suffix_array_query.hpp¶
基于后缀数组与 LCP 结构回答子串比较、最长公共前缀和模式出现区间。
Complexity: Time: \(O(n \log (n + 1))\) build, \(O(1)\) LCP, \(O(m \log (n + 1))\) interval. Space: \(O(N \log (N + 1))\) retained capacity; \(N\) is the largest built length.
AC 记录：suffixarray。
Implementation¶
当前头文件，省略 include guard；依赖见 #include。
/// @complexity Time: O(n log(n+1)) build, O(1) LCP, O(m log(n+1)) interval.
/// Space: O(N log(N+1)) retained capacity; N is the largest built length.
#include "atcoder/string.hpp"
#include <algorithm>
#include <cassert>
#include <string>
#include <string_view>
#include <utility>
#include <vector>
namespace noya {
/// @brief Suffix array with O(1) suffix LCP queries and lexicographic pattern
/// interval/search in unsigned-byte order, including embedded NUL bytes.
/// Length must be less than INT_MAX. Rebuilding replaces the indexed string.
struct suffix_array_query {
std::string s;
std::vector<int> sa;
std::vector<int> rk;
std::vector<int> lg;
std::vector<std::vector<int>> st;
suffix_array_query() = default;
explicit suffix_array_query(std::string val) { build(std::move(val)); }
void build(std::string val) {
s = std::move(val);
sa = [&] {
std::vector<int> bytes(s.size());
for (int i = 0; i < int(s.size()); ++i)
bytes[i] = static_cast<unsigned char>(s[i]);
return atcoder::suffix_array(bytes, 255);
}();
int n = int(s.size());
rk.resize(n);
for (int i = 0; i < n; ++i) rk[sa[i]] = i;
lg.assign(std::max(2, n + 1), 0);
for (int i = 2; i < int(lg.size()); ++i) lg[i] = lg[i / 2] + 1;
int levels = n > 1 ? lg[n - 1] + 1 : 0;
st.resize(levels);
if (n < 2) return;
st[0].resize(n - 1);
int h = 0;
for (int i = 0; i < n; ++i) {
if (h) --h;
if (!rk[i]) continue; // Kasai reuses the already-built inverse ranks.
int j = sa[rk[i] - 1];
while (h < n - i && h < n - j && s[i + h] == s[j + h]) ++h;
st[0][rk[i] - 1] = h;
}
for (int dep = 1; dep < levels; ++dep) {
int half = 1 << (dep - 1), len = n - (1 << dep);
st[dep].resize(len);
for (int i = 0; i < len; ++i)
st[dep][i] = std::min(st[dep - 1][i], st[dep - 1][i + half]);
}
}
int longest_common_prefix(int a, int b) const {
assert(0 <= a && a < int(s.size()));
assert(0 <= b && b < int(s.size()));
if (a == b) {
return int(s.size()) - a;
}
int l = rk[a];
int r = rk[b];
if (l > r) {
std::swap(l, r);
}
int len = r - l;
int dep = lg[len];
return std::min(st[dep][l], st[dep][r - (1 << dep)]);
}
/// @brief Return the half-open suffix-array interval whose suffixes start
/// with pattern. Empty pattern matches every nonempty suffix.
std::pair<int, int> interval(std::string_view t) const {
int n = int(sa.size());
if (t.empty()) return {0, n};
int l = 0, r = n, hit = -1;
while (l < r) {
int mid = l + (r - l) / 2;
int cmp = std::string_view(s).substr(sa[mid], t.size()).compare(t);
if (cmp < 0) l = mid + 1;
else {
r = mid;
if (cmp == 0) hit = mid;
}
}
if (hit < 0) return {l, l};
int first = l;
l = hit + 1; r = n;
// Matching suffixes are contiguous; their LCP with hit determines the end.
while (l < r) {
int mid = l + (r - l) / 2;
if (std::size_t(longest_common_prefix(sa[hit], sa[mid])) >= t.size())
l = mid + 1;
else r = mid;
}
return {first, l};
}
/// @brief Return starts in text order (to=true) or suffix-array order.
