// an arc iterator, useful for FST composition.  In particular,
// Reach(aiter, ...) is true if labels on the input (output) side of
// the transitions of the arc iterator, when iter_input is true
// (false), can be reached from the state s. The iterator labels must
// have already been relabeled.
//
// With the arc iterator test of reachability, the begin position, end
// position and accumulated arc weight of the matches can be
// returned. The optional template argument controls how reachable arc
// weights are accumulated.  The default uses the semiring
// Plus(). Alternative ones can be used to distribute the weights in
// composition in various ways.
template <class A, class S = DefaultAccumulator<A> >
class LabelReachable {
 public:
  typedef A Arc;
  typedef typename A::StateId StateId;
  typedef typename A::Label Label;
  typedef typename A::Weight Weight;
  typedef typename IntervalSet<Label>::Interval Interval;

  LabelReachable(const Fst<A> &fst, bool reach_input, S *s = 0,
                 bool keep_relabel_data = true)
      : fst_(new VectorFst<Arc>(fst)),
        s_(kNoStateId),
        data_(new LabelReachableData<Label>(reach_input, keep_relabel_data)),
        accumulator_(s ? s : new S()),
        ncalls_(0),
        nintervals_(0),
        error_(false) {
    StateId ins = fst_->NumStates();
    TransformFst();
    FindIntervals(ins);
    delete fst_;
  }

  explicit LabelReachable(LabelReachableData<Label> *data, S *s = 0)
    : fst_(0),
      s_(kNoStateId),
      data_(data),
      accumulator_(s ? s : new S()),
      ncalls_(0),
      nintervals_(0),
      error_(false) {
    data_->IncrRefCount();
  }

  LabelReachable(const LabelReachable<A, S> &reachable) :
      fst_(0),
      s_(kNoStateId),
      data_(reachable.data_),
      accumulator_(new S(*reachable.accumulator_)),
      ncalls_(0),
      nintervals_(0),
      error_(reachable.error_) {
    data_->IncrRefCount();
  }

  ~LabelReachable() {
    if (!data_->DecrRefCount())
      delete data_;
    delete accumulator_;
    if (ncalls_ > 0) {
      VLOG(2) << "# of calls: " << ncalls_;
      VLOG(2) << "# of intervals/call: " << (nintervals_ / ncalls_);
    }
  }

  // Relabels w.r.t labels that give compact label sets.
  Label Relabel(Label label) {
    if (label == 0 || error_)
      return label;
    unordered_map<Label, Label> &label2index = *data_->Label2Index();
    Label &relabel = label2index[label];
    if (!relabel)  // Add new label
      relabel = label2index.size() + 1;
    return relabel;
  }

  // Relabels Fst w.r.t to labels that give compact label sets.
  void Relabel(MutableFst<Arc> *fst, bool relabel_input) {
    for (StateIterator< MutableFst<Arc> > siter(*fst);
         !siter.Done(); siter.Next()) {
      StateId s = siter.Value();
      for (MutableArcIterator< MutableFst<Arc> > aiter(fst, s);
           !aiter.Done();
           aiter.Next()) {
        Arc arc = aiter.Value();
        if (relabel_input)
          arc.ilabel = Relabel(arc.ilabel);
        else
          arc.olabel = Relabel(arc.olabel);
        aiter.SetValue(arc);
      }
    }
    if (relabel_input) {
      ArcSort(fst, ILabelCompare<Arc>());
      fst->SetInputSymbols(0);
    } else {
      ArcSort(fst, OLabelCompare<Arc>());
      fst->SetOutputSymbols(0);
    }
  }

  // Returns relabeling pairs (cf. relabel.h::Relabel()).
  // If 'avoid_collisions' is true, extra pairs are added to
  // ensure no collisions when relabeling automata that have
  // labels unseen here.
  void RelabelPairs(vector<pair<Label, Label> > *pairs,
                    bool avoid_collisions = false) {
    pairs->clear();
    unordered_map<Label, Label> &label2index = *data_->Label2Index();
    // Maps labels to their new values in [1, label2index().size()]
    for (typename unordered_map<Label, Label>::const_iterator
             it = label2index.begin(); it != label2index.end(); ++it)
      if (it->second != data_->FinalLabel())
        pairs->push_back(pair<Label, Label>(it->first, it->second));
    if (avoid_collisions) {
      // Ensures any label in [1, label2index().size()] is mapped either
      // by the above step or to label2index() + 1 (to avoid collisions).
      for (int i = 1; i <= label2index.size(); ++i) {
        typename unordered_map<Label, Label>::const_iterator
            it = label2index.find(i);
        if (it == label2index.end() || it->second == data_->FinalLabel())
          pairs->push_back(pair<Label, Label>(i, label2index.size() + 1));
      }
    }
  }

  // Set current state. Optionally set state associated
  // with arc iterator to be passed to Reach.
  void SetState(StateId s, StateId aiter_s = kNoStateId) {
    s_ = s;
    if (aiter_s != kNoStateId) {
      accumulator_->SetState(aiter_s);
      if (accumulator_->Error()) error_ = true;
    }
  }

  // Can reach this label from current state?
  // Original labels must be transformed by the Relabel methods above.
  bool Reach(Label label) {
    if (label == 0 || error_)
      return false;
    vector< IntervalSet<Label> > &isets = *data_->IntervalSets();
    return isets[s_].Member(label);

  }

  // Can reach final state (via epsilon transitions) from this state?
  bool ReachFinal() {
    if (error_) return false;
    vector< IntervalSet<Label> > &isets = *data_->IntervalSets();
    return isets[s_].Member(data_->FinalLabel());
  }

  // Initialize with secondary FST to be used with Reach(Iterator,...).
  // If copy is true, then 'fst' is a copy of the FST used in the
  // previous call to this method (useful to avoid unnecessary updates).
  template <class F>
  void ReachInit(const F &fst, bool copy = false) {
    accumulator_->Init(fst, copy);
    if (accumulator_->Error()) error_ = true;
  }

  // Can reach any arc iterator label between iterator positions
  // aiter_begin and aiter_end?  If aiter_input = true, then iterator
  // input labels are considered, o.w. output labels are considered.
  // Arc iterator labels must be transformed by the Relabel methods
  // above. If compute_weight is true, user may call ReachWeight().
  template <class Iterator>
  bool Reach(Iterator *aiter, ssize_t aiter_begin,
             ssize_t aiter_end, bool aiter_input, bool compute_weight) {
    if (error_) return false;
    vector< IntervalSet<Label> > &isets = *data_->IntervalSets();
    const vector<Interval> *intervals = isets[s_].Intervals();
    ++ncalls_;
    nintervals_ += intervals->size();

    reach_begin_ = -1;
    reach_end_ = -1;
    reach_weight_ = Weight::Zero();

    uint32 flags = aiter->Flags();  // save flags to restore them on exit
    aiter->SetFlags(kArcNoCache, kArcNoCache);  // make caching optional
    aiter->Seek(aiter_begin);

    if (2 * (aiter_end - aiter_begin) < intervals->size()) {
      // Check each arc against intervals.
      // Set arc iterator flags to only compute the ilabel or olabel values,
      // since they are the only values required for most of the arcs processed.
      aiter->SetFlags(aiter_input ? kArcILabelValue : kArcOLabelValue,
                      kArcValueFlags);
      Label reach_label = kNoLabel;
      for (ssize_t aiter_pos = aiter_begin;
           aiter_pos < aiter_end; aiter->Next(), ++aiter_pos) {
        const A &arc = aiter->Value();
        Label label = aiter_input ? arc.ilabel : arc.olabel;
        if (label == reach_label || Reach(label)) {
          reach_label = label;
          if (reach_begin_ < 0)
            reach_begin_ = aiter_pos;
          reach_end_ = aiter_pos + 1;
          if (compute_weight) {
            if (!(aiter->Flags() & kArcWeightValue)) {
              // If the 'arc.weight' wasn't computed by the call
              // to 'aiter->Value()' above, we need to call
              // 'aiter->Value()' again after having set the arc iterator
              // flags to compute the arc weight value.
              aiter->SetFlags(kArcWeightValue, kArcValueFlags);
              const A &arcb = aiter->Value();
              // Call the accumulator.
              reach_weight_ = accumulator_->Sum(reach_weight_, arcb.weight);
              // Only ilabel or olabel required to process the following
              // arcs.
              aiter->SetFlags(aiter_input ? kArcILabelValue : kArcOLabelValue,
                              kArcValueFlags);
            } else {
              // Call the accumulator.
              reach_weight_ = accumulator_->Sum(reach_weight_, arc.weight);
            }
          }
        }
      }
    } else {
      // Check each interval against arcs
      ssize_t begin_low, end_low = aiter_begin;
      for (typename vector<Interval>::const_iterator
               iiter = intervals->begin();
           iiter != intervals->end(); ++iiter) {
        begin_low = LowerBound(aiter, end_low, aiter_end,
                               aiter_input, iiter->begin);
        end_low = LowerBound(aiter, begin_low, aiter_end,
                             aiter_input, iiter->end);
        if (end_low - begin_low > 0) {
          if (reach_begin_ < 0)
            reach_begin_ = begin_low;
          reach_end_ = end_low;
          if (compute_weight) {
            aiter->SetFlags(kArcWeightValue, kArcValueFlags);
            reach_weight_ = accumulator_->Sum(reach_weight_, aiter,
                                              begin_low, end_low);
          }
        }
      }
    }

    aiter->SetFlags(flags, kArcFlags);  // restore original flag values
    return reach_begin_ >= 0;
  }

  // Returns iterator position of first matching arc.
  ssize_t ReachBegin() const { return reach_begin_;  }

  // Returns iterator position one past last matching arc.
  ssize_t ReachEnd() const { return reach_end_; }

  // Return the sum of the weights for matching arcs.
  // Valid only if compute_weight was true in Reach() call.
  Weight ReachWeight() const { return reach_weight_; }

  // Access to the relabeling map. Excludes epsilon (0) label but
  // includes kNoLabel that is used internally for super-final
  // transitons.
  const unordered_map<Label, Label>& Label2Index() const {
    return *data_->Label2Index();
  }

  LabelReachableData<Label> *GetData() const { return data_; }

  bool Error() const { return error_ || accumulator_->Error(); }

 private:
  // Redirects labeled arcs (input or output labels determined by
  // ReachInput()) to new label-specific final states.  Each original
  // final state is redirected via a transition labeled with kNoLabel
  // to a new kNoLabel-specific final state.  Creates super-initial
  // state for all states with zero in-degree.
  void TransformFst() {
    StateId ins = fst_->NumStates();
    StateId ons = ins;

    vector<ssize_t> indeg(ins, 0);

    // Redirects labeled arcs to new final states.
    for (StateId s = 0; s < ins; ++s) {
      for (MutableArcIterator< VectorFst<Arc> > aiter(fst_, s);
           !aiter.Done();
           aiter.Next()) {
        Arc arc = aiter.Value();
        Label label = data_->ReachInput() ? arc.ilabel : arc.olabel;
        if (label) {
          if (label2state_.find(label) == label2state_.end()) {
            label2state_[label] = ons;
            indeg.push_back(0);
            ++ons;
          }
          arc.nextstate = label2state_[label];
          aiter.SetValue(arc);
        }
        ++indeg[arc.nextstate];      // Finds in-degrees for next step.
      }

      // Redirects final weights to new final state.
      Weight final = fst_->Final(s);
      if (final != Weight::Zero()) {
        if (label2state_.find(kNoLabel) == label2state_.end()) {
          label2state_[kNoLabel] = ons;
          indeg.push_back(0);
          ++ons;
        }
        Arc arc(kNoLabel, kNoLabel, final, label2state_[kNoLabel]);
        fst_->AddArc(s, arc);
        ++indeg[arc.nextstate];      // Finds in-degrees for next step.

