cp-library
競技プログラミング用 C++ ライブラリ
Edit Distance
string/edit_distance.hpp · GitHub で見る
共通ページ
#include "lib/string/edit_distance.hpp"
int distance = edit_distance("kitten", "sitting"); // 3
| 操作 | 内容・返り値 | 計算量 |
|---|---|---|
edit_distance(s,t) |
挿入・削除・置換のコストを各 1 とする編集距離 | \(O(n\lceil m/64\rceil)\) |
std::string_view で 2 つの文字列を受け取り、挿入・削除・置換をそれぞれコスト 1 とする編集距離を返します。文字はバイト単位で扱います。
長い方の長さを \(n\)、短い方を \(m\) として、時間は \(O(n\lceil m/64\rceil)\)、補助空間は \(O(m)\) です。
依存ライブラリ
コード
#ifndef EDIT_DISTANCE_HPP
#define EDIT_DISTANCE_HPP
#include "../components/sequence_compare.hpp"
#include <algorithm>
#include <array>
#include <bit>
#include <cassert>
#include <cstdint>
#include <cstring>
#include <limits>
#include <string_view>
#include <utility>
#include <vector>
#if defined(__x86_64__)
#include <immintrin.h>
#endif
namespace edit_distance_detail {
using Word = std::uint64_t;
#if defined(__x86_64__)
#if defined(__GNUC__) && !defined(__clang__)
#pragma GCC push_options
#pragma GCC optimize("O3")
#endif
__attribute__((target("avx2"))) inline void avx2(std::string_view s, const std::array<const Word *, 256> &masks, Word *__restrict positive, Word *__restrict negative, int words) {
const __m256i ones = _mm256_set1_epi64x(-1), one = _mm256_set1_epi64x(1), positions = _mm256_setr_epi64x(0, 1, 2, 3);
for (unsigned char c : s) {
const Word *__restrict mask = masks[c];
unsigned carry = 0;
__m256i previous_p = _mm256_set1_epi64x(std::numeric_limits<long long>::min()), previous_m = _mm256_setzero_si256();
for (int j = 0; j < words; j += 4) {
__m256i eq = _mm256_load_si256(reinterpret_cast<const __m256i *>(mask + j));
__m256i p = _mm256_load_si256(reinterpret_cast<const __m256i *>(positive + j));
__m256i m = _mm256_load_si256(reinterpret_cast<const __m256i *>(negative + j));
__m256i x = _mm256_and_si256(eq, p), sum = _mm256_add_epi64(x, p);
unsigned g = unsigned(_mm256_movemask_pd(_mm256_castsi256_pd(_mm256_or_si256(x, _mm256_andnot_si256(sum, p)))));
unsigned propagation = unsigned(_mm256_movemask_pd(_mm256_castsi256_pd(_mm256_cmpeq_epi64(sum, ones))));
unsigned incoming = (propagation + (g << 1) + carry) ^ propagation;
carry = incoming >> 4;
__m256i increments = _mm256_and_si256(_mm256_srlv_epi64(_mm256_set1_epi64x(incoming), positions), one);
__m256i xv = _mm256_or_si256(eq, m);
__m256i xh = _mm256_or_si256(_mm256_xor_si256(_mm256_add_epi64(sum, increments), p), eq);
__m256i ph = _mm256_or_si256(m, _mm256_andnot_si256(_mm256_or_si256(xh, p), ones)), mh = _mm256_and_si256(p, xh);
__m256i in_p = _mm256_blend_epi32(_mm256_permute4x64_epi64(ph, 0x90), _mm256_permute4x64_epi64(previous_p, 0xff), 3);
__m256i in_m = _mm256_blend_epi32(_mm256_permute4x64_epi64(mh, 0x90), _mm256_permute4x64_epi64(previous_m, 0xff), 3);
previous_p = ph;
previous_m = mh;
ph = _mm256_or_si256(_mm256_slli_epi64(ph, 1), _mm256_srli_epi64(in_p, 63));
mh = _mm256_or_si256(_mm256_slli_epi64(mh, 1), _mm256_srli_epi64(in_m, 63));
_mm256_store_si256(reinterpret_cast<__m256i *>(positive + j), _mm256_or_si256(mh, _mm256_andnot_si256(_mm256_or_si256(xv, ph), ones)));
_mm256_store_si256(reinterpret_cast<__m256i *>(negative + j), _mm256_and_si256(ph, xv));
}
}
}
__attribute__((target("avx512f"))) inline void avx512(std::string_view s, const std::array<const Word *, 256> &masks, Word *__restrict positive, Word *__restrict negative, int words) {
const __m512i ones = _mm512_set1_epi64(-1), one = _mm512_set1_epi64(1);
for (unsigned char c : s) {
const Word *__restrict mask = masks[c];
unsigned carry = 0;
__m512i previous_p = _mm512_set1_epi64(std::numeric_limits<long long>::min()), previous_m = _mm512_setzero_si512();
for (int j = 0; j < words; j += 8) {
__m512i eq = _mm512_load_si512(mask + j), p = _mm512_load_si512(positive + j), m = _mm512_load_si512(negative + j);
__m512i x = _mm512_and_si512(eq, p), sum = _mm512_add_epi64(x, p);
unsigned g = unsigned(_mm512_cmp_epu64_mask(sum, x, _MM_CMPINT_LT));
unsigned propagation = unsigned(_mm512_cmpeq_epi64_mask(sum, ones));
unsigned incoming = (propagation + (g << 1) + carry) ^ propagation;
carry = incoming >> 8;
sum = _mm512_mask_add_epi64(sum, __mmask8(incoming), sum, one);
__m512i xv = _mm512_or_si512(eq, m), xh = _mm512_ternarylogic_epi64(sum, p, eq, 0xbe);
__m512i ph = _mm512_ternarylogic_epi64(m, xh, p, 0xf1), mh = _mm512_and_si512(p, xh);
__m512i in_p = _mm512_alignr_epi64(ph, previous_p, 7), in_m = _mm512_alignr_epi64(mh, previous_m, 7);
previous_p = ph;
previous_m = mh;
ph = _mm512_or_si512(_mm512_slli_epi64(ph, 1), _mm512_srli_epi64(in_p, 63));
mh = _mm512_or_si512(_mm512_slli_epi64(mh, 1), _mm512_srli_epi64(in_m, 63));
_mm512_store_si512(positive + j, _mm512_ternarylogic_epi64(mh, xv, ph, 0xf1));
_mm512_store_si512(negative + j, _mm512_and_si512(ph, xv));
}
}
}
#if defined(__GNUC__) && !defined(__clang__)
#pragma GCC pop_options
#endif
#endif
inline int count(Word *positive, Word *negative, int n, int m) {
int words = (m - 1) / 64 + 1;
if (m % 64) {
Word valid = (Word(1) << (m % 64)) - 1;
positive[words - 1] &= valid;
negative[words - 1] &= valid;
}
int result = n;
for (int j = 0; j < words; ++j) result += std::popcount(positive[j]) - std::popcount(negative[j]);
return result;
}
template <int backend = 0>
inline int bit_parallel(std::string_view s, std::string_view t) {
if (t.empty()) return int(s.size());
if (t.size() <= 64) {
std::array<Word, 256> masks{};
for (int j = 0; j < int(t.size()); ++j) masks[static_cast<unsigned char>(t[j])] |= Word(1) << j;
Word p = ~Word(0), m = 0;
for (unsigned char c : s) {
Word eq = masks[c], xv = eq | m, xh = (((eq & p) + p) ^ p) | eq;
Word ph = (m | ~(xh | p)) << 1 | 1, mh = (p & xh) << 1;
p = mh | ~(xv | ph);
m = ph & xv;
}
Word valid = ~Word(0) >> (64 - t.size());
return int(s.size()) + (std::popcount(p & valid) - std::popcount(m & valid));
}
const int words = int((t.size() + 63) / 64);
std::array<int, 256> ids;
ids.fill(0);
int alphabet = 1;
for (unsigned char c : t)
if (!ids[c]) ids[c] = alphabet++;
#if defined(__x86_64__)
int kernel = backend;
if (backend == 0 && words >= 8) {
if (__builtin_cpu_supports("avx512f")) kernel = 3;
else if (__builtin_cpu_supports("avx2")) kernel = 2;
}
if (kernel >= 2) {
int stride = (words + 7) & ~7;
std::vector<Word> storage(std::size_t(alphabet + 2) * stride + 7);
Word *data = storage.data() + ((-reinterpret_cast<std::uintptr_t>(storage.data()) & 63) / sizeof(Word));
Word *positive = data + std::size_t(alphabet) * stride, *negative = positive + stride;
std::fill_n(positive, stride, ~Word(0));
std::array<const Word *, 256> masks;
for (int c = 0; c < 256; ++c) masks[c] = data + std::size_t(ids[c]) * stride;
for (int j = 0, m = int(t.size()); j < m; ++j) data[std::size_t(ids[static_cast<unsigned char>(t[j])]) * stride + j / 64] |= Word(1) << (j % 64);
if (kernel == 3) avx512(s, masks, positive, negative, stride);
else avx2(s, masks, positive, negative, stride);
return count(positive, negative, int(s.size()), int(t.size()));
}
#endif
std::vector<Word> masks(std::size_t(alphabet) * words), positive(words, ~Word(0)), negative(words);
for (int j = 0, m = int(t.size()); j < m; ++j) masks[std::size_t(ids[static_cast<unsigned char>(t[j])]) * words + j / 64] |= Word(1) << (j % 64);
for (unsigned char c : s) {
const Word *mask = masks.data() + std::size_t(ids[c]) * words;
Word carry_p = 1, carry_m = 0, carry_add = 0;
for (int j = 0; j < words; ++j) {
Word p = positive[j], m = negative[j], eq = mask[j], xv = eq | m;
__uint128_t sum = __uint128_t(eq & p) + p + carry_add;
carry_add = Word(sum >> 64);
Word xh = (Word(sum) ^ p) | eq;
Word ph = m | ~(xh | p), mh = p & xh;
Word next_p = ph >> 63, next_m = mh >> 63;
ph = (ph << 1) | carry_p;
mh = (mh << 1) | carry_m;
positive[j] = mh | ~(xv | ph);
negative[j] = ph & xv;
carry_p = next_p;
carry_m = next_m;
}
}
return count(positive.data(), negative.data(), int(s.size()), int(t.size()));
}
inline int extend(std::string_view s, std::string_view t, int x, int y, int &budget) {
int limit = std::min(int(s.size()) - x, int(t.size()) - y);
while (limit >= 8) {
if (--budget < 0) return -1;
Word a, b;
std::memcpy(&a, s.data() + x, 8);
std::memcpy(&b, t.data() + y, 8);
Word diff = a ^ b;
if (diff) {
if constexpr (std::endian::native == std::endian::little) return x + std::countr_zero(diff) / 8;
else return x + std::countl_zero(diff) / 8;
}
x += 8;
y += 8;
limit -= 8;
}
while (limit--) {
if (--budget < 0) return -1;
if (s[x] != t[y]) break;
++x;
++y;
}
return x;
}
inline int wavefront(std::string_view s, std::string_view t, int cap, int budget) {
int n = int(s.size()), m = int(t.size()), base = cap + 1;
std::vector<int> previous(2 * cap + 3, -1), current(2 * cap + 3, -1);
previous[base] = extend(s, t, 0, 0, budget);
if (previous[base] < 0) return -1;
if (previous[base] == n && n == m) return 0;
for (int d = 1; d <= cap; ++d) {
for (int k = std::max(-d, -m), last = std::min(d, n); k <= last; ++k) {
if (--budget < 0) return -1;
int x = -1, a = previous[base + k - 1], b = previous[base + k], c = previous[base + k + 1];
if (a >= 0 && a < n) x = a + 1;
if (b >= 0 && b < n && b - k < m) x = std::max(x, b + 1);
if (c >= 0 && c - (k + 1) < m) x = std::max(x, c);
if (x >= 0) {
x = extend(s, t, x, x - k, budget);
if (x < 0) return -1;
if (x == n && x - k == m) return d;
}
current[base + k] = x;
}
previous.swap(current);
}
return -1;
}
}
inline int edit_distance(std::string_view s, std::string_view t) {
assert(s.size() <= std::size_t(std::numeric_limits<int>::max()) && t.size() <= std::size_t(std::numeric_limits<int>::max()));
std::size_t limit = std::min(s.size(), t.size());
std::size_t prefix = sequence_compare_detail::prefix(s.data(), t.data(), int(limit));
s.remove_prefix(prefix);
t.remove_prefix(prefix);
limit -= prefix;
std::size_t suffix = limit ? sequence_compare_detail::suffix(s.data() + s.size(), t.data() + t.size(), int(limit)) : 0;
s.remove_suffix(suffix);
t.remove_suffix(suffix);
if (s.size() < t.size()) std::swap(s, t);
if (t.empty()) return int(s.size());
if (s.size() != t.size()) {
std::size_t matched = 0;
for (char c : s)
if (c == t[matched] && ++matched == t.size()) return int(s.size() - t.size());
}
std::array<bool, 256> present{};
for (unsigned char c : t) present[c] = true;
bool common = false;
for (unsigned char c : s)
if (present[c]) {
common = true;
break;
}
if (!common) return int(s.size());
std::size_t work = s.size() * ((t.size() + 63) / 64);
if (work >= 65536 && s.size() - t.size() <= 1024) {
int result = edit_distance_detail::wavefront(s, t, 1024, int(std::min<std::size_t>(1 << 22, work / 8)));
if (result >= 0) return result;
}
return edit_distance_detail::bit_parallel(s, t);
}
#endif
#line 1 "string/edit_distance.hpp"
#line 1 "components/sequence_compare.hpp"
#include <bit>
#include <cstddef>
#include <cstdint>
#include <cstring>
#include <type_traits>
#if defined(__x86_64__)
#include <immintrin.h>
#endif
namespace sequence_compare_detail {
#if defined(__x86_64__)
__attribute__((target("avx2"))) inline std::size_t forward_avx2(const unsigned char *a, const unsigned char *b, std::size_t size) {
std::size_t i = 0;
for (; size - i >= 32; i += 32) {
auto x = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + i));
auto y = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(b + i));
auto difference = ~std::uint32_t(_mm256_movemask_epi8(_mm256_cmpeq_epi8(x, y)));
if (difference) return i + std::countr_zero(difference);
}
while (i < size && a[i] == b[i]) ++i;
return i;
}
__attribute__((target("avx2"))) inline std::size_t backward_avx2(const unsigned char *a, const unsigned char *b, std::size_t size) {
std::size_t i = 0;
for (; size - i >= 32; i += 32) {
auto x = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a - i - 32));
auto y = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(b - i - 32));
auto difference = ~std::uint32_t(_mm256_movemask_epi8(_mm256_cmpeq_epi8(x, y)));
if (difference) return i + std::countl_zero(difference);
}
while (i < size && a[-std::ptrdiff_t(i) - 1] == b[-std::ptrdiff_t(i) - 1]) ++i;
return i;
}
#endif
template<bool Vectorize = true, class T>
inline int prefix(const T *first, const T *second, int limit) {
if (!limit) return 0;
int matched = 0;
if constexpr (std::is_integral_v<T> && std::has_unique_object_representations_v<T>) {
const auto *a = reinterpret_cast<const unsigned char *>(first);
const auto *b = reinterpret_cast<const unsigned char *>(second);
std::size_t offset = 0, size = std::size_t(limit) * sizeof(T);
while (size - offset >= 8) {
std::uint64_t x, y;
std::memcpy(&x, a + offset, 8);
std::memcpy(&y, b + offset, 8);
auto difference = x ^ y;
if (difference) {
int bits = std::endian::native == std::endian::little ? std::countr_zero(difference) : std::countl_zero(difference);
return static_cast<int>((offset + bits / 8) / sizeof(T));
}
offset += 8;
#if defined(__x86_64__)
if constexpr (Vectorize) if (size - offset >= 64 && __builtin_cpu_supports("avx2"))
return static_cast<int>((offset + forward_avx2(a + offset, b + offset, size - offset)) / sizeof(T));
#endif
}
matched = static_cast<int>(offset / sizeof(T));
}
while (matched < limit && first[matched] == second[matched]) ++matched;
return matched;
}
template<bool Vectorize = true, class T>
inline int suffix(const T *first_end, const T *second_end, int limit) {
if (!limit) return 0;
int matched = 0;
if constexpr (std::is_integral_v<T> && std::has_unique_object_representations_v<T>) {
const auto *a = reinterpret_cast<const unsigned char *>(first_end);
const auto *b = reinterpret_cast<const unsigned char *>(second_end);
std::size_t offset = 0, size = std::size_t(limit) * sizeof(T);
while (size - offset >= 8) {
std::uint64_t x, y;
std::memcpy(&x, a - offset - 8, 8);
std::memcpy(&y, b - offset - 8, 8);
auto difference = x ^ y;
if (difference) {
int bits = std::endian::native == std::endian::little ? std::countl_zero(difference) : std::countr_zero(difference);
return static_cast<int>((offset + bits / 8) / sizeof(T));
}
offset += 8;
#if defined(__x86_64__)
if constexpr (Vectorize) if (size - offset >= 64 && __builtin_cpu_supports("avx2"))
return static_cast<int>((offset + backward_avx2(a - offset, b - offset, size - offset)) / sizeof(T));
#endif
}
matched = static_cast<int>(offset / sizeof(T));
}
while (matched < limit && first_end[-matched - 1] == second_end[-matched - 1]) ++matched;
return matched;
}
}
#line 5 "string/edit_distance.hpp"
#include <algorithm>
#include <array>
#line 8 "string/edit_distance.hpp"
#include <cassert>
#line 11 "string/edit_distance.hpp"
#include <limits>
#include <string_view>
#include <utility>
#include <vector>
#if defined(__x86_64__)
#include <immintrin.h>
#endif
namespace edit_distance_detail {
using Word = std::uint64_t;
#if defined(__x86_64__)
#if defined(__GNUC__) && !defined(__clang__)
#pragma GCC push_options
#pragma GCC optimize("O3")
#endif
__attribute__((target("avx2"))) inline void avx2(std::string_view s, const std::array<const Word *, 256> &masks, Word *__restrict positive, Word *__restrict negative, int words) {
const __m256i ones = _mm256_set1_epi64x(-1), one = _mm256_set1_epi64x(1), positions = _mm256_setr_epi64x(0, 1, 2, 3);
for (unsigned char c : s) {
const Word *__restrict mask = masks[c];
unsigned carry = 0;
__m256i previous_p = _mm256_set1_epi64x(std::numeric_limits<long long>::min()), previous_m = _mm256_setzero_si256();
for (int j = 0; j < words; j += 4) {
__m256i eq = _mm256_load_si256(reinterpret_cast<const __m256i *>(mask + j));
__m256i p = _mm256_load_si256(reinterpret_cast<const __m256i *>(positive + j));
__m256i m = _mm256_load_si256(reinterpret_cast<const __m256i *>(negative + j));
__m256i x = _mm256_and_si256(eq, p), sum = _mm256_add_epi64(x, p);
unsigned g = unsigned(_mm256_movemask_pd(_mm256_castsi256_pd(_mm256_or_si256(x, _mm256_andnot_si256(sum, p)))));
unsigned propagation = unsigned(_mm256_movemask_pd(_mm256_castsi256_pd(_mm256_cmpeq_epi64(sum, ones))));
unsigned incoming = (propagation + (g << 1) + carry) ^ propagation;
carry = incoming >> 4;
__m256i increments = _mm256_and_si256(_mm256_srlv_epi64(_mm256_set1_epi64x(incoming), positions), one);
__m256i xv = _mm256_or_si256(eq, m);
__m256i xh = _mm256_or_si256(_mm256_xor_si256(_mm256_add_epi64(sum, increments), p), eq);
__m256i ph = _mm256_or_si256(m, _mm256_andnot_si256(_mm256_or_si256(xh, p), ones)), mh = _mm256_and_si256(p, xh);
__m256i in_p = _mm256_blend_epi32(_mm256_permute4x64_epi64(ph, 0x90), _mm256_permute4x64_epi64(previous_p, 0xff), 3);
__m256i in_m = _mm256_blend_epi32(_mm256_permute4x64_epi64(mh, 0x90), _mm256_permute4x64_epi64(previous_m, 0xff), 3);
previous_p = ph;
previous_m = mh;
ph = _mm256_or_si256(_mm256_slli_epi64(ph, 1), _mm256_srli_epi64(in_p, 63));
mh = _mm256_or_si256(_mm256_slli_epi64(mh, 1), _mm256_srli_epi64(in_m, 63));
_mm256_store_si256(reinterpret_cast<__m256i *>(positive + j), _mm256_or_si256(mh, _mm256_andnot_si256(_mm256_or_si256(xv, ph), ones)));
_mm256_store_si256(reinterpret_cast<__m256i *>(negative + j), _mm256_and_si256(ph, xv));
}
}
}
__attribute__((target("avx512f"))) inline void avx512(std::string_view s, const std::array<const Word *, 256> &masks, Word *__restrict positive, Word *__restrict negative, int words) {
const __m512i ones = _mm512_set1_epi64(-1), one = _mm512_set1_epi64(1);
for (unsigned char c : s) {
const Word *__restrict mask = masks[c];
unsigned carry = 0;
__m512i previous_p = _mm512_set1_epi64(std::numeric_limits<long long>::min()), previous_m = _mm512_setzero_si512();
for (int j = 0; j < words; j += 8) {
__m512i eq = _mm512_load_si512(mask + j), p = _mm512_load_si512(positive + j), m = _mm512_load_si512(negative + j);
__m512i x = _mm512_and_si512(eq, p), sum = _mm512_add_epi64(x, p);
unsigned g = unsigned(_mm512_cmp_epu64_mask(sum, x, _MM_CMPINT_LT));
unsigned propagation = unsigned(_mm512_cmpeq_epi64_mask(sum, ones));
unsigned incoming = (propagation + (g << 1) + carry) ^ propagation;
carry = incoming >> 8;
sum = _mm512_mask_add_epi64(sum, __mmask8(incoming), sum, one);
__m512i xv = _mm512_or_si512(eq, m), xh = _mm512_ternarylogic_epi64(sum, p, eq, 0xbe);
__m512i ph = _mm512_ternarylogic_epi64(m, xh, p, 0xf1), mh = _mm512_and_si512(p, xh);
__m512i in_p = _mm512_alignr_epi64(ph, previous_p, 7), in_m = _mm512_alignr_epi64(mh, previous_m, 7);
previous_p = ph;
previous_m = mh;
ph = _mm512_or_si512(_mm512_slli_epi64(ph, 1), _mm512_srli_epi64(in_p, 63));
mh = _mm512_or_si512(_mm512_slli_epi64(mh, 1), _mm512_srli_epi64(in_m, 63));
_mm512_store_si512(positive + j, _mm512_ternarylogic_epi64(mh, xv, ph, 0xf1));
_mm512_store_si512(negative + j, _mm512_and_si512(ph, xv));
}
}
}
#if defined(__GNUC__) && !defined(__clang__)
#pragma GCC pop_options
#endif
#endif
inline int count(Word *positive, Word *negative, int n, int m) {
int words = (m - 1) / 64 + 1;
if (m % 64) {
Word valid = (Word(1) << (m % 64)) - 1;
positive[words - 1] &= valid;
negative[words - 1] &= valid;
}
int result = n;
for (int j = 0; j < words; ++j) result += std::popcount(positive[j]) - std::popcount(negative[j]);
return result;
}
template <int backend = 0>
inline int bit_parallel(std::string_view s, std::string_view t) {
if (t.empty()) return int(s.size());
if (t.size() <= 64) {
std::array<Word, 256> masks{};
for (int j = 0; j < int(t.size()); ++j) masks[static_cast<unsigned char>(t[j])] |= Word(1) << j;
Word p = ~Word(0), m = 0;
for (unsigned char c : s) {
Word eq = masks[c], xv = eq | m, xh = (((eq & p) + p) ^ p) | eq;
Word ph = (m | ~(xh | p)) << 1 | 1, mh = (p & xh) << 1;
p = mh | ~(xv | ph);
m = ph & xv;
}
Word valid = ~Word(0) >> (64 - t.size());
return int(s.size()) + (std::popcount(p & valid) - std::popcount(m & valid));
}
const int words = int((t.size() + 63) / 64);
std::array<int, 256> ids;
ids.fill(0);
int alphabet = 1;
for (unsigned char c : t)
if (!ids[c]) ids[c] = alphabet++;
#if defined(__x86_64__)
int kernel = backend;
if (backend == 0 && words >= 8) {
if (__builtin_cpu_supports("avx512f")) kernel = 3;
else if (__builtin_cpu_supports("avx2")) kernel = 2;
}
if (kernel >= 2) {
int stride = (words + 7) & ~7;
std::vector<Word> storage(std::size_t(alphabet + 2) * stride + 7);
Word *data = storage.data() + ((-reinterpret_cast<std::uintptr_t>(storage.data()) & 63) / sizeof(Word));
Word *positive = data + std::size_t(alphabet) * stride, *negative = positive + stride;
std::fill_n(positive, stride, ~Word(0));
std::array<const Word *, 256> masks;
for (int c = 0; c < 256; ++c) masks[c] = data + std::size_t(ids[c]) * stride;
for (int j = 0, m = int(t.size()); j < m; ++j) data[std::size_t(ids[static_cast<unsigned char>(t[j])]) * stride + j / 64] |= Word(1) << (j % 64);
if (kernel == 3) avx512(s, masks, positive, negative, stride);
else avx2(s, masks, positive, negative, stride);
return count(positive, negative, int(s.size()), int(t.size()));
}
#endif
std::vector<Word> masks(std::size_t(alphabet) * words), positive(words, ~Word(0)), negative(words);
for (int j = 0, m = int(t.size()); j < m; ++j) masks[std::size_t(ids[static_cast<unsigned char>(t[j])]) * words + j / 64] |= Word(1) << (j % 64);
for (unsigned char c : s) {
const Word *mask = masks.data() + std::size_t(ids[c]) * words;
Word carry_p = 1, carry_m = 0, carry_add = 0;
for (int j = 0; j < words; ++j) {
Word p = positive[j], m = negative[j], eq = mask[j], xv = eq | m;
__uint128_t sum = __uint128_t(eq & p) + p + carry_add;
carry_add = Word(sum >> 64);
Word xh = (Word(sum) ^ p) | eq;
Word ph = m | ~(xh | p), mh = p & xh;
Word next_p = ph >> 63, next_m = mh >> 63;
ph = (ph << 1) | carry_p;
mh = (mh << 1) | carry_m;
positive[j] = mh | ~(xv | ph);
negative[j] = ph & xv;
carry_p = next_p;
carry_m = next_m;
}
}
return count(positive.data(), negative.data(), int(s.size()), int(t.size()));
}
inline int extend(std::string_view s, std::string_view t, int x, int y, int &budget) {
int limit = std::min(int(s.size()) - x, int(t.size()) - y);
while (limit >= 8) {
if (--budget < 0) return -1;
Word a, b;
std::memcpy(&a, s.data() + x, 8);
std::memcpy(&b, t.data() + y, 8);
Word diff = a ^ b;
if (diff) {
if constexpr (std::endian::native == std::endian::little) return x + std::countr_zero(diff) / 8;
else return x + std::countl_zero(diff) / 8;
}
x += 8;
y += 8;
limit -= 8;
}
while (limit--) {
if (--budget < 0) return -1;
if (s[x] != t[y]) break;
++x;
++y;
}
return x;
}
inline int wavefront(std::string_view s, std::string_view t, int cap, int budget) {
int n = int(s.size()), m = int(t.size()), base = cap + 1;
std::vector<int> previous(2 * cap + 3, -1), current(2 * cap + 3, -1);
previous[base] = extend(s, t, 0, 0, budget);
if (previous[base] < 0) return -1;
if (previous[base] == n && n == m) return 0;
for (int d = 1; d <= cap; ++d) {
for (int k = std::max(-d, -m), last = std::min(d, n); k <= last; ++k) {
if (--budget < 0) return -1;
int x = -1, a = previous[base + k - 1], b = previous[base + k], c = previous[base + k + 1];
if (a >= 0 && a < n) x = a + 1;
if (b >= 0 && b < n && b - k < m) x = std::max(x, b + 1);
if (c >= 0 && c - (k + 1) < m) x = std::max(x, c);
if (x >= 0) {
x = extend(s, t, x, x - k, budget);
if (x < 0) return -1;
if (x == n && x - k == m) return d;
}
current[base + k] = x;
}
previous.swap(current);
}
return -1;
}
}
inline int edit_distance(std::string_view s, std::string_view t) {
assert(s.size() <= std::size_t(std::numeric_limits<int>::max()) && t.size() <= std::size_t(std::numeric_limits<int>::max()));
std::size_t limit = std::min(s.size(), t.size());
std::size_t prefix = sequence_compare_detail::prefix(s.data(), t.data(), int(limit));
s.remove_prefix(prefix);
t.remove_prefix(prefix);
limit -= prefix;
std::size_t suffix = limit ? sequence_compare_detail::suffix(s.data() + s.size(), t.data() + t.size(), int(limit)) : 0;
s.remove_suffix(suffix);
t.remove_suffix(suffix);
if (s.size() < t.size()) std::swap(s, t);
if (t.empty()) return int(s.size());
if (s.size() != t.size()) {
std::size_t matched = 0;
for (char c : s)
if (c == t[matched] && ++matched == t.size()) return int(s.size() - t.size());
}
std::array<bool, 256> present{};
for (unsigned char c : t) present[c] = true;
bool common = false;
for (unsigned char c : s)
if (present[c]) {
common = true;
break;
}
if (!common) return int(s.size());
std::size_t work = s.size() * ((t.size() + 63) / 64);
if (work >= 65536 && s.size() - t.size() <= 1024) {
int result = edit_distance_detail::wavefront(s, t, 1024, int(std::min<std::size_t>(1 << 22, work / 8)));
if (result >= 0) return result;
}
return edit_distance_detail::bit_parallel(s, t);
}