#define PROBLEM "https://judge.yosupo.jp/problem/zalgorithm" #include "../../template/template.hpp" #include "../../string/suffix-array.hpp" using namespace Nyaan; void Nyaan::solve(){ ins(S); SuffixArray sa(S); LCPArray lcp(sa); StringSearch search(lcp); rep(i,sz(S)){ cout << (i?" ":"") << search.ArbitaryLCP(0 , i); } out(); }
#line 1 "verify/verify-yosupo-string/yosupo-zalgo-suffixarray.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/zalgorithm" #line 2 "template/template.hpp" using namespace std; // intrinstic #include <immintrin.h> #include <algorithm> #include <array> #include <bitset> #include <cassert> #include <cctype> #include <cfenv> #include <cfloat> #include <chrono> #include <cinttypes> #include <climits> #include <cmath> #include <complex> #include <cstdarg> #include <cstddef> #include <cstdint> #include <cstdio> #include <cstdlib> #include <cstring> #include <deque> #include <fstream> #include <functional> #include <initializer_list> #include <iomanip> #include <ios> #include <iostream> #include <istream> #include <iterator> #include <limits> #include <list> #include <map> #include <memory> #include <new> #include <numeric> #include <ostream> #include <queue> #include <random> #include <set> #include <sstream> #include <stack> #include <streambuf> #include <string> #include <tuple> #include <type_traits> #include <typeinfo> #include <unordered_map> #include <unordered_set> #include <utility> #include <vector> // utility #line 1 "template/util.hpp" namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template <typename T> using V = vector<T>; template <typename T> using VV = vector<vector<T>>; using vi = vector<int>; using vl = vector<long long>; using vd = V<double>; using vs = V<string>; using vvi = vector<vector<int>>; using vvl = vector<vector<long long>>; template <typename T> using minpq = priority_queue<T, vector<T>, greater<T>>; template <typename T, typename U> struct P : pair<T, U> { template <typename... Args> P(Args... args) : pair<T, U>(args...) {} using pair<T, U>::first; using pair<T, U>::second; P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } template <typename S> P &operator*=(const S &r) { first *= r, second *= r; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } template <typename S> P operator*(const S &r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P<ll, ll>; using pi = P<int, int>; using vp = V<pl>; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template <typename T> int sz(const T &t) { return t.size(); } template <typename T, typename U> inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template <typename T, typename U> inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template <typename T> inline T Max(const vector<T> &v) { return *max_element(begin(v), end(v)); } template <typename T> inline T Min(const vector<T> &v) { return *min_element(begin(v), end(v)); } template <typename T> inline long long Sum(const vector<T> &v) { return accumulate(begin(v), end(v), 0LL); } template <typename T> int lb(const vector<T> &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template <typename T> int ub(const vector<T> &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template <typename T, typename U> pair<T, U> mkp(const T &t, const U &u) { return make_pair(t, u); } template <typename T> vector<T> mkrui(const vector<T> &v, bool rev = false) { vector<T> ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template <typename T> vector<T> mkuni(const vector<T> &v) { vector<T> ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template <typename F> vector<int> mkord(int N, F f) { vector<int> ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template <typename T> vector<int> mkinv(vector<T> &v) { int max_val = *max_element(begin(v), end(v)); vector<int> inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector<int> mkiota(int n) { vector<int> ret(n); iota(begin(ret), end(ret), 0); return ret; } template <typename T> T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template <typename T> bool nxp(vector<T> &v) { return next_permutation(begin(v), end(v)); } // 返り値の型は入力の T に依存 // i 要素目 : [0, a[i]) template <typename T> vector<vector<T>> product(const vector<T> &a) { vector<vector<T>> ret; vector<T> v; auto dfs = [&](auto rc, int i) -> void { if (i == (int)a.size()) { ret.push_back(v); return; } for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back(); }; dfs(dfs, 