/// Adds O(z log(z+1)) or O(z) time and O(z) output space for z matches.
std::vector<int> occurrences(std::string_view t, bool to = true) const {
auto [l, r] = interval(t);
std::vector<int> res(sa.begin() + l, sa.begin() + r);
if (to) {
std::sort(res.begin(), res.end());
}
return res;
}
};
} // namespace noya
// NOYA_SUFFIX_ARRAY_QUERY_HPP
#ifndef NOYA_SUFFIX_ARRAY_QUERY_HPP
#define NOYA_SUFFIX_ARRAY_QUERY_HPP 1
/// @complexity Time: O(n log(n+1)) build, O(1) LCP, O(m log(n+1)) interval.
/// Space: O(N log(N+1)) retained capacity; N is the largest built length.
#include "atcoder/string.hpp"
#include <algorithm>
#include <cassert>
#include <string>
#include <string_view>
#include <utility>
#include <vector>
namespace noya {
/// @brief Suffix array with O(1) suffix LCP queries and lexicographic pattern
/// interval/search in unsigned-byte order, including embedded NUL bytes.
/// Length must be less than INT_MAX. Rebuilding replaces the indexed string.
struct suffix_array_query {
std::string s;
std::vector<int> sa;
std::vector<int> rk;
std::vector<int> lg;
std::vector<std::vector<int>> st;
suffix_array_query() = default;
explicit suffix_array_query(std::string val) { build(std::move(val)); }
void build(std::string val) {
s = std::move(val);
sa = [&] {
std::vector<int> bytes(s.size());
for (int i = 0; i < int(s.size()); ++i)
bytes[i] = static_cast<unsigned char>(s[i]);
return atcoder::suffix_array(bytes, 255);
}();
int n = int(s.size());
rk.resize(n);
for (int i = 0; i < n; ++i) rk[sa[i]] = i;
lg.assign(std::max(2, n + 1), 0);
for (int i = 2; i < int(lg.size()); ++i) lg[i] = lg[i / 2] + 1;
int levels = n > 1 ? lg[n - 1] + 1 : 0;
st.resize(levels);
if (n < 2) return;
st[0].resize(n - 1);
int h = 0;
for (int i = 0; i < n; ++i) {
if (h) --h;
if (!rk[i]) continue; // Kasai reuses the already-built inverse ranks.
int j = sa[rk[i] - 1];
while (h < n - i && h < n - j && s[i + h] == s[j + h]) ++h;
st[0][rk[i] - 1] = h;
}
for (int dep = 1; dep < levels; ++dep) {
int half = 1 << (dep - 1), len = n - (1 << dep);
st[dep].resize(len);
for (int i = 0; i < len; ++i)
st[dep][i] = std::min(st[dep - 1][i], st[dep - 1][i + half]);
}
}
int longest_common_prefix(int a, int b) const {
assert(0 <= a && a < int(s.size()));
assert(0 <= b && b < int(s.size()));
if (a == b) {
return int(s.size()) - a;
}
int l = rk[a];
int r = rk[b];
if (l > r) {
std::swap(l, r);
}
int len = r - l;
int dep = lg[len];
return std::min(st[dep][l], st[dep][r - (1 << dep)]);
}
/// @brief Return the half-open suffix-array interval whose suffixes start
/// with pattern. Empty pattern matches every nonempty suffix.
std::pair<int, int> interval(std::string_view t) const {
int n = int(sa.size());
if (t.empty()) return {0, n};
int l = 0, r = n, hit = -1;
while (l < r) {
int mid = l + (r - l) / 2;
int cmp = std::string_view(s).substr(sa[mid], t.size()).compare(t);
if (cmp < 0) l = mid + 1;
else {
r = mid;
if (cmp == 0) hit = mid;
}
}
if (hit < 0) return {l, l};
int first = l;
l = hit + 1; r = n;
// Matching suffixes are contiguous; their LCP with hit determines the end.
while (l < r) {
int mid = l + (r - l) / 2;
if (std::size_t(longest_common_prefix(sa[hit], sa[mid])) >= t.size())
l = mid + 1;
else r = mid;
}
return {first, l};
}
/// @brief Return starts in text order (to=true) or suffix-array order.
/// Adds O(z log(z+1)) or O(z) time and O(z) output space for z matches.
std::vector<int> occurrences(std::string_view t, bool to = true) const {
auto [l, r] = interval(t);
std::vector<int> res(sa.begin() + l, sa.begin() + r);
if (to) {
std::sort(res.begin(), res.end());
}
return res;
}
};
} // namespace noya
#endif // NOYA_SUFFIX_ARRAY_QUERY_HPP
/// @complexity Time: O(n log(n+1)) build, O(1) LCP, O(m log(n+1)) interval.
/// Space: O(N log(N+1)) retained capacity; N is the largest built length.
#include <algorithm>
#include <cassert>
#include <numeric>
#include <string>
#include <vector>
namespace atcoder {
namespace internal {
std::vector<int> sa_naive(const std::vector<int>& s) {
int n = int(s.size());
std::vector<int> sa(n);
std::iota(sa.begin(), sa.end(), 0);
std::sort(sa.begin(), sa.end(), [&](int l, int r) {
if (l == r) return false;
while (l < n && r < n) {
if (s[l] != s[r]) return s[l] < s[r];
l++;
r++;
}
return l == n;
});
return sa;
}
std::vector<int> sa_doubling(const std::vector<int>& s) {
int n = int(s.size());
std::vector<int> sa(n), rnk = s, tmp(n);
std::iota(sa.begin(), sa.end(), 0);
for (int k = 1; k < n; k *= 2) {
auto cmp = [&](int x, int y) {
if (rnk[x] != rnk[y]) return rnk[x] < rnk[y];
int rx = x + k < n ? rnk[x + k] : -1;
int ry = y + k < n ? rnk[y + k] : -1;
return rx < ry;
};
std::sort(sa.begin(), sa.end(), cmp);
tmp[sa[0]] = 0;
for (int i = 1; i < n; i++) {
tmp[sa[i]] = tmp[sa[i - 1]] + (cmp(sa[i - 1], sa[i]) ? 1 : 0);
}
std::swap(tmp, rnk);
}
return sa;
}
// SA-IS, linear-time suffix array construction
// Reference:
// G. Nong, S. Zhang, and W. H. Chan,
// Two Efficient Algorithms for Linear Time Suffix Array Construction
template <int THRESHOLD_NAIVE = 10, int THRESHOLD_DOUBLING = 40>
std::vector<int> sa_is(const std::vector<int>& s, int upper) {
int n = int(s.size());
if (n == 0) return {};
if (n == 1) return {0};
if (n == 2) {
if (s[0] < s[1]) {
return {0, 1};
} else {
return {1, 0};
}
}
if (n < THRESHOLD_NAIVE) {
return sa_naive(s);
}
if (n < THRESHOLD_DOUBLING) {
return sa_doubling(s);
}
std::vector<int> sa(n);
std::vector<bool> ls(n);
for (int i = n - 2; i >= 0; i--) {
ls[i] = (s[i] == s[i + 1]) ? ls[i + 1] : (s[i] < s[i + 1]);
}
std::vector<int> sum_l(upper + 1), sum_s(upper + 1);
for (int i = 0; i < n; i++) {
if (!ls[i]) {
sum_s[s[i]]++;
} else {
sum_l[s[i] + 1]++;
}
}
for (int i = 0; i <= upper; i++) {
sum_s[i] += sum_l[i];
if (i < upper) sum_l[i + 1] += sum_s[i];
}
auto induce = [&](const std::vector<int>& lms) {
std::fill(sa.begin(), sa.end(), -1);
std::vector<int> buf(upper + 1);
std::copy(sum_s.begin(), sum_s.end(), buf.begin());
for (auto d : lms) {
if (d == n) continue;
sa[buf[s[d]]++] = d;
}
std::copy(sum_l.begin(), sum_l.end(), buf.begin());
sa[buf[s[n - 1]]++] = n - 1;
for (int i = 0; i < n; i++) {
int v = sa[i];
if (v >= 1 && !ls[v - 1]) {
sa[buf[s[v - 1]]++] = v - 1;
}
}
std::copy(sum_l.begin(), sum_l.end(), buf.begin());
for (int i = n - 1; i >= 0; i--) {
int v = sa[i];
if (v >= 1 && ls[v - 1]) {
sa[--buf[s[v - 1] + 1]] = v - 1;
}
}
};
std::vector<int> lms_map(n + 1, -1);
int m = 0;
for (int i = 1; i < n; i++) {
if (!ls[i - 1] && ls[i]) {
lms_map[i] = m++;
}
}
std::vector<int> lms;
lms.reserve(m);
for (int i = 1; i < n; i++) {
if (!ls[i - 1] && ls[i]) {
lms.push_back(i);
}
}
induce(lms);
if (m) {
std::vector<int> sorted_lms;
sorted_lms.reserve(m);
for (int v : sa) {
if (lms_map[v] != -1) sorted_lms.push_back(v);
}
std::vector<int> rec_s(m);
int rec_upper = 0;
rec_s[lms_map[sorted_lms[0]]] = 0;
for (int i = 1; i < m; i++) {
int l = sorted_lms[i - 1], r = sorted_lms[i];
int end_l = (lms_map[l] + 1 < m) ? lms[lms_map[l] + 1] : n;
int end_r = (lms_map[r] + 1 < m) ? lms[lms_map[r] + 1] : n;
bool same = true;
if (end_l - l != end_r - r) {
same = false;
} else {
while (l < end_l) {
if (s[l] != s[r]) {
break;
}
l++;
r++;
}
if (l == n || s[l] != s[r]) same = false;
}
if (!same) rec_upper++;
rec_s[lms_map[sorted_lms[i]]] = rec_upper;
}
auto rec_sa =
sa_is<THRESHOLD_NAIVE, THRESHOLD_DOUBLING>(rec_s, rec_upper);
for (int i = 0; i < m; i++) {
sorted_lms[i] = lms[rec_sa[i]];
}
induce(sorted_lms);
}
return sa;
}
} // namespace internal
std::vector<int> suffix_array(const std::vector<int>& s, int upper) {
assert(0 <= upper);
for (int d : s) {
assert(0 <= d && d <= upper);
}
auto sa = internal::sa_is(s, upper);
return sa;
}
template <class T> std::vector<int> suffix_array(const std::vector<T>& s) {
int n = int(s.size());
std::vector<int> idx(n);
iota(idx.begin(), idx.end(), 0);
sort(idx.begin(), idx.end(), [&](int l, int r) { return s[l] < s[r]; });
std::vector<int> s2(n);
int now = 0;
for (int i = 0; i < n; i++) {
if (i && s[idx[i - 1]] != s[idx[i]]) now++;
s2[idx[i]] = now;
}
return internal::sa_is(s2, now);
}
std::vector<int> suffix_array(const std::string& s) {
int n = int(s.size());
std::vector<int> s2(n);
for (int i = 0; i < n; i++) {
s2[i] = s[i];
}
return internal::sa_is(s2, 255);
}
// Reference:
// T. Kasai, G. Lee, H. Arimura, S. Arikawa, and K. Park,
// Linear-Time Longest-Common-Prefix Computation in Suffix Arrays and Its
// Applications
template <class T>
std::vector<int> lcp_array(const std::vector<T>& s,
const std::vector<int>& sa) {
assert(s.size() == sa.size());
int n = int(s.size());
assert(n >= 1);
std::vector<int> rnk(n);
for (int i = 0; i < n; i++) {
assert(0 <= sa[i] && sa[i] < n);
rnk[sa[i]] = i;
}
std::vector<int> lcp(n - 1);
int h = 0;
for (int i = 0; i < n; i++) {
if (h > 0) h--;
if (rnk[i] == 0) continue;
int j = sa[rnk[i] - 1];
for (; j + h < n && i + h < n; h++) {
if (s[j + h] != s[i + h]) break;
}
lcp[rnk[i] - 1] = h;
}
return lcp;
}
std::vector<int> lcp_array(const std::string& s, const std::vector<int>& sa) {
int n = int(s.size());
std::vector<int> s2(n);
for (int i = 0; i < n; i++) {
s2[i] = s[i];
}
return lcp_array(s2, sa);
}
// Reference:
// D. Gusfield,
// Algorithms on Strings, Trees, and Sequences: Computer Science and
// Computational Biology
template <class T> std::vector<int> z_algorithm(const std::vector<T>& s) {
int n = int(s.size());
if (n == 0) return {};
std::vector<int> z(n);
z[0] = 0;
for (int i = 1, j = 0; i < n; i++) {
int& k = z[i];
k = (j + z[j] <= i) ? 0 : std::min(j + z[j] - i, z[i - j]);
while (i + k < n && s[k] == s[i + k]) k++;
if (j + z[j] < i + z[i]) j = i;
}
z[0] = n;
return z;
}
std::vector<int> z_algorithm(const std::string& s) {
int n = int(s.size());
std::vector<int> s2(n);
for (int i = 0; i < n; i++) {
s2[i] = s[i];
}
return z_algorithm(s2);
}
} // namespace atcoder
#include <algorithm>
#include <cassert>
#include <string>
#include <string_view>
#include <utility>
#include <vector>
namespace noya {
/// @brief Suffix array with O(1) suffix LCP queries and lexicographic pattern
/// interval/search in unsigned-byte order, including embedded NUL bytes.
/// Length must be less than INT_MAX. Rebuilding replaces the indexed string.
struct suffix_array_query {
std::string s;
std::vector<int> sa;
std::vector<int> rk;
std::vector<int> lg;
std::vector<std::vector<int>> st;
suffix_array_query() = default;
explicit suffix_array_query(std::string val) { build(std::move(val)); }
void build(std::string val) {
s = std::move(val);
sa = [&] {
std::vector<int> bytes(s.size());
for (int i = 0; i < int(s.size()); ++i)
bytes[i] = static_cast<unsigned char>(s[i]);
return atcoder::suffix_array(bytes, 255);
}();
int n = int(s.size());
rk.resize(n);
for (int i = 0; i < n; ++i) rk[sa[i]] = i;
lg.assign(std::max(2, n + 1), 0);
for (int i = 2; i < int(lg.size()); ++i) lg[i] = lg[i / 2] + 1;
int levels = n > 1 ? lg[n - 1] + 1 : 0;
st.resize(levels);
if (n < 2) return;
st[0].resize(n - 1);
int h = 0;
for (int i = 0; i < n; ++i) {
if (h) --h;
if (!rk[i]) continue; // Kasai reuses the already-built inverse ranks.
int j = sa[rk[i] - 1];
while (h < n - i && h < n - j && s[i + h] == s[j + h]) ++h;
st[0][rk[i] - 1] = h;
}
for (int dep = 1; dep < levels; ++dep) {
int half = 1 << (dep - 1), len = n - (1 << dep);
st[dep].resize(len);
for (int i = 0; i < len; ++i)
st[dep][i] = std::min(st[dep - 1][i], st[dep - 1][i + half]);
}
}
int longest_common_prefix(int a, int b) const {
assert(0 <= a && a < int(s.size()));
assert(0 <= b && b < int(s.size()));
if (a == b) {
return int(s.size()) - a;
}
int l = rk[a];
int r = rk[b];
if (l > r) {
std::swap(l, r);
}
int len = r - l;
int dep = lg[len];
return std::min(st[dep][l], st[dep][r - (1 << dep)]);
}
/// @brief Return the half-open suffix-array interval whose suffixes start
/// with pattern. Empty pattern matches every nonempty suffix.
std::pair<int, int> interval(std::string_view t) const {
int n = int(sa.size());
if (t.empty()) return {0, n};
int l = 0, r = n, hit = -1;
while (l < r) {
int mid = l + (r - l) / 2;
int cmp = std::string_view(s).substr(sa[mid], t.size()).compare(t);
if (cmp < 0) l = mid + 1;
else {
r = mid;
if (cmp == 0) hit = mid;
}
}
if (hit < 0) return {l, l};
int first = l;
l = hit + 1; r = n;
// Matching suffixes are contiguous; their LCP with hit determines the end.
while (l < r) {
int mid = l + (r - l) / 2;
if (std::size_t(longest_common_prefix(sa[hit], sa[mid])) >= t.size())
l = mid + 1;
else r = mid;
}
return {first, l};
}
/// @brief Return starts in text order (to=true) or suffix-array order.
/// Adds O(z log(z+1)) or O(z) time and O(z) output space for z matches.
std::vector<int> occurrences(std::string_view t, bool to = true) const {
auto [l, r] = interval(t);
std::vector<int> res(sa.begin() + l, sa.begin() + r);
if (to) {
std::sort(res.begin(), res.end());
}
return res;
}
};
} // namespace noya
// NOYA_SUFFIX_ARRAY_QUERY_HPP