lstm/recodebeam.cpp

///////////////////////////////////////////////////////////////////////
// File:        recodebeam.cpp
// Description: Beam search to decode from the re-encoded CJK as a sequence of
//              smaller numbers in place of a single large code.
// Author:      Ray Smith
// Created:     Fri Mar 13 09:39:01 PDT 2015
//
// (C) Copyright 2015, Google Inc.
// 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.
//
///////////////////////////////////////////////////////////////////////

#include "recodebeam.h"
#include "networkio.h"
#include "pageres.h"
#include "unicharcompress.h"

namespace tesseract {

// Clipping value for certainty inside Tesseract. Reflects the minimum value
// of certainty that will be returned by ExtractBestPathAsUnicharIds.
// Supposedly on a uniform scale that can be compared across languages and
// engines.
const float RecodeBeamSearch::kMinCertainty = -20.0f;

// The beam width at each code position.
const int RecodeBeamSearch::kBeamWidths[RecodedCharID::kMaxCodeLen + 1] = {
    5, 10, 16, 16, 16, 16, 16, 16, 16, 16,
};

const char* kNodeContNames[] = {"Anything", "OnlyDup", "NoDup"};

// Prints debug details of the node.
void RecodeNode::Print(int null_char, const UNICHARSET& unicharset,
                       int depth) const {
  if (code == null_char) {
    tprintf("null_char");
  } else {
    tprintf("label=%d, uid=%d=%s", code, unichar_id,
            unicharset.debug_str(unichar_id).string());
  }
  tprintf(" score=%g, c=%g,%s%s%s perm=%d, hash=%lx", score, certainty,
          start_of_dawg ? " DawgStart" : "", start_of_word ? " Start" : "",
          end_of_word ? " End" : "", permuter, code_hash);
  if (depth > 0 && prev != nullptr) {
    tprintf(" prev:");
    prev->Print(null_char, unicharset, depth - 1);
  } else {
    tprintf("\n");
  }
}

// Borrows the pointer, which is expected to survive until *this is deleted.
RecodeBeamSearch::RecodeBeamSearch(const UnicharCompress& recoder,
                                   int null_char, bool simple_text, Dict* dict)
    : recoder_(recoder),
      beam_size_(0),
      top_code_(-1),
      second_code_(-1),
      dict_(dict),
      space_delimited_(true),
      is_simple_text_(simple_text),
      null_char_(null_char) {
  if (dict_ != NULL && !dict_->IsSpaceDelimitedLang()) space_delimited_ = false;
}

// Decodes the set of network outputs, storing the lattice internally.
void RecodeBeamSearch::Decode(const NetworkIO& output, double dict_ratio,
                              double cert_offset, double worst_dict_cert,
                              const UNICHARSET* charset) {
  beam_size_ = 0;
  int width = output.Width();
  for (int t = 0; t < width; ++t) {
    ComputeTopN(output.f(t), output.NumFeatures(), kBeamWidths[0]);
    DecodeStep(output.f(t), t, dict_ratio, cert_offset, worst_dict_cert,
               charset);
  }
}
void RecodeBeamSearch::Decode(const GENERIC_2D_ARRAY<float>& output,
                              double dict_ratio, double cert_offset,
                              double worst_dict_cert,
                              const UNICHARSET* charset) {
  beam_size_ = 0;
  int width = output.dim1();
  for (int t = 0; t < width; ++t) {
    ComputeTopN(output[t], output.dim2(), kBeamWidths[0]);
    DecodeStep(output[t], t, dict_ratio, cert_offset, worst_dict_cert, charset);
  }
}

// Returns the best path as labels/scores/xcoords similar to simple CTC.
void RecodeBeamSearch::ExtractBestPathAsLabels(
    GenericVector<int>* labels, GenericVector<int>* xcoords) const {
  labels->truncate(0);
  xcoords->truncate(0);
  GenericVector<const RecodeNode*> best_nodes;
  ExtractBestPaths(&best_nodes, NULL);
  // Now just run CTC on the best nodes.
  int t = 0;
  int width = best_nodes.size();
  while (t < width) {
    int label = best_nodes[t]->code;
    if (label != null_char_) {
      labels->push_back(label);
      xcoords->push_back(t);
    }
    while (++t < width && !is_simple_text_ && best_nodes[t]->code == label) {
    }
  }
  xcoords->push_back(width);
}

// Returns the best path as unichar-ids/certs/ratings/xcoords skipping
// duplicates, nulls and intermediate parts.
void RecodeBeamSearch::ExtractBestPathAsUnicharIds(
    bool debug, const UNICHARSET* unicharset, GenericVector<int>* unichar_ids,
    GenericVector<float>* certs, GenericVector<float>* ratings,
    GenericVector<int>* xcoords) const {
  GenericVector<const RecodeNode*> best_nodes;
  ExtractBestPaths(&best_nodes, NULL);
  ExtractPathAsUnicharIds(best_nodes, unichar_ids, certs, ratings, xcoords);
  if (debug) {
    DebugPath(unicharset, best_nodes);
    DebugUnicharPath(unicharset, best_nodes, *unichar_ids, *certs, *ratings,
                     *xcoords);
  }
}

