proconlib
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tests/suffix_array.test.cpp
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- Last update: 2025-01-25 08:45:50+09:00
- Problem: https://atcoder.jp/contests/abc272/tasks/abc272_f
Depends on
chmax function (tools/chmax.hpp)- chmin function (tools/chmin.hpp)
- Wrapper of atcoder::suffix_array and atcoder::lcp_array (tools/suffix_array.hpp)
Code
// competitive-verifier: PROBLEM https://atcoder.jp/contests/abc272/tasks/abc272_f
// competitive-verifier: IGNORE
#include <iostream>
#include <string>
#include "tools/suffix_array.hpp"
#include "tools/chmin.hpp"
using ll = long long;
int main() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
ll N;
std::string S, T;
std::cin >> N >> S >> T;
tools::suffix_array SSTT{S + S, T + T};
SSTT.erase_if([&](const auto, const auto j) {
return N <= j;
});
for (auto& lcpa_i : SSTT.lcpa) {
tools::chmin(lcpa_i, N);
}
ll answer = 0;
ll partial_answer = 0;
for (ll l = 0, r = 0; l < 2 * N; l = r) {
for (++r; r < 2 * N && SSTT.lcpa[r - 1] == N; ++r);
for (ll i = l; i < r; ++i) {
if (SSTT.sa[i].first == 0) ++partial_answer;
}
for (ll i = l; i < r; ++i) {
if (SSTT.sa[i].first == 1) answer += partial_answer;
}
}
std::cout << answer << '\n';
return 0;
}
#line 1 "tests/suffix_array.test.cpp"
// competitive-verifier: PROBLEM https://atcoder.jp/contests/abc272/tasks/abc272_f
// competitive-verifier: IGNORE
#include <iostream>
#include <string>
#line 1 "tools/suffix_array.hpp"
#include <vector>
#include <utility>
#include <type_traits>
#line 8 "tools/suffix_array.hpp"
#include <cstddef>
#include <limits>
#include <algorithm>
#include <iterator>
#include <initializer_list>
#line 1 "lib/ac-library/atcoder/string.hpp"
#line 5 "lib/ac-library/atcoder/string.hpp"
#include <cassert>
#include <numeric>
#line 9 "lib/ac-library/atcoder/string.hpp"
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) {
int n = int(s.size());
assert(n >= 1);
std::vector<int> rnk(n);
for (int i = 0; i < n; i++) {
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
#line 1 "tools/chmin.hpp"
#line 6 "tools/chmin.hpp"
namespace tools {
template <typename M, typename N>
bool chmin(M& lhs, const N& rhs) {
bool updated;
if constexpr (::std::is_integral_v<M> && ::std::is_integral_v<N>) {
updated = ::std::cmp_less(rhs, lhs);
} else {
updated = rhs < lhs;
}
if (updated) lhs = rhs;
return updated;
}
}
#line 1 "tools/chmax.hpp"
#line 6 "tools/chmax.hpp"
namespace tools {
template <typename M, typename N>
bool chmax(M& lhs, const N& rhs) {
bool updated;
if constexpr (::std::is_integral_v<M> && ::std::is_integral_v<N>) {
updated = ::std::cmp_less(lhs, rhs);
} else {
updated = lhs < rhs;
}
if (updated) lhs = rhs;
return updated;
}
}
#line 16 "tools/suffix_array.hpp"
namespace tools {
class suffix_array {
public:
::std::vector<::std::pair<int, int>> sa;
::std::vector<int> lcpa;
suffix_array() = default;
template <typename InputIterator>
suffix_array(const InputIterator begin, const InputIterator end) {
using Container = ::std::decay_t<decltype(*::std::declval<InputIterator>())>;
static_assert(
::std::is_same_v<Container, ::std::string> ||
::std::is_same_v<Container, ::std::vector<int>> ||
::std::is_same_v<Container, ::std::vector<unsigned int>> ||
::std::is_same_v<Container, ::std::vector<long long>> ||
::std::is_same_v<Container, ::std::vector<unsigned long long>>
);
if (begin == end) return;
::std::vector<Container> orig(begin, end);
::std::vector<::std::size_t> offsets(orig.size());
offsets[0] = 0;
for (::std::size_t i = 1; i < orig.size(); ++i) {
offsets[i] = offsets[i - 1] + orig[i - 1].size() + 1;
}
::std::vector<int> concat;
concat.reserve(offsets.back() + orig.back().size() + 1);
int upper;
if constexpr (::std::is_same_v<Container, ::std::string>) {