0); return ret; } // F : function(void(T&)), mod を取る操作 // T : 整数型のときはオーバーフローに注意する template <typename T> T Power(T a, long long n, const T &I, const function<void(T &)> &f) { T res = I; for (; n; f(a = a * a), n >>= 1) { if (n & 1) f(res = res * a); } return res; } // T : 整数型のときはオーバーフローに注意する template <typename T> T Power(T a, long long n, const T &I) { return Power(a, n, I, function<void(T &)>{[](T &) -> void {}}); } } // namespace Nyaan #line 58 "template/template.hpp" // bit operation #line 1 "template/bitop.hpp" namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return _mm_popcnt_u64(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template <typename T> inline int gbit(const T &a, int i) { return (a >> i) & 1; } template <typename T> inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan #line 61 "template/template.hpp" // inout #line 1 "template/inout.hpp" namespace Nyaan { template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &p) { os << p.first << " " << p.second; return os; } template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &p) { is >> p.first >> p.second; return is; } template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template <typename T> istream &operator>>(istream &is, vector<T> &v) { for (auto &x : v) is >> x; return is; } istream &operator>>(istream &is, __int128_t &x) { string S; is >> S; x = 0; int flag = 0; for (auto &c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream &operator>>(istream &is, __uint128_t &x) { string S; is >> S; x = 0; for (auto &c : S) { x *= 10; x += c - '0'; } return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } void in() {} template <typename T, class... U> void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template <typename T, class... U, char sep = ' '> void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan #line 64 "template/template.hpp" // debug #line 1 "template/debug.hpp" namespace DebugImpl { template <typename U, typename = void> struct is_specialize : false_type {}; template <typename U> struct is_specialize< U, typename conditional<false, typename U::iterator, void>::type> : true_type {}; template <typename U> struct is_specialize< U, typename conditional<false, decltype(U::first), void>::type> : true_type {}; template <typename U> struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type { }; void dump(const char& t) { cerr << t; } void dump(const string& t) { cerr << t; } void dump(const bool& t) { cerr << (t ? "true" : "false"); } void dump(__int128_t t) { if (t == 0) cerr << 0; if (t < 0) cerr << '-', t = -t; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } void dump(__uint128_t t) { if (t == 0) cerr << 0; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } template <typename U, enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr> void dump(const U& t) { cerr << t; } template <typename T> void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) { string res; if (t == Nyaan::inf) res = "inf"; if constexpr (is_signed<T>::value) { if (t == -Nyaan::inf) res = "-inf"; } if constexpr (sizeof(T) == 8) { if (t == Nyaan::infLL) res = "inf"; if constexpr (is_signed<T>::value) { if (t == -Nyaan::infLL) res = "-inf"; } } if (res.empty()) res = to_string(t); cerr << res; } template <typename T, typename U> void dump(const pair<T, U>&); template <typename T> void dump(const pair<T*, int>&); template <typename T> void dump(const T& t, enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) { cerr << "[ "; for (auto it = t.begin(); it != t.end();) { dump(*it); cerr << (++it == t.end() ? "" : ", "); } cerr << " ]"; } template <typename T, typename U> void dump(const pair<T, U>& t) { cerr << "( "; dump(t.first); cerr << ", "; dump(t.second); cerr << " )"; } template <typename T> void dump(const pair<T*, int>& t) { cerr << "[ "; for (int i = 0; i < t.second; i++) { dump(t.first[i]); cerr << (i == t.second - 1 ? "" : ", "); } cerr << " ]"; } void trace() { cerr << endl; } template <typename Head, typename... Tail> void trace(Head&& head, Tail&&... tail) { cerr << " "; dump(head); if (sizeof...