// Returns the best path as a set of WERD_RES.
void RecodeBeamSearch::ExtractBestPathAsWords(const TBOX& line_box,
                                              float scale_factor, bool debug,
                                              const UNICHARSET* unicharset,
                                              PointerVector<WERD_RES>* words) {
  words->truncate(0);
  GenericVector<int> unichar_ids;
  GenericVector<float> certs;
  GenericVector<float> ratings;
  GenericVector<int> xcoords;
  GenericVector<const RecodeNode*> best_nodes;
  GenericVector<const RecodeNode*> second_nodes;
  ExtractBestPaths(&best_nodes, &second_nodes);
  if (debug) {
    DebugPath(unicharset, best_nodes);
    ExtractPathAsUnicharIds(second_nodes, &unichar_ids, &certs, &ratings,
                            &xcoords);
    tprintf("\nSecond choice path:\n");
    DebugUnicharPath(unicharset, second_nodes, unichar_ids, certs, ratings,
                     xcoords);
  }
  ExtractPathAsUnicharIds(best_nodes, &unichar_ids, &certs, &ratings, &xcoords);
  int num_ids = unichar_ids.size();
  if (debug) {
    DebugUnicharPath(unicharset, best_nodes, unichar_ids, certs, ratings,
                     xcoords);
  }
  // Convert labels to unichar-ids.
  int word_end = 0;
  float prev_space_cert = 0.0f;
  for (int word_start = 0; word_start < num_ids; word_start = word_end) {
    for (word_end = word_start + 1; word_end < num_ids; ++word_end) {
      // A word is terminated when a space character or start_of_word flag is
      // hit. We also want to force a separate word for every non
      // space-delimited character when not in a dictionary context.
      if (unichar_ids[word_end] == UNICHAR_SPACE) break;
      int index = xcoords[word_end];
      if (best_nodes[index]->start_of_word) break;
      if (best_nodes[index]->permuter == TOP_CHOICE_PERM &&
          (!unicharset->IsSpaceDelimited(unichar_ids[word_end]) ||
           !unicharset->IsSpaceDelimited(unichar_ids[word_end - 1])))
        break;
    }
    float space_cert = 0.0f;
    if (word_end < num_ids && unichar_ids[word_end] == UNICHAR_SPACE)
      space_cert = certs[word_end];
    bool leading_space =
        word_start > 0 && unichar_ids[word_start - 1] == UNICHAR_SPACE;
    // Create a WERD_RES for the output word.
    WERD_RES* word_res = InitializeWord(
        leading_space, line_box, word_start, word_end,
        MIN(space_cert, prev_space_cert), unicharset, xcoords, scale_factor);
    for (int i = word_start; i < word_end; ++i) {
      BLOB_CHOICE_LIST* choices = new BLOB_CHOICE_LIST;
      BLOB_CHOICE_IT bc_it(choices);
      BLOB_CHOICE* choice = new BLOB_CHOICE(
          unichar_ids[i], ratings[i], certs[i], -1, 1.0f,
          static_cast<float>(MAX_INT16), 0.0f, BCC_STATIC_CLASSIFIER);
      int col = i - word_start;
      choice->set_matrix_cell(col, col);
      bc_it.add_after_then_move(choice);
      word_res->ratings->put(col, col, choices);
    }
    int index = xcoords[word_end - 1];
    word_res->FakeWordFromRatings(best_nodes[index]->permuter);
    words->push_back(word_res);
    prev_space_cert = space_cert;
    if (word_end < num_ids && unichar_ids[word_end] == UNICHAR_SPACE)
      ++word_end;
  }
}

// Generates debug output of the content of the beams after a Decode.
void RecodeBeamSearch::DebugBeams(const UNICHARSET& unicharset) const {
  for (int p = 0; p < beam_size_; ++p) {
    for (int d = 0; d < 2; ++d) {
      for (int c = 0; c < NC_COUNT; ++c) {
        NodeContinuation cont = static_cast<NodeContinuation>(c);
        int index = BeamIndex(d, cont, 0);
        if (beam_[p]->beams_[index].empty()) continue;
        // Print all the best scoring nodes for each unichar found.
        tprintf("Position %d: %s+%s beam\n", p, d ? "Dict" : "Non-Dict",
                kNodeContNames[c]);
        DebugBeamPos(unicharset, beam_[p]->beams_[index]);
      }
    }
  }
}

// Generates debug output of the content of a single beam position.
void RecodeBeamSearch::DebugBeamPos(const UNICHARSET& unicharset,
                                    const RecodeHeap& heap) const {
  GenericVector<const RecodeNode*> unichar_bests;
  unichar_bests.init_to_size(unicharset.size(), NULL);
  const RecodeNode* null_best = NULL;
  int heap_size = heap.size();
  for (int i = 0; i < heap_size; ++i) {
    const RecodeNode* node = &heap.get(i).data;
    if (node->unichar_id == INVALID_UNICHAR_ID) {
      if (null_best == NULL || null_best->score < node->score) null_best = node;
    } else {
      if (unichar_bests[node->unichar_id] == NULL ||
          unichar_bests[node->unichar_id]->score < node->score) {
        unichar_bests[node->unichar_id] = node;
      }
    }
  }
  for (int u = 0; u < unichar_bests.size(); ++u) {
    if (unichar_bests[u] != NULL) {
      const RecodeNode& node = *unichar_bests[u];
      node.Print(null_char_, unicharset, 1);
    }
  }
  if (null_best != NULL) {
    null_best->Print(null_char_, unicharset, 1);
  }
}

// Returns the given best_nodes as unichar-ids/certs/ratings/xcoords skipping
// duplicates, nulls and intermediate parts.
/* static */
void RecodeBeamSearch::ExtractPathAsUnicharIds(
    const GenericVector<const RecodeNode*>& best_nodes,
    GenericVector<int>* unichar_ids, GenericVector<float>* certs,
    GenericVector<float>* ratings, GenericVector<int>* xcoords) {
  unichar_ids->truncate(0);
  certs->truncate(0);
  ratings->truncate(0);
  xcoords->truncate(0);
  // Backtrack extracting only valid, non-duplicate unichar-ids.
  int t = 0;
  int width = best_nodes.size();
  while (t < width) {
    double certainty = 0.0;
    double rating = 0.0;
    while (t < width && best_nodes[t]->unichar_id == INVALID_UNICHAR_ID) {
      double cert = best_nodes[t++]->certainty;
      if (cert < certainty) certainty = cert;
      rating -= cert;
    }
    if (t < width) {
      int unichar_id = best_nodes[t]->unichar_id;
      if (unichar_id == UNICHAR_SPACE && !certs->empty() &&
          best_nodes[t]->permuter != NO_PERM) {
        // All the rating and certainty go on the previous character except
        // for the space itself.
        if (certainty < certs->back()) certs->back() = certainty;
        ratings->back() += rating;
        certainty = 0.0;
        rating = 0.0;
      }
      unichar_ids->push_back(unichar_id);
      xcoords->push_back(t);
      do {
        double cert = best_nodes[t++]->certainty;
        // Special-case NO-PERM space to forget the certainty of the previous
        // nulls. See long comment in ContinueContext.
        if (cert < certainty || (unichar_id == UNICHAR_SPACE &&
                                 best_nodes[t - 1]->permuter == NO_PERM)) {
          certainty = cert;
        }
        rating -= cert;
      } while (t < width && best_nodes[t]->duplicate);
      certs->push_back(certainty);
      ratings->push_back(rating);
    } else if (!certs->empty()) {
      if (certainty < certs->back()) certs->back() = certainty;
      ratings->back() += rating;
    }
  }
  xcoords->push_back(width);
}

// Sets up a word with the ratings matrix and fake blobs with boxes in the
// right places.
WERD_RES* RecodeBeamSearch::InitializeWord(bool leading_space,
                                           const TBOX& line_box, int word_start,
                                           int word_end, float space_certainty,
                                           const UNICHARSET* unicharset,
                                           const GenericVector<int>& xcoords,
                                           float scale_factor) {
  // Make a fake blob for each non-zero label.
  C_BLOB_LIST blobs;
  C_BLOB_IT b_it(&blobs);
  for (int i = word_start; i < word_end; ++i) {
    int min_half_width = xcoords[i + 1] - xcoords[i];
    if (i > 0 && xcoords[i] - xcoords[i - 1] < min_half_width)
      min_half_width = xcoords[i] - xcoords[i - 1];
    if (min_half_width < 1) min_half_width = 1;
    // Make a fake blob.
    TBOX box(xcoords[i] - min_half_width, 0, xcoords[i] + min_half_width,
             line_box.height());
    box.scale(scale_factor);
    box.move(ICOORD(line_box.left(), line_box.bottom()));
    box.set_top(line_box.top());
    b_it.add_after_then_move(C_BLOB::FakeBlob(box));
  }
  // Make a fake word from the blobs.
  WERD* word = new WERD(&blobs, leading_space, NULL);
  // Make a WERD_RES from the word.
  WERD_RES* word_res = new WERD_RES(word);
  word_res->uch_set = unicharset;
  word_res->combination = true;  // Give it ownership of the word.
  word_res->space_certainty = space_certainty;
  word_res->ratings = new MATRIX(word_end - word_start, 1);
  return word_res;
}

// Fills top_n_flags_ with bools that are true iff the corresponding output
// is one of the top_n.
void RecodeBeamSearch::ComputeTopN(const float* outputs, int num_outputs,
                                   int top_n) {
  top_n_flags_.init_to_size(num_outputs, TN_ALSO_RAN);
  top_code_ = -1;
  second_code_ = -1;
  top_heap_.clear();
  for (int i = 0; i < num_outputs; ++i) {
    if (top_heap_.size() < top_n || outputs[i] > top_heap_.PeekTop().key) {
      TopPair entry(outputs[i], i);
      top_heap_.Push(&entry);
      if (top_heap_.size() > top_n) top_heap_.Pop(&entry);
    }
  }
  while (!top_heap_.empty()) {
    TopPair entry;
    top_heap_.Pop(&entry);
    if (top_heap_.size() > 1) {
      top_n_flags_[entry.data] = TN_TOPN;
    } else {
      top_n_flags_[entry.data] = TN_TOP2;
      if (top_heap_.empty())
        top_code_ = entry.data;
      else
        second_code_ = entry.data;
    }
  }
  top_n_flags_[null_char_] = TN_TOP2;
}

// Adds the computation for the current time-step to the beam. Call at each
// time-step in sequence from left to right. outputs is the activation vector
// for the current timestep.
void RecodeBeamSearch::DecodeStep(const float* outputs, int t,
                                  double dict_ratio, double cert_offset,
                                  double worst_dict_cert,
                                  const UNICHARSET* charset) {
  if (t == beam_.size()) beam_.push_back(new RecodeBeam);
  RecodeBeam* step = beam_[t];
  beam_size_ = t + 1;
  step->Clear();
  if (t == 0) {
    // The first step can only use singles and initials.
    ContinueContext(nullptr, BeamIndex(false, NC_ANYTHING, 0), outputs, TN_TOP2,
                    dict_ratio, cert_offset, worst_dict_cert, step);
    if (dict_ != nullptr) {
      ContinueContext(nullptr, BeamIndex(true, NC_ANYTHING, 0), outputs,
                      TN_TOP2, dict_ratio, cert_offset, worst_dict_cert, step);
    }
  } else {
    RecodeBeam* prev = beam_[t - 1];
    if (charset != NULL) {
      int beam_index = BeamIndex(true, NC_ANYTHING, 0);
      for (int i = prev->beams_[beam_index].size() - 1; i >= 0; --i) {
        GenericVector<const RecodeNode*> path;
        ExtractPath(&prev->beams_[beam_index].get(i).data, &path);
        tprintf("Step %d: Dawg beam %d:\n", t, i);
        DebugPath(charset, path);
      }
      beam_index = BeamIndex(false, NC_ANYTHING, 0);
      for (int i = prev->beams_[beam_index].size() - 1; i >= 0; --i) {
        GenericVector<const RecodeNode*> path;
        ExtractPath(&prev->beams_[beam_index].get(i).data, &path);
        tprintf("Step %d: Non-Dawg beam %d:\n", t, i);
        DebugPath(charset, path);
      }
    }
    int total_beam = 0;
    // Work through the scores by group (top-2, top-n, the rest) while the beam
    // is empty. This enables extending the context using only the top-n results
    // first, which may have an empty intersection with the valid codes, so we
    // fall back to the rest if the beam is empty.
    for (int tn = 0; tn < TN_COUNT && total_beam == 0; ++tn) {
      TopNState top_n = static_cast<TopNState>(tn);
      for (int index = 0; index < kNumBeams; ++index) {
        // Working backwards through the heaps doesn't guarantee that we see the
        // best first, but it comes before a lot of the worst, so it is slightly
        // more efficient than going forwards.
        for (int i = prev->beams_[index].size() - 1; i >= 0; --i) {
          ContinueContext(&prev->beams_[index].get(i).data, index, outputs,
                          top_n, dict_ratio, cert_offset, worst_dict_cert,
                          step);
        }
      }
      for (int index = 0; index < kNumBeams; ++index) {
        if (ContinuationFromBeamsIndex(index) == NC_ANYTHING)
          total_beam += step->beams_[index].size();
      }
    }
    // Special case for the best initial dawg. Push it on the heap if good
    // enough, but there is only one, so it doesn't blow up the beam.
    for (int c = 0; c < NC_COUNT; ++c) {
      if (step->best_initial_dawgs_[c].code >= 0) {
        int index = BeamIndex(true, static_cast<NodeContinuation>(c), 0);
        RecodeHeap* dawg_heap = &step->beams_[index];
        PushHeapIfBetter(kBeamWidths[0], &step->best_initial_dawgs_[c],
                         dawg_heap);
      }
    }
  }
}

// Adds to the appropriate beams the legal (according to recoder)
// continuations of context prev, which is of the given length, using the
// given network outputs to provide scores to the choices. Uses only those
// choices for which top_n_flags[index] == top_n_flag.
void RecodeBeamSearch::ContinueContext(const RecodeNode* prev, int index,
                                       const float* outputs,
                                       TopNState top_n_flag, double dict_ratio,
                                       double cert_offset,
                                       double worst_dict_cert,
                                       RecodeBeam* step) {
  RecodedCharID prefix;
  RecodedCharID full_code;
  const RecodeNode* previous = prev;
  int length = LengthFromBeamsIndex(index);
  bool use_dawgs = IsDawgFromBeamsIndex(index);
  NodeContinuation prev_cont = ContinuationFromBeamsIndex(index);
  for (int p = length - 1; p >= 0; --p, previous = previous->prev) {
    while (previous != NULL &&
           (previous->duplicate || previous->code == null_char_)) {
      previous = previous->prev;
    }
    prefix.Set(p, previous->code);
    full_code.Set(p, previous->code);
  }
  if (prev != nullptr && !is_simple_text_) {
    if (top_n_flags_[prev->code] == top_n_flag) {
      if (prev_cont != NC_NO_DUP) {
        float cert =
            NetworkIO::ProbToCertainty(outputs[prev->code]) + cert_offset;
        PushDupOrNoDawgIfBetter(length, true, prev->code, prev->unichar_id,
                                cert, worst_dict_cert, dict_ratio, use_dawgs,
                                NC_ANYTHING, prev, step);
      }
      if (prev_cont == NC_ANYTHING && top_n_flag == TN_TOP2 &&
          prev->code != null_char_) {
        float cert = NetworkIO::ProbToCertainty(outputs[prev->code] +
                                                outputs[null_char_]) +
                     cert_offset;
        PushDupOrNoDawgIfBetter(length, true, prev->code, prev->unichar_id,
                                cert, worst_dict_cert, dict_ratio, use_dawgs,
                                NC_NO_DUP, prev, step);
      }
    }
    if (prev_cont == NC_ONLY_DUP) return;
    if (prev->code != null_char_ && length > 0 &&
        top_n_flags_[null_char_] == top_n_flag) {
      // Allow nulls within multi code sequences, as the nulls within are not
      // explicitly included in the code sequence.
      float cert =
          NetworkIO::ProbToCertainty(outputs[null_char_]) + cert_offset;
      PushDupOrNoDawgIfBetter(length, false, null_char_, INVALID_UNICHAR_ID,
                              cert, worst_dict_cert, dict_ratio, use_dawgs,
                              NC_ANYTHING, prev, step);
    }
  }
  const GenericVector<int>* final_codes = recoder_.GetFinalCodes(prefix);
  if (final_codes != NULL) {
    for (int i = 0; i < final_codes->size(); ++i) {
      int code = (*final_codes)[i];
      if (top_n_flags_[code] != top_n_flag) continue;
      if (prev != nullptr && prev->code == code && !is_simple_text_) continue;
      float cert = NetworkIO::ProbToCertainty(outputs[code]) + cert_offset;
      if (cert < kMinCertainty && code != null_char_) continue;
      full_code.Set(length, code);
      int unichar_id = recoder_.DecodeUnichar(full_code);
      // Map the null char to INVALID.
      if (length == 0 && code == null_char_) unichar_id = INVALID_UNICHAR_ID;
      ContinueUnichar(code, unichar_id, cert, worst_dict_cert, dict_ratio,
                      use_dawgs, NC_ANYTHING, prev, step);
      if (top_n_flag == TN_TOP2 && code != null_char_) {
        float prob = outputs[code] + outputs[null_char_];
        if (prev != nullptr && prev_cont == NC_ANYTHING &&
            prev->code != null_char_ &&
            ((prev->code == top_code_ && code == second_code_) ||
             (code == top_code_ && prev->code == second_code_))) {
          prob += outputs[prev->code];
        }
        float cert = NetworkIO::ProbToCertainty(prob) + cert_offset;
        ContinueUnichar(code, unichar_id, cert, worst_dict_cert, dict_ratio,
                        use_dawgs, NC_ONLY_DUP, prev, step);
      }
    }
  }
  const GenericVector<int>* next_codes = recoder_.GetNextCodes(prefix);
  if (next_codes != NULL) {
    for (int i = 0; i < next_codes->size(); ++i) {
      int code = (*next_codes)[i];
      if (top_n_flags_[code] != top_n_flag) continue;
      if (prev != nullptr && prev->code == code && !is_simple_text_) continue;
      float cert = NetworkIO::ProbToCertainty(outputs[code]) + cert_offset;
      PushDupOrNoDawgIfBetter(length + 1, false, code, INVALID_UNICHAR_ID, cert,
                              worst_dict_cert, dict_ratio, use_dawgs,
                              NC_ANYTHING, prev, step);
      if (top_n_flag == TN_TOP2 && code != null_char_) {
        float prob = outputs[code] + outputs[null_char_];
        if (prev != nullptr && prev_cont == NC_ANYTHING &&
            prev->code != null_char_ &&
            ((prev->code == top_code_ && code == second_code_) ||
             (code == top_code_ && prev->code == second_code_))) {
          prob += outputs[prev->code];
        }
        float cert = NetworkIO::ProbToCertainty(prob) + cert_offset;
        PushDupOrNoDawgIfBetter(length + 1, false, code, INVALID_UNICHAR_ID,
                                cert, worst_dict_cert, dict_ratio, use_dawgs,
                                NC_ONLY_DUP, prev, step);
      }
    }
  }
}

// Continues for a new unichar, using dawg or non-dawg as per flag.
void RecodeBeamSearch::ContinueUnichar(int code, int unichar_id, float cert,
                                       float worst_dict_cert, float dict_ratio,
                                       bool use_dawgs, NodeContinuation cont,
                                       const RecodeNode* prev,
                                       RecodeBeam* step) {
  if (use_dawgs) {
    if (cert > worst_dict_cert) {
      ContinueDawg(code, unichar_id, cert, cont, prev, step);
    }
  } else {
    RecodeHeap* nodawg_heap = &step->beams_[BeamIndex(false, cont, 0)];
    PushHeapIfBetter(kBeamWidths[0], code, unichar_id, TOP_CHOICE_PERM, false,
                     false, false, false, cert * dict_ratio, prev, nullptr,
                     nodawg_heap);
    if (dict_ != nullptr &&
        ((unichar_id == UNICHAR_SPACE && cert > worst_dict_cert) ||
         !dict_->getUnicharset().IsSpaceDelimited(unichar_id))) {
      // Any top choice position that can start a new word, ie a space or
      // any non-space-delimited character, should also be considered
      // by the dawg search, so push initial dawg to the dawg heap.
      float dawg_cert = cert;
      PermuterType permuter = TOP_CHOICE_PERM;
      // Since we use the space either side of a dictionary word in the
      // certainty of the word, (to properly handle weak spaces) and the
      // space is coming from a non-dict word, we need special conditions
      // to avoid degrading the certainty of the dict word that follows.
      // With a space we don't multiply the certainty by dict_ratio, and we
      // flag the space with NO_PERM to indicate that we should not use the
      // predecessor nulls to generate the confidence for the space, as they
      // have already been multiplied by dict_ratio, and we can't go back to
      // insert more entries in any previous heaps.
      if (unichar_id == UNICHAR_SPACE)
        permuter = NO_PERM;
      else
        dawg_cert *= dict_ratio;
      PushInitialDawgIfBetter(code, unichar_id, permuter, false, false,
                              dawg_cert, cont, prev, step);
    }
  }
}

// Adds a RecodeNode composed of the tuple (code, unichar_id, cert, prev,
// appropriate-dawg-args, cert) to the given heap (dawg_beam_) if unichar_id
// is a valid continuation of whatever is in prev.
void RecodeBeamSearch::ContinueDawg(int code, int unichar_id, float cert,
                                    NodeContinuation cont,
                                    const RecodeNode* prev, RecodeBeam* step) {
  RecodeHeap* dawg_heap = &step->beams_[BeamIndex(true, cont, 0)];
  RecodeHeap* nodawg_heap = &step->beams_[BeamIndex(false, cont, 0)];
  if (unichar_id == INVALID_UNICHAR_ID) {
    PushHeapIfBetter(kBeamWidths[0], code, unichar_id, NO_PERM, false, false,
                     false, false, cert, prev, nullptr, dawg_heap);
    return;
  }
  // Avoid dictionary probe if score a total loss.
  float score = cert;
  if (prev != NULL) score += prev->score;
  if (dawg_heap->size() >= kBeamWidths[0] &&
      score <= dawg_heap->PeekTop().data.score &&
      nodawg_heap->size() >= kBeamWidths[0] &&
      score <= nodawg_heap->PeekTop().data.score) {
    return;
  }
  const RecodeNode* uni_prev = prev;
  // Prev may be a partial code, null_char, or duplicate, so scan back to the
  // last valid unichar_id.
  while (uni_prev != NULL &&
         (uni_prev->unichar_id == INVALID_UNICHAR_ID || uni_prev->duplicate))
    uni_prev = uni_prev->prev;
  if (unichar_id == UNICHAR_SPACE) {
    if (uni_prev != NULL && uni_prev->end_of_word) {
      // Space is good. Push initial state, to the dawg beam and a regular
      // space to the top choice beam.
      PushInitialDawgIfBetter(code, unichar_id, uni_prev->permuter, false,
                              false, cert, cont, prev, step);
      PushHeapIfBetter(kBeamWidths[0], code, unichar_id, uni_prev->permuter,
                       false, false, false, false, cert, prev, nullptr,
                       nodawg_heap);
    }
    return;
  } else if (uni_prev != NULL && uni_prev->start_of_dawg &&
             uni_prev->unichar_id != UNICHAR_SPACE &&
             dict_->getUnicharset().IsSpaceDelimited(uni_prev->unichar_id) &&
             dict_->getUnicharset().IsSpaceDelimited(unichar_id)) {
    return;  // Can't break words between space delimited chars.
  }
  DawgPositionVector initial_dawgs;
  DawgPositionVector* updated_dawgs = new DawgPositionVector;
  DawgArgs dawg_args(&initial_dawgs, updated_dawgs, NO_PERM);
  bool word_start = false;
  if (uni_prev == NULL) {
    // Starting from beginning of line.
    dict_->default_dawgs(&initial_dawgs, false);
    word_start = true;
  } else if (uni_prev->dawgs != NULL) {
    // Continuing a previous dict word.
    dawg_args.active_dawgs = uni_prev->dawgs;
    word_start = uni_prev->start_of_dawg;
  } else {
    return;  // Can't continue if not a dict word.
  }
  PermuterType permuter = static_cast<PermuterType>(
      dict_->def_letter_is_okay(&dawg_args, unichar_id, false));
  if (permuter != NO_PERM) {
    PushHeapIfBetter(kBeamWidths[0], code, unichar_id, permuter, false,
                     word_start, dawg_args.valid_end, false, cert, prev,
                     dawg_args.updated_dawgs, dawg_heap);
    if (dawg_args.valid_end && !space_delimited_) {
      // We can start another word right away, so push initial state as well,
      // to the dawg beam, and the regular character to the top choice beam,
      // since non-dict words can start here too.
      PushInitialDawgIfBetter(code, unichar_id, permuter, word_start, true,
                              cert, cont, prev, step);
      PushHeapIfBetter(kBeamWidths[0], code, unichar_id, permuter, false,
                       word_start, true, false, cert, prev, NULL, nodawg_heap);
    }
  } else {
    delete updated_dawgs;
  }
}

// Adds a RecodeNode composed of the tuple (code, unichar_id,
// initial-dawg-state, prev, cert) to the given heap if/ there is room or if
// better than the current worst element if already full.
void RecodeBeamSearch::PushInitialDawgIfBetter(int code, int unichar_id,
                                               PermuterType permuter,
                                               bool start, bool end, float cert,
                                               NodeContinuation cont,
                                               const RecodeNode* prev,
                                               RecodeBeam* step) {
  RecodeNode* best_initial_dawg = &step->best_initial_dawgs_[cont];
  float score = cert;
  if (prev != NULL) score += prev->score;
  if (best_initial_dawg->code < 0 || score > best_initial_dawg->score) {
    DawgPositionVector* initial_dawgs = new DawgPositionVector;
    dict_->default_dawgs(initial_dawgs, false);
    RecodeNode node(code, unichar_id, permuter, true, start, end, false, cert,
                    score, prev, initial_dawgs,
                    ComputeCodeHash(code, false, prev));
    *best_initial_dawg = node;
  }
}

// Adds a RecodeNode composed of the tuple (code, unichar_id, permuter,
// false, false, false, false, cert, prev, NULL) to heap if there is room
// or if better than the current worst element if already full.
/* static */
void RecodeBeamSearch::PushDupOrNoDawgIfBetter(
    int length, bool dup, int code, int unichar_id, float cert,
    float worst_dict_cert, float dict_ratio, bool use_dawgs,
    NodeContinuation cont, const RecodeNode* prev, RecodeBeam* step) {
  int index = BeamIndex(use_dawgs, cont, length);
  if (use_dawgs) {
    if (cert > worst_dict_cert) {
      PushHeapIfBetter(kBeamWidths[length], code, unichar_id,
                       prev ? prev->permuter : NO_PERM, false, false, false,
                       dup, cert, prev, nullptr, &step->beams_[index]);
    }
  } else {
    cert *= dict_ratio;
    if (cert >= kMinCertainty || code == null_char_) {
      PushHeapIfBetter(kBeamWidths[length], code, unichar_id,
                       prev ? prev->permuter : TOP_CHOICE_PERM, false, false,
                       false, dup, cert, prev, nullptr, &step->beams_[index]);
    }
  }
}

// Adds a RecodeNode composed of the tuple (code, unichar_id, permuter,
// dawg_start, word_start, end, dup, cert, prev, d) to heap if there is room
// or if better than the current worst element if already full.
void RecodeBeamSearch::PushHeapIfBetter(int max_size, int code, int unichar_id,
                                        PermuterType permuter, bool dawg_start,
                                        bool word_start, bool end, bool dup,
                                        float cert, const RecodeNode* prev,
                                        DawgPositionVector* d,
                                        RecodeHeap* heap) {
  float score = cert;
  if (prev != NULL) score += prev->score;
  if (heap->size() < max_size || score > heap->PeekTop().data.score) {
    uinT64 hash = ComputeCodeHash(code, dup, prev);
    RecodeNode node(code, unichar_id, permuter, dawg_start, word_start, end,
                    dup, cert, score, prev, d, hash);
    if (UpdateHeapIfMatched(&node, heap)) return;
    RecodePair entry(score, node);
    heap->Push(&entry);
    ASSERT_HOST(entry.data.dawgs == NULL);
    if (heap->size() > max_size) heap->Pop(&entry);
  } else {
    delete d;
  }
}

// Adds a RecodeNode to heap if there is room
// or if better than the current worst element if already full.
void RecodeBeamSearch::PushHeapIfBetter(int max_size, RecodeNode* node,
                                        RecodeHeap* heap) {
  if (heap->size() < max_size || node->score > heap->PeekTop().data.score) {
    if (UpdateHeapIfMatched(node, heap)) {
      return;
    }
    RecodePair entry(node->score, *node);
    heap->Push(&entry);
    ASSERT_HOST(entry.data.dawgs == NULL);
    if (heap->size() > max_size) heap->Pop(&entry);
  }
}

// Searches the heap for a matching entry, and updates the score with
// reshuffle if needed. Returns true if there was a match.
bool RecodeBeamSearch::UpdateHeapIfMatched(RecodeNode* new_node,
                                           RecodeHeap* heap) {
  // TODO(rays) consider hash map instead of linear search.
  // It might not be faster because the hash map would have to be updated
  // every time a heap reshuffle happens, and that would be a lot of overhead.
  GenericVector<RecodePair>* nodes = heap->heap();
  for (int i = 0; i < nodes->size(); ++i) {
    RecodeNode& node = (*nodes)[i].data;
    if (node.code == new_node->code && node.code_hash == new_node->code_hash &&
        node.permuter == new_node->permuter &&
        node.start_of_dawg == new_node->start_of_dawg) {
      if (new_node->score > node.score) {
        // The new one is better. Update the entire node in the heap and
        // reshuffle.
        node = *new_node;
        (*nodes)[i].key = node.score;
        heap->Reshuffle(&(*nodes)[i]);
      }
      return true;
    }
  }
  return false;
}

// Computes and returns the code-hash for the given code and prev.
uinT64 RecodeBeamSearch::ComputeCodeHash(int code, bool dup,
                                         const RecodeNode* prev) const {
  uinT64 hash = prev == nullptr ? 0 : prev->code_hash;
  if (!dup && code != null_char_) {
    int num_classes = recoder_.code_range();
    uinT64 carry = (((hash >> 32) * num_classes) >> 32);
    hash *= num_classes;
    hash += carry;
    hash += code;
  }
  return hash;
}

// Backtracks to extract the best path through the lattice that was built
// during Decode. On return the best_nodes vector essentially contains the set
// of code, score pairs that make the optimal path with the constraint that
// the recoder can decode the code sequence back to a sequence of unichar-ids.
void RecodeBeamSearch::ExtractBestPaths(
    GenericVector<const RecodeNode*>* best_nodes,
    GenericVector<const RecodeNode*>* second_nodes) const {
  // Scan both beams to extract the best and second best paths.
  const RecodeNode* best_node = NULL;
  const RecodeNode* second_best_node = NULL;
  const RecodeBeam* last_beam = beam_[beam_size_ - 1];
  for (int c = 0; c < NC_COUNT; ++c) {
    if (c == NC_ONLY_DUP) continue;
    NodeContinuation cont = static_cast<NodeContinuation>(c);
    for (int is_dawg = 0; is_dawg < 2; ++is_dawg) {
      int beam_index = BeamIndex(is_dawg, cont, 0);
      int heap_size = last_beam->beams_[beam_index].size();
      for (int h = 0; h < heap_size; ++h) {
        const RecodeNode* node = &last_beam->beams_[beam_index].get(h).data;
        if (is_dawg) {
          // dawg_node may be a null_char, or duplicate, so scan back to the
          // last valid unichar_id.
          const RecodeNode* dawg_node = node;
          while (dawg_node != NULL &&
                 (dawg_node->unichar_id == INVALID_UNICHAR_ID ||
                  dawg_node->duplicate))
            dawg_node = dawg_node->prev;
          if (dawg_node == NULL || (!dawg_node->end_of_word &&
                                    dawg_node->unichar_id != UNICHAR_SPACE)) {
            // Dawg node is not valid.
            continue;
          }
        }
        if (best_node == NULL || node->score > best_node->score) {
          second_best_node = best_node;
          best_node = node;
        } else if (second_best_node == NULL ||
                   node->score > second_best_node->score) {
          second_best_node = node;
        }
      }
    }
  }
  if (second_nodes != NULL) ExtractPath(second_best_node, second_nodes);
  ExtractPath(best_node, best_nodes);
}

// Helper backtracks through the lattice from the given node, storing the
// path and reversing it.
void RecodeBeamSearch::ExtractPath(
    const RecodeNode* node, GenericVector<const RecodeNode*>* path) const {
  path->truncate(0);
  while (node != NULL) {
    path->push_back(node);
    node = node->prev;
  }
  path->reverse();
}

// Helper prints debug information on the given lattice path.
void RecodeBeamSearch::DebugPath(
    const UNICHARSET* unicharset,
    const GenericVector<const RecodeNode*>& path) const {
  for (int c = 0; c < path.size(); ++c) {
    const RecodeNode& node = *path[c];
    tprintf("%d ", c);
    node.Print(null_char_, *unicharset, 1);
  }
}

// Helper prints debug information on the given unichar path.
void RecodeBeamSearch::DebugUnicharPath(
    const UNICHARSET* unicharset, const GenericVector<const RecodeNode*>& path,
    const GenericVector<int>& unichar_ids, const GenericVector<float>& certs,
    const GenericVector<float>& ratings,
    const GenericVector<int>& xcoords) const {
  int num_ids = unichar_ids.size();
  double total_rating = 0.0;
  for (int c = 0; c < num_ids; ++c) {
    int coord = xcoords[c];
    tprintf("%d %d=%s r=%g, c=%g, s=%d, e=%d, perm=%d\n", coord, unichar_ids[c],
            unicharset->debug_str(unichar_ids[c]).string(), ratings[c],
            certs[c], path[coord]->start_of_word, path[coord]->end_of_word,
            path[coord]->permuter);
    total_rating += ratings[c];
  }
  tprintf("Path total rating = %g\n", total_rating);
}

}  // namespace tesseract.