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- // Copyright 2017 The Chromium Authors. All rights reserved.
- // Use of this source code is governed by a BSD-style license that can be
- // found in the LICENSE file.
- #ifndef COMPONENTS_ZUCCHINI_SUFFIX_ARRAY_H_
- #define COMPONENTS_ZUCCHINI_SUFFIX_ARRAY_H_
- #include <algorithm>
- #include <iterator>
- #include <numeric>
- #include <vector>
- #include "base/check.h"
- #include "base/containers/adapters.h"
- namespace zucchini {
- // A functor class that implements the naive suffix sorting algorithm that uses
- // std::sort with lexicographical compare. This is only meant as reference of
- // the interface.
- class NaiveSuffixSort {
- public:
- // Type requirements:
- // |InputRng| is an input random access range.
- // |KeyType| is an unsigned integer type.
- // |SAIt| is a random access iterator with mutable references.
- template <class InputRng, class KeyType, class SAIt>
- // |str| is the input string on which suffix sort is applied.
- // Characters found in |str| must be in the range [0, |key_bound|)
- // |suffix_array| is the beginning of the destination range, which is at least
- // as large as |str|.
- void operator()(const InputRng& str,
- KeyType key_bound,
- SAIt suffix_array) const {
- using size_type = typename SAIt::value_type;
- size_type n = static_cast<size_type>(std::end(str) - std::begin(str));
- // |suffix_array| is first filled with ordered indices of |str|.
- // Those indices are then sorted with lexicographical comparisons in |str|.
- std::iota(suffix_array, suffix_array + n, 0);
- std::sort(suffix_array, suffix_array + n, [&str](size_type i, size_type j) {
- return std::lexicographical_compare(std::begin(str) + i, std::end(str),
- std::begin(str) + j, std::end(str));
- });
- }
- };
- // A functor class that implements suffix array induced sorting (SA-IS)
- // algorithm with linear time and memory complexity,
- // see http://ieeexplore.ieee.org/abstract/document/5582081/
- class InducedSuffixSort {
- public:
- // Type requirements:
- // |InputRng| is an input random access range.
- // |KeyType| is an unsigned integer type.
- // |SAIt| is a random access iterator with mutable values.
- template <class InputRng, class KeyType, class SAIt>
- // |str| is the input string on which suffix sort is applied.
- // Characters found in |str| must be in the range [0, |key_bound|)
- // |suffix_array| is the beginning of the destination range, which is at least
- // as large as |str|.
- void operator()(const InputRng& str,
- KeyType key_bound,
- SAIt suffix_array) const {
- using value_type = typename InputRng::value_type;
- using size_type = typename SAIt::value_type;
- static_assert(std::is_unsigned<value_type>::value,
- "SA-IS only supports input string with unsigned values");
- static_assert(std::is_unsigned<KeyType>::value, "KeyType must be unsigned");
- size_type n = static_cast<size_type>(std::end(str) - std::begin(str));
- Implementation<size_type, KeyType>::SuffixSort(std::begin(str), n,
- key_bound, suffix_array);
- }
- // Given string S of length n. We assume S is terminated by a unique sentinel
- // $, which is considered as the smallest character. This sentinel does not
- // exist in memory and is only treated implicitly, hence |n| does not count
- // the sentinel in this implementation. We denote suf(S,i) the suffix formed
- // by S[i..n).
- // A suffix suf(S,i) is said to be S-type or L-type, if suf(S,i) < suf(S,i+1)
- // or suf(S,i) > suf(S,i+1), respectively.
- enum SLType : bool { SType, LType };
- // A character S[i] is said to be S-type or L-type if the suffix suf(S,i) is
- // S-type or L-type, respectively.
- // A character S[i] is called LMS (leftmost S-type), if S[i] is S-type and
- // S[i-1] is L-type. A suffix suf(S,i) is called LMS, if S[i] is an LMS
- // character.
- // A substring S[i..j) is an LMS-substring if
- // (1) S[i] is LMS, S[j] is LMS or the sentinel $, and S[i..j) has no other
- // LMS characters, or
- // (2) S[i..j) is the sentinel $.
- template <class SizeType, class KeyType>
- struct Implementation {
- static_assert(std::is_unsigned<SizeType>::value,
- "SizeType must be unsigned");
- static_assert(std::is_unsigned<KeyType>::value, "KeyType must be unsigned");
- using size_type = SizeType;
- using key_type = KeyType;
- using iterator = typename std::vector<size_type>::iterator;
- using const_iterator = typename std::vector<size_type>::const_iterator;
- // Partition every suffix based on SL-type. Returns the number of LMS
- // suffixes.
- template <class StrIt>
- static size_type BuildSLPartition(
- StrIt str,
- size_type length,
- key_type key_bound,
- std::vector<SLType>::reverse_iterator sl_partition_it) {
- // We will count LMS suffixes (S to L-type or last S-type).