(tail) != 0) cerr << ","; trace(forward<Tail>(tail)...); } } // namespace DebugImpl #ifdef NyaanDebug #define trc(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc(...) (void(0)) #endif #ifdef NyaanLocal #define trc2(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc2(...) (void(0)) #endif #line 67 "template/template.hpp" // macro #line 1 "template/macro.hpp" #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) #line 70 "template/template.hpp" namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } #line 2 "string/suffix-array.hpp" #line 2 "data-structure/sparse-table.hpp" #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 6 "string/suffix-array.hpp" // remind: SA including empty string // verify https://judge.yosupo.jp/submission/240 struct SuffixArray { int _size; vector<int> sa; string &s; SuffixArray(string &str) : _size(str.size()), s(str) { s.push_back(0); sa.resize(s.size()); iota(begin(sa), end(sa), 0); sort(begin(sa), end(sa), [&](int a, int b) { return s[a] == s[b] ? a > b : s[a] < s[b]; }); vector<int> classes(s.size()), c(s.begin(), s.end()), cnt(s.size()); for (int len = 1; len < (int)s.size(); len <<= 1) { for (int i = 0; i < (int)s.size(); i++) { if (i > 0 && c[sa[i - 1]] == c[sa[i]] && sa[i - 1] + len < (int)s.size() && c[sa[i - 1] + len / 2] == c[sa[i] + len / 2]) { classes[sa[i]] = classes[sa[i - 1]]; } else { classes[sa[i]] = i; } } iota(begin(cnt), end(cnt), 0); copy(begin(sa), end(sa), begin(c)); for (int i = 0; i < (int)s.size(); i++) { int s1 = c[i] - len; if (s1 >= 0) sa[cnt[classes[s1]]++] = s1; } classes.swap(c); } s.pop_back(); } void output() { cout << "SA\tidx\tstr" << endl; for (int i = 0; i < size(); i++) { cout << i << ": \t" << sa[i] << " \t"; if (sa[i] != _size) cout << s.substr(sa[i], _size - sa[i]) << endl; else cout << "$" << endl; } cout << endl; } int size() const { return _size + 1; } int operator[](int k) const { return sa[k]; } }; struct LCPArray { const SuffixArray &SA; vector<int> LCP, rank; LCPArray(const SuffixArray &sa) : SA(sa) { LCP.resize(SA.size()); rank.resize(SA.size()); for (int i = 0; i < SA.size(); i++) { rank[SA[i]] = i; } LCP[0] = 0; for (int i = 0, h = 0; i < SA.size() - 1; i++) { int j = SA[rank[i] - 1]; h ? h-- : h; while ((i > j ? i : j) + h < SA.size() - 1 && SA.s[i + h] == SA.s[j + h] && ++h) ; LCP[rank[i] - 1] = h; } } void output() { cout << "SA\tidx\tLCP\tstr" << endl; for (int i = 0; i < SA.size(); i++) { cout << i << "\t" << SA[i] << " \t" << LCP[i] << "\t"; if (SA[i] == SA.size() - 1) cout << "$"; else cout << SA.s.substr(SA[i], SA.size() - 1 - SA[i]); cout << endl; } } }; // verify // https://onlinejudge.u-aizu.ac.jp/status/users/NyaanNyaan/submissions/1/ALDS1_14_D/judge/3874273/C++14 // https://atcoder.jp/contests/abc135/submissions/7574225 // https://judge.yosupo.jp/submission/241 // https://atcoder.jp/contests/abc141/submissions/7577295 struct StringSearch { string &s; const SuffixArray &sa; const LCPArray &lcp; SparseTable<int> sparse; StringSearch(LCPArray &lcp) : s(lcp.SA.s), sa(lcp.SA), lcp(lcp), sparse(lcp.LCP) {} pair<int, int> comp(const string &t, int len, int si, int ti = 0) { int sn = (int)s.size(), tn = (int)t.size(); si += len, ti += len; while (si < sn && ti < tn) { if (s[si] != t[ti]) return make_pair(s[si] < t[ti], ti); si++, ti++; } return make_pair((si >= sn && ti < tn), ti); } pair<int, int> find_range(int left, int med, int right, int len) { { int ng = left - 1, ok = med; while (ng + 1 < ok) { int cur = (ng + ok) / 2; if (sparse.query(cur, med) >= len) ok = cur; else ng = cur; } left = ok; } { int ok = med, ng = right + 1; while (ok + 1 < ng) { int cur = (ng + ok) / 2; if (sparse.query(med, cur) >= len) ok = cur; else ng = cur; } right = ok; } return make_pair(left, right); } public: // Longest Common Prefix between S[i , N) and S[j , N) int ArbitaryLCP(int i, int j) { if (i == j) return (int)(s.size()) - i; return sparse.query(min(lcp.rank[i], lcp.rank[j]), max(lcp.rank[i], lcp.rank[j])); } // String Search O(|T| + log |S|) // return : [l, r], l and r are indices of Suffix Array // if T doesn't exist, return (-1, -1) pair<int, int> find(string &t) { int left = 1, right = sa.size() - 1, med = left; int leftlen = 0, rightlen = 0, tlen = t.size(); pair<int, int> ret; while (left + 1 < right) { med = (left + right) / 2; int corres_len = max(min(leftlen, sparse.query(left, med)), min(rightlen, sparse.query(med, right))); if (corres_len < max(leftlen, rightlen)) { if (leftlen < rightlen) left = med, leftlen = corres_len; else right = med, rightlen = corres_len; continue; } ret = comp(t, corres_len, sa[med]); if (ret.second == tlen) return find_range(left, med, right, tlen); if (ret.first == 0) right = med, rightlen = ret.second; else left = med, leftlen = ret.second; } if (sa.size() <= