EVOLUTION-MANAGER

Edit File: edit_distance.h

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
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http://www.apache.org/licenses/LICENSE-2.0

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distributed under the License is distributed on an "AS IS" BASIS,
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==============================================================================*/

#ifndef TENSORFLOW_LIB_GTL_EDIT_DISTANCE_H_
#define TENSORFLOW_LIB_GTL_EDIT_DISTANCE_H_

#include <numeric>

#include "tensorflow/core/lib/gtl/array_slice.h"
#include "tensorflow/core/lib/gtl/inlined_vector.h"

namespace tensorflow {
namespace gtl {

// Calculate the Levenshtein Edit Distance between two contiguous
// sequences, s and t, of type T.
//
// The Levenshtein distance is a symmetric distance defined as the
// smallest number of insertions, deletions, and substitutions
// required to convert sequence s to t (and vice versa).
// Note, this distance does not consider transpositions.
//
// For more details and a reference implementation, see:
//   https://en.wikipedia.org/wiki/Levenshtein_distance
//
// This implementation has time complexity O(|s|*|t|)
// and space complexity O(min(|s|, |t|)), where
//   |x| := x.size()
//
// A simple call to LevenshteinDistance looks like:
//
//  int64 dist = LevenshteinDistance("hi", "bye", std::equal_to<char>());
//
template <typename T, typename Cmp>
inline int64 LevenshteinDistance(const gtl::ArraySlice<T>& s,
                                 const gtl::ArraySlice<T>& t, const Cmp& cmp) {
  const int64 s_size = s.size();
  const int64 t_size = t.size();

if (t_size > s_size) return LevenshteinDistance(t, s, cmp);

const T* s_data = s.data();
  const T* t_data = t.data();

if (t_size == 0) return s_size;
  if (s == t) return 0;

// Create work vector
  gtl::InlinedVector<int64, 32> scratch_holder(t_size);

int64* scratch = scratch_holder.data();

// Special case for i = 0: Distance between empty string and string
  // of length j is just j.
  for (size_t j = 1; j < t_size; ++j) scratch[j - 1] = j;

for (size_t i = 1; i <= s_size; ++i) {
    // Invariant: scratch[j - 1] equals cost(i - 1, j).
    int substitution_base_cost = i - 1;
    int insertion_cost = i + 1;
    for (size_t j = 1; j <= t_size; ++j) {
      // Invariants:
      //  scratch[k - 1] = cost(i, k)  for 0 < k < j.
      //  scratch[k - 1] = cost(i - 1, k)  for j <= k <= t_size.
      //  substitution_base_cost = cost(i - 1, j - 1)
      //  insertion_cost = cost(i, j - 1)
      const int replacement_cost = cmp(s_data[i - 1], t_data[j - 1]) ? 0 : 1;
      const int substitution_cost = substitution_base_cost + replacement_cost;
      const int deletion_cost = scratch[j - 1] + 1;

// Select the cheapest edit.
      const int cheapest =  // = cost(i, j)
          std::min(deletion_cost, std::min(insertion_cost, substitution_cost));

// Restore invariant for the next iteration of the loop.
      substitution_base_cost = scratch[j - 1];  // = cost(i - 1, j)
      scratch[j - 1] = cheapest;                // = cost(i, j)
      insertion_cost = cheapest + 1;            // = cost(i, j) + 1
    }
  }
  return scratch[t_size - 1];
}

template <typename Container1, typename Container2, typename Cmp>
inline int64 LevenshteinDistance(const Container1& s, const Container2& t,
                                 const Cmp& cmp) {
  return LevenshteinDistance(
      gtl::ArraySlice<typename Container1::value_type>(s.data(), s.size()),
      gtl::ArraySlice<typename Container1::value_type>(t.data(), t.size()),
      cmp);
}

}  // namespace gtl
}  // namespace tensorflow

#endif  // TENSORFLOW_LIB_GTL_EDIT_DISTANCE_H_