- size_type lms_count = 0;
- // |previous_type| is initialized to L-type to avoid counting an extra
- // LMS suffix at the end
- SLType previous_type = LType;
- // Initialized to dummy, impossible key.
- key_type previous_key = key_bound;
- // We're travelling backward to determine the partition,
- // as if we prepend one character at a time to the string, ex:
- // b$ is L-type because b > $.
- // ab$ is S-type because a < b, implying ab$ < b$.
- // bab$ is L-type because b > a, implying bab$ > ab$.
- // bbab$ is L-type, because bab$ was also L-type, implying bbab$ > bab$.
- for (auto str_it = std::reverse_iterator<StrIt>(str + length);
- str_it != std::reverse_iterator<StrIt>(str);
- ++str_it, ++sl_partition_it) {
- key_type current_key = *str_it;
- if (current_key > previous_key || previous_key == key_bound) {
- // S[i] > S[i + 1] or S[i] is last character.
- if (previous_type == SType)
- // suf(S,i) is L-type and suf(S,i + 1) is S-type, therefore,
- // suf(S,i+1) was a LMS suffix.
- ++lms_count;
- previous_type = LType; // For next round.
- } else if (current_key < previous_key) {
- // S[i] < S[i + 1]
- previous_type = SType; // For next round.
- }
- // Else, S[i] == S[i + 1]:
- // The next character that differs determines the SL-type,
- // so we reuse the last seen type.
- *sl_partition_it = previous_type;
- previous_key = current_key; // For next round.
- }
- return lms_count;
- }
- // Find indices of LMS suffixes and write result to |lms_indices|.
- static void FindLmsSuffixes(const std::vector<SLType>& sl_partition,
- iterator lms_indices) {
- // |previous_type| is initialized to S-type to avoid counting an extra
- // LMS suffix at the beginning
- SLType previous_type = SType;
- for (size_type i = 0; i < sl_partition.size(); ++i) {
- if (sl_partition[i] == SType && previous_type == LType)
- *lms_indices++ = i;
- previous_type = sl_partition[i];
- }
- }
- template <class StrIt>
- static std::vector<size_type> MakeBucketCount(StrIt str,
- size_type length,
- key_type key_bound) {
- // Occurrence of every unique character is counted in |buckets|
- std::vector<size_type> buckets(static_cast<size_type>(key_bound));
- for (auto it = str; it != str + length; ++it)
- ++buckets[*it];
- return buckets;
- }
- // Apply induced sort from |lms_indices| to |suffix_array| associated with
- // the string |str|.
- template <class StrIt, class SAIt>
- static void InducedSort(StrIt str,
- size_type length,
- const std::vector<SLType>& sl_partition,
- const std::vector<size_type>& lms_indices,
- const std::vector<size_type>& buckets,
- SAIt suffix_array) {
- // All indices are first marked as unset with the illegal value |length|.
- std::fill(suffix_array, suffix_array + length, length);
- // Used to mark bucket boundaries (head or end) as indices in str.
- DCHECK(!buckets.empty());
- std::vector<size_type> bucket_bounds(buckets.size());
- // Step 1: Assign indices for LMS suffixes, populating the end of
- // respective buckets but keeping relative order.
- // Find the end of each bucket and write it to |bucket_bounds|.
- std::partial_sum(buckets.begin(), buckets.end(), bucket_bounds.begin());
- // Process each |lms_indices| backward, and assign them to the end of
- // their respective buckets, so relative order is preserved.
- for (size_t lms_index : base::Reversed(lms_indices)) {
- key_type key = str[lms_index];
- suffix_array[--bucket_bounds[key]] = lms_index;
- }
- // Step 2
- // Scan forward |suffix_array|; for each modified suf(S,i) for which
- // suf(S,SA(i) - 1) is L-type, place suf(S,SA(i) - 1) to the current
- // head of the corresponding bucket and forward the bucket head to the
- // right.
- // Find the head of each bucket and write it to |bucket_bounds|. Since
- // only LMS suffixes where inserted in |suffix_array| during Step 1,
- // |bucket_bounds| does not contains the head of each bucket and needs to
- // be updated.
- bucket_bounds[0] = 0;
- std::partial_sum(buckets.begin(), buckets.end() - 1,
- bucket_bounds.begin() + 1);
- // From Step 1, the sentinel $, which we treat implicitly, would have
- // been placed at the beginning of |suffix_array|, since $ is always
- // considered as the smallest character. We then have to deal with the
- // previous (last) suffix.
- if (sl_partition[length - 1] == LType) {
- key_type key = str[length - 1];
- suffix_array[bucket_bounds[key]++] = length - 1;
- }
- for (auto it = suffix_array; it != suffix_array + length; ++it) {
- size_type suffix_index = *it;
- // While the original algorithm marks unset suffixes with -1,
- // we found that marking them with |length| is also possible and more
- // convenient because we are working with unsigned integers.
- if (suffix_index != length && suffix_index > 0 &&
- sl_partition[--suffix_index] == LType) {
- key_type key = str[suffix_index];
- suffix_array[bucket_bounds[key]++] = suffix_index;
- }
- }
- // Step 3
- // Scan backward |suffix_array|; for each modified suf(S, i) for which
- // suf(S,SA(i) - 1) is S-type, place suf(S,SA(i) - 1) to the current
- // end of the corresponding bucket and forward the bucket head to the
- // left.
- // Find the end of each bucket and write it to |bucket_bounds|. Since
- // only L-type suffixes where inserted in |suffix_array| during Step 2,
- // |bucket_bounds| does not contain the end of each bucket and needs to
- // be updated.
- std::partial_sum(buckets.begin(), buckets.end(), bucket_bounds.begin());
- for (auto it = std::reverse_iterator<SAIt>(suffix_array + length);
- it != std::reverse_iterator<SAIt>(suffix_array); ++it) {
- size_type suffix_index = *it;
- if (suffix_index != length && suffix_index > 0 &&
- sl_partition[--suffix_index] == SType) {
- key_type key = str[suffix_index];
- suffix_array[--bucket_bounds[key]] = suffix_index;
- }
- }
- // Deals with the last suffix, because of the sentinel.
- if (sl_partition[length - 1] == SType) {
- key_type key = str[length - 1];
- suffix_array[--bucket_bounds[key]] = length - 1;
- }
- }
- // Given a string S starting at |str| with length |length|, an array
- // starting at |substring_array| containing lexicographically ordered LMS
- // terminated substring indices of S and an SL-Type partition |sl_partition|
- // of S, assigns a unique label to every unique LMS substring. The sorted
- // labels for all LMS substrings are written to |lms_str|, while the indices
- // of LMS suffixes are written to |lms_indices|. In addition, returns the
- // total number of unique labels.
- template <class StrIt, class SAIt>
- static size_type LabelLmsSubstrings(StrIt str,
- size_type length,
- const std::vector<SLType>& sl_partition,
- SAIt suffix_array,
- iterator lms_indices,
- iterator lms_str) {
- // Labelling starts at 0.
- size_type label = 0;
- // |previous_lms| is initialized to 0 to indicate it is unset.
- // Note that suf(S,0) is never a LMS suffix. Substrings will be visited in
- // lexicographical order.
- size_type previous_lms = 0;
- for (auto it = suffix_array; it != suffix_array + length; ++it) {
- if (*it > 0 && sl_partition[*it] == SType &&
- sl_partition[*it - 1] == LType) {
- // suf(S, *it) is a LMS suffix.
- size_type current_lms = *it;
- if (previous_lms != 0) {
- // There was a previous LMS suffix. Check if the current LMS
- // substring is equal to the previous one.
- SLType current_lms_type = SType;
- SLType previous_lms_type = SType;
- for (size_type k = 0;; ++k) {
- // |current_lms_end| and |previous_lms_end| denote whether we have
- // reached the end of the current and previous LMS substring,
- // respectively
- bool current_lms_end = false;
- bool previous_lms_end = false;
- // Check for both previous and current substring ends.
- // Note that it is more convenient to check if
- // suf(S,current_lms + k) is an LMS suffix than to retrieve it
- // from lms_indices.
- if (current_lms + k >= length ||
- (current_lms_type == LType &&
- sl_partition[current_lms + k] == SType)) {
- current_lms_end = true;
- }
- if (previous_lms + k >= length ||
- (previous_lms_type == LType &&
- sl_partition[previous_lms + k] == SType)) {
- previous_lms_end = true;
- }
- if (current_lms_end && previous_lms_end) {
- break; // Previous and current substrings are identical.
- } else if (current_lms_end != previous_lms_end ||
- str[current_lms + k] != str[previous_lms + k]) {
- // Previous and current substrings differ, a new label is used.
- ++label;
- break;
- }
- current_lms_type = sl_partition[current_lms + k];
- previous_lms_type = sl_partition[previous_lms + k];
- }
- }
- *lms_indices++ = *it;
- *lms_str++ = label;
- previous_lms = current_lms;
- }
- }
- return label + 1;
- }
- // Implementation of the SA-IS algorithm. |str| must be a random access
- // iterator pointing at the beginning of S with length |length|. The result
- // is writtend in |suffix_array|, a random access iterator.
- template <class StrIt, class SAIt>
- static void SuffixSort(StrIt str,
- size_type length,
- key_type key_bound,
- SAIt suffix_array) {
- if (length == 1)
- *suffix_array = 0;
- if (length < 2)
- return;
- std::vector<SLType> sl_partition(length);
- size_type lms_count =
- BuildSLPartition(str, length, key_bound, sl_partition.rbegin());
- std::vector<size_type> lms_indices(lms_count);
- FindLmsSuffixes(sl_partition, lms_indices.begin());
- std::vector<size_type> buckets = MakeBucketCount(str, length, key_bound);
- if (lms_indices.size() > 1) {
- // Given |lms_indices| in the same order they appear in |str|, induce
- // LMS substrings relative order and write result to |suffix_array|.
- InducedSort(str, length, sl_partition, lms_indices, buckets,
- suffix_array);
- std::vector<size_type> lms_str(lms_indices.size());
- // Given LMS substrings in relative order found in |suffix_array|,
- // map LMS substrings to unique labels to form a new string, |lms_str|.
- size_type label_count =
- LabelLmsSubstrings(str, length, sl_partition, suffix_array,
- lms_indices.begin(), lms_str.begin());
- if (label_count < lms_str.size()) {
- // Reorder |lms_str| to have LMS suffixes in the same order they
- // appear in |str|.
- for (size_type i = 0; i < lms_indices.size(); ++i)
- suffix_array[lms_indices[i]] = lms_str[i];
- SLType previous_type = SType;
- for (size_type i = 0, j = 0; i < sl_partition.size(); ++i) {
- if (sl_partition[i] == SType && previous_type == LType) {
- lms_str[j] = suffix_array[i];
- lms_indices[j++] = i;
- }
- previous_type = sl_partition[i];
- }
- // Recursively apply SuffixSort on |lms_str|, which is formed from
- // labeled LMS suffixes in the same order they appear in |str|.
- // Note that |KeyType| will be size_type because |lms_str| contains
- // indices. |lms_str| is at most half the length of |str|.
- Implementation<size_type, size_type>::SuffixSort(
- lms_str.begin(), static_cast<size_type>(lms_str.size()),
- label_count, suffix_array);
- // Map LMS labels back to indices in |str| and write result to
- // |lms_indices|. We're using |suffix_array| as a temporary buffer.
- for (size_type i = 0; i < lms_indices.size(); ++i)
- suffix_array[i] = lms_indices[suffix_array[i]];
- std::copy_n(suffix_array, lms_indices.size(), lms_indices.begin());
- // At this point, |lms_indices| contains sorted LMS suffixes of |str|.
- }
- }
- // Given |lms_indices| where LMS suffixes are sorted, induce the full
- // order of suffixes in |str|.
- InducedSort(str, length, sl_partition, lms_indices, buckets,
- suffix_array);
- }
- Implementation() = delete;
- Implementation(const Implementation&) = delete;
- const Implementation& operator=(const Implementation&) = delete;
- };
- };
- // Generates a sorted suffix array for the input string |str| using the functor
- // |Algorithm| which provides an interface equivalent to NaiveSuffixSort.
- /// Characters found in |str| are assumed to be in range [0, |key_bound|).
- // Returns the suffix array as a vector.
- // |StrRng| is an input random access range.
- // |KeyType| is an unsigned integer type.
- template <class Algorithm, class StrRng, class KeyType>
- std::vector<typename StrRng::size_type> MakeSuffixArray(const StrRng& str,
- KeyType key_bound) {
- Algorithm sort;
- std::vector<typename StrRng::size_type> suffix_array(str.end() - str.begin());
- sort(str, key_bound, suffix_array.begin());
- return suffix_array;
- }
- // Type requirements:
- // |SARng| is an input random access range.
- // |StrIt1| is a random access iterator.
- // |StrIt2| is a forward iterator.
- template <class SARng, class StrIt1, class StrIt2>
- // Lexicographical lower bound using binary search for
- // [|str2_first|, |str2_last|) in the suffix array |suffix_array| of a string
- // starting at |str1_first|. This does not necessarily return the index of
- // the longest matching substring.
- auto SuffixLowerBound(const SARng& suffix_array,
- StrIt1 str1_first,
- StrIt2 str2_first,
- StrIt2 str2_last) -> decltype(std::begin(suffix_array)) {
- using size_type = typename SARng::value_type;
- size_t n = std::end(suffix_array) - std::begin(suffix_array);
- auto it = std::lower_bound(
- std::begin(suffix_array), std::end(suffix_array), str2_first,
- [str1_first, str2_last, n](size_type a, StrIt2 b) {
- return std::lexicographical_compare(str1_first + a, str1_first + n, b,
- str2_last);
- });
- return it;
- }
- } // namespace zucchini
- #endif // COMPONENTS_ZUCCHINI_SUFFIX_ARRAY_H_
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