        fst_->SetFinal(s, Weight::Zero());
      }
    }

    // Add new final states to Fst.
    while (fst_->NumStates() < ons) {
      StateId s = fst_->AddState();
      fst_->SetFinal(s, Weight::One());
    }

    // Creates a super-initial state for all states with zero in-degree.
    StateId start = fst_->AddState();
    fst_->SetStart(start);
    for (StateId s = 0; s < start; ++s) {
      if (indeg[s] == 0) {
        Arc arc(0, 0, Weight::One(), s);
        fst_->AddArc(start, arc);
      }
    }
  }

  void FindIntervals(StateId ins) {
    StateReachable<A, Label> state_reachable(*fst_);
    if (state_reachable.Error()) {
      error_ = true;
      return;
    }

    vector<Label> &state2index = state_reachable.State2Index();
    vector< IntervalSet<Label> > &isets = *data_->IntervalSets();
    isets = state_reachable.IntervalSets();
    isets.resize(ins);

    unordered_map<Label, Label> &label2index = *data_->Label2Index();
    for (typename unordered_map<Label, StateId>::const_iterator
             it = label2state_.begin();
         it != label2state_.end();
         ++it) {
      Label l = it->first;
      StateId s = it->second;
      Label i = state2index[s];
      label2index[l] = i;
    }
    label2state_.clear();

    double nintervals = 0;
    ssize_t non_intervals = 0;
    for (ssize_t s = 0; s < ins; ++s) {
      nintervals += isets[s].Size();
      if (isets[s].Size() > 1) {
        ++non_intervals;
        VLOG(3) << "state: " << s << " # of intervals: " << isets[s].Size();
      }
    }
    VLOG(2) << "# of states: " << ins;
    VLOG(2) << "# of intervals: " << nintervals;
    VLOG(2) << "# of intervals/state: " << nintervals/ins;
    VLOG(2) << "# of non-interval states: " << non_intervals;
  }

  template <class Iterator>
  ssize_t LowerBound(Iterator *aiter, ssize_t aiter_begin,
                     ssize_t aiter_end, bool aiter_input,
                     Label match_label) const {
    // Only need to compute the ilabel or olabel of arcs when
    // performing the binary search.
    aiter->SetFlags(aiter_input ?  kArcILabelValue : kArcOLabelValue,
                    kArcValueFlags);
    ssize_t low = aiter_begin;
    ssize_t high = aiter_end;
    while (low < high) {
      ssize_t mid = (low + high) / 2;
      aiter->Seek(mid);
      Label label = aiter_input ?
          aiter->Value().ilabel : aiter->Value().olabel;
      if (label > match_label) {
        high = mid;
      } else if (label < match_label) {
        low = mid + 1;
      } else {
        // Find first matching label (when non-deterministic)
        for (ssize_t i = mid; i > low; --i) {
          aiter->Seek(i - 1);
          label = aiter_input ? aiter->Value().ilabel : aiter->Value().olabel;
          if (label != match_label) {
            aiter->Seek(i);
            aiter->SetFlags(kArcValueFlags, kArcValueFlags);
            return i;
          }
        }
        aiter->SetFlags(kArcValueFlags, kArcValueFlags);
        return low;
      }
    }
    aiter->Seek(low);
    aiter->SetFlags(kArcValueFlags, kArcValueFlags);
    return low;
  }

  VectorFst<Arc> *fst_;
  StateId s_;                             // Current state
  unordered_map<Label, StateId> label2state_;  // Finds final state for a label

  ssize_t reach_begin_;                   // Iterator pos of first match
  ssize_t reach_end_;                     // Iterator pos after last match
  Weight reach_weight_;                   // Gives weight sum of arc iterator
                                          // arcs with reachable labels.
  LabelReachableData<Label> *data_;       // Shareable data between copies
  S *accumulator_;                        // Sums arc weights

  double ncalls_;
  double nintervals_;
  bool error_;

  void operator=(const LabelReachable<A, S> &);   // Disallow
};

}  // namespace fst

#endif  // FST_LIB_LABEL_REACHABLE_H__