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#include "string/longest_common_prefix.hpp"
#pragma once #include "../sparse_table/rmq_sparse_table.hpp" #include "suffix_array.hpp" #include <algorithm> #include <string> #include <utility> #include <vector> // CUT begin struct LCPsparsetable { const int N; std::vector<int> sainv; // len = N StaticRMQ<int> rmq; template <typename String> LCPsparsetable(const String &s) : N(s.size()) { auto sa = suffix_array(s); auto lcp = lcp_array(s, sa); sainv.resize(N); for (int i = 0; i < N; i++) sainv[sa[i]] = i; rmq = {lcp, N}; } int lcplen(int l1, int l2) const { if (l1 == l2) return N - l1; if (l1 == N or l2 == N) return 0; l1 = sainv[l1], l2 = sainv[l2]; if (l1 > l2) std::swap(l1, l2); return rmq.get(l1, l2); } };
#line 2 "sparse_table/rmq_sparse_table.hpp" #include <algorithm> #include <cassert> #include <vector> // CUT begin // Range Minimum Query for static sequence by sparse table // Complexity: $O(N \log N)$ for precalculation, $O(1)$ per query template <typename T> struct StaticRMQ { inline T func(const T &l, const T &r) const noexcept { return std::min<T>(l, r); } int N, lgN; T defaultT; std::vector<std::vector<T>> data; std::vector<int> lgx_table; StaticRMQ() = default; StaticRMQ(const std::vector<T> &sequence, T defaultT) : N(sequence.size()), defaultT(defaultT) { lgx_table.resize(N + 1); for (int i = 2; i < N + 1; i++) lgx_table[i] = lgx_table[i >> 1] + 1; lgN = lgx_table[N] + 1; data.assign(lgN, std::vector<T>(N, defaultT)); data[0] = sequence; for (int d = 1; d < lgN; d++) { for (int i = 0; i + (1 << d) <= N; i++) { data[d][i] = func(data[d - 1][i], data[d - 1][i + (1 << (d - 1))]); } } } T get(int l, int r) const { // [l, r), 0-indexed assert(l >= 0 and r <= N); if (l >= r) return defaultT; int d = lgx_table[r - l]; return func(data[d][l], data[d][r - (1 << d)]); } }; #line 4 "string/suffix_array.hpp" #include <numeric> #include <string> #line 7 "string/suffix_array.hpp" // CUT begin // Suffix array algorithms from AtCoder Library // Document: <https://atcoder.github.io/ac-library/master/document_ja/string.html> 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); } // Count keyword occurence in str // Complexity: O(min(|str|, |keyword|) * lg |str|) int count_keyword_occurence(const std::string &str, const std::vector<int> &suffarr, const std::string &keyword) { const int n = str.size(), m = keyword.size(); assert(n == suffarr.size()); if (n < m) return 0; auto f1 = [&](int h) { for (int j = 0; h + j < n and j < m; j++) { if (str[h + j] < keyword[j]) return true; if (str[h + j] > keyword[j]) return false; } return n - h < m; }; auto f2 = [&](int h) { for (int j = 0; h + j < n and j < m; j++) { // if (str[h + j] < keyword[j]) return true; if (str[h + j] > keyword[j]) return false; } return true; }; const auto L = std::partition_point(suffarr.begin(), suffarr.end(), f1); const auto R = std::partition_point(L, suffarr.end(), f2); return std::distance(L, R); // return std::vector<int>(L, R); // if you need occurence positions } #line 6 "string/longest_common_prefix.hpp" #include <utility> #line 8 "string/longest_common_prefix.hpp" // CUT begin struct LCPsparsetable { const int N; std::vector<int> sainv; // len = N StaticRMQ<int> rmq; template <typename String> LCPsparsetable(const String &s) : N(s.size()) { auto sa = suffix_array(s); auto lcp = lcp_array(s, sa); sainv.resize(N); for (int i = 0; i < N; i++) sainv[sa[i]] = i; rmq = {lcp, N}; } int lcplen(int l1, int l2) const { if (l1 == l2) return N - l1; if (l1 == N or l2 == N) return 0; l1 = sainv[l1], l2 = sainv[l2]; if (l1 > l2) std::swap(l1, l2); return rmq.get(l1, l2); } };