#pragma once
#include "../atcoder/string.hpp"
#include "../data-structure/sparse-table.hpp"
template <typename Container>
struct StringSearch {
const Container& S;
int N;
vector<int> sa, la, invsa;
SparseTable<int> sparse;
StringSearch(const Container& _s) : S(_s), N(S.size()) {
sa = atcoder::suffix_array(S);
la = atcoder::lcp_array(S, sa);
invsa.resize(N);
for (int i = 0; i < N; i++) invsa[sa[i]] = i;
sparse = SparseTable<int>{la};
}
// lcp(s[i, N), s[j, N))
int lcp(int i, int j) {
assert(0 <= min(i, j) and max(i, j) < N);
if (i == j) return N - i;
int x = min(invsa[i], invsa[j]);
int y = max(invsa[i], invsa[j]);
return sparse.query(x, y);
}
// lcp(s[a, b), s[c, d))
int lcp(int a, int b, int c, int d) {
assert(0 <= a and a <= b and b <= N);
assert(0 <= c and c <= d and d <= N);
int l = lcp(a, c);
return min({l, b - a, d - c});
}
// lcp(s[a, b), s[c, d))
template <typename Int>
int lcp(pair<Int, Int> p, pair<Int, Int> q) {
return lcp(p.first, p.second, q.first, q.second);
}
// s[i, N) > s[j, N) : 1
// s[i, N) = s[j, N) : 0
// s[i, N) < s[j, N) : -1
int strcmp(int i, int j) {
assert(0 <= min(i, j) and max(i, j) < N);
if (i == j) return 0;
return invsa[i] < invsa[j] ? -1 : 1;
}
// s[a, b) > s[c, d) : 1
// s[a, b) = s[c, d) : 0
// s[a, b) < s[c, d) : -1
int strcmp(int a, int b, int c, int d) {
int l = lcp(a, b, c, d);
return a + l == b ? (c + l == d ? 0 : -1)
: c + l == d ? 1
: S[a + l] < S[c + l] ? -1
: 1;
}
// s[a, b) > s[c, d) : 1
// s[a, b) = s[c, d) : 0
// s[a, b) < s[c, d) : -1
template <typename Int>
int strcmp(pair<Int, Int> p, pair<Int, Int> q) {
return strcmp(p.first, p.second, q.first, q.second);
}
};
#line 2 "string/string-search.hpp"
#line 1 "atcoder/string.hpp"
#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) {
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 2 "data-structure/sparse-table.hpp"
#line 4 "data-structure/sparse-table.hpp"
#include <limits>
#line 6 "data-structure/sparse-table.hpp"
using namespace std;
template <typename T>
struct SparseTable {
inline static constexpr T INF = numeric_limits<T>::max() / 2;
int N;
vector<vector<T> > table;
T f(T a, T b) { return min(a, b); }
SparseTable() {}
SparseTable(const vector<T> &v) : N(v.size()) {
int b = 1;
while ((1 << b) <= N) ++b;
table.push_back(v);
for (int i = 1; i < b; i++) {
table.push_back(vector<T>(N, INF));
for (int j = 0; j + (1 << i) <= N; j++) {
table[i][j] = f(table[i - 1][j], table[i - 1][j + (1 << (i - 1))]);
}
}
}
// [l, r)
T query(int l, int r) {
assert(0 <= l and l <= r and r <= N);
if (l == r) return INF;
int b = 31 - __builtin_clz(r - l);
return f(table[b][l], table[b][r - (1 << b)]);
}
};
/**
* @brief Sparse Table
*/
#line 5 "string/string-search.hpp"
template <typename Container>
struct StringSearch {
const Container& S;
int N;
vector<int> sa, la, invsa;
SparseTable<int> sparse;
StringSearch(const Container& _s) : S(_s), N(S.size()) {
sa = atcoder::suffix_array(S);
la = atcoder::lcp_array(S, sa);
invsa.resize(N);
for (int i = 0; i < N; i++) invsa[sa[i]] = i;
sparse = SparseTable<int>{la};
}
// lcp(s[i, N), s[j, N))
int lcp(int i, int j) {
assert(0 <= min(i, j) and max(i, j) < N);
if (i == j) return N - i;
int x = min(invsa[i], invsa[j]);
int y = max(invsa[i], invsa[j]);
return sparse.query(x, y);
}
// lcp(s[a, b), s[c, d))
int lcp(int a, int b, int c, int d) {
assert(0 <= a and a <= b and b <= N);
assert(0 <= c and c <= d and d <= N);
int l = lcp(a, c);
return min({l, b - a, d - c});
}
// lcp(s[a, b), s[c, d))
template <typename Int>
int lcp(pair<Int, Int> p, pair<Int, Int> q) {
return lcp(p.first, p.second, q.first, q.second);
}
// s[i, N) > s[j, N) : 1
// s[i, N) = s[j, N) : 0
// s[i, N) < s[j, N) : -1
int strcmp(int i, int j) {
assert(0 <= min(i, j) and max(i, j) < N);
if (i == j) return 0;
return invsa[i] < invsa[j] ? -1 : 1;
}
// s[a, b) > s[c, d) : 1
// s[a, b) = s[c, d) : 0
// s[a, b) < s[c, d) : -1
int strcmp(int a, int b, int c, int d) {
int l = lcp(a, b, c, d);
return a + l == b ? (c + l == d ? 0 : -1)
: c + l == d ? 1
: S[a + l] < S[c + l] ? -1
: 1;
}
// s[a, b) > s[c, d) : 1
// s[a, b) = s[c, d) : 0
// s[a, b) < s[c, d) : -1
template <typename Int>
int strcmp(pair<Int, Int> p, pair<Int, Int> q) {
return strcmp(p.first, p.second, q.first, q.second);
}
};
string/string-search.hpp