int lower = ::std::numeric_limits<int>::max();
upper = ::std::numeric_limits<int>::min();
for (const auto& s : orig) {
for (const auto s_i : s) {
::tools::chmin(lower, s_i);
::tools::chmax(upper, s_i);
}
}
for (const auto& s : orig) {
for (const auto s_i : s) {
concat.push_back(s_i + (lower == 0));
}
concat.push_back(0);
}
if (lower == 0) ++upper;
} else {
Container compress;
compress.reserve(concat.size() - orig.size());
for (const auto& s : orig) {
::std::copy(s.begin(), s.end(), ::std::back_inserter(compress));
}
::std::sort(compress.begin(), compress.end());
compress.erase(::std::unique(compress.begin(), compress.end()), compress.end());
for (const auto& s : orig) {
for (const auto s_i : s) {
concat.push_back(::std::distance(compress.begin(), ::std::lower_bound(compress.begin(), compress.end(), s_i)) + 1);
}
concat.push_back(0);
}
upper = compress.size();
}
::std::vector<::std::size_t> belongs;
belongs.reserve(concat.size());
for (::std::size_t i = 0; i < orig.size(); ++i) {
for (::std::size_t j = 0; j <= orig[i].size(); ++j) {
belongs.push_back(i);
}
}
const auto concat_sa = ::atcoder::suffix_array(concat, upper);
this->lcpa = ::atcoder::lcp_array(concat, concat_sa);
this->sa.reserve(concat_sa.size());
for (const auto ij : concat_sa) {
const int i = belongs[ij];
const int j = ij - offsets[i];
this->sa.emplace_back(i, j);
}
for (::std::size_t i = 0; i < this->lcpa.size(); ++i) {
::tools::chmin(this->lcpa[i], orig[this->sa[i].first].size() - this->sa[i].second);
::tools::chmin(this->lcpa[i], orig[this->sa[i + 1].first].size() - this->sa[i + 1].second);
}
this->erase_if([&](const int i, const int j) {
return ::std::cmp_equal(j, orig[i].size());
});
}
template <typename Container>
suffix_array(const ::std::initializer_list<Container> il) : suffix_array(il.begin(), il.end()) {
}
template <typename Predicate>
::std::size_t erase_if(const Predicate pred) {
if (this->sa.empty()) return 0;
const auto N = this->sa.size();
::std::size_t erased = 0;
::std::size_t sa_vl = 0, lcpa_vl = 0;
for (::std::size_t sa_vr = 0, sa_al = 0, sa_ar = 0, lcpa_vr = 0; sa_al < N; sa_vl = sa_vr, sa_al = sa_ar, lcpa_vl = lcpa_vr) {
const bool removes = pred(this->sa[sa_al].first, this->sa[sa_al].second);
for (; sa_ar < N && removes == pred(this->sa[sa_ar].first, this->sa[sa_ar].second); ++sa_vr, ++sa_ar);
if (sa_vl < sa_al) ::std::move(this->sa.begin() + sa_al, this->sa.begin() + sa_ar, this->sa.begin() + sa_vl);
const auto lcpa_al = sa_al == 0 ? 0 : sa_al - removes;
const auto lcpa_ar = ::std::min(sa_ar - !removes, N - 1);
lcpa_vr = lcpa_vl + (lcpa_ar - lcpa_al);
if (lcpa_vl < lcpa_al) ::std::move(this->lcpa.begin() + lcpa_al, this->lcpa.begin() + lcpa_ar, this->lcpa.begin() + lcpa_vl);
if (removes) {
erased += sa_vr - sa_vl;
sa_vr = sa_vl;
if (0 < sa_al && sa_ar < N) {
this->lcpa[lcpa_vl] = *::std::min_element(this->lcpa.begin() + lcpa_vl, this->lcpa.begin() + lcpa_vr);
lcpa_vr = lcpa_vl + 1;
} else {
lcpa_vr = lcpa_vl;
}
}
}
this->sa.erase(this->sa.begin() + sa_vl, this->sa.end());
this->lcpa.erase(this->lcpa.begin() + lcpa_vl, this->lcpa.end());
return erased;
}
};
}
#line 8 "tests/suffix_array.test.cpp"
using ll = long long;
int main() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
ll N;
std::string S, T;
std::cin >> N >> S >> T;
tools::suffix_array SSTT{S + S, T + T};
SSTT.erase_if([&](const auto, const auto j) {
return N <= j;
});
for (auto& lcpa_i : SSTT.lcpa) {
tools::chmin(lcpa_i, N);
}
ll answer = 0;
ll partial_answer = 0;
for (ll l = 0, r = 0; l < 2 * N; l = r) {
for (++r; r < 2 * N && SSTT.lcpa[r - 1] == N; ++r);
for (ll i = l; i < r; ++i) {
if (SSTT.sa[i].first == 0) ++partial_answer;
}
for (ll i = l; i < r; ++i) {
if (SSTT.sa[i].first == 1) answer += partial_answer;
}
}
std::cout << answer << '\n';
return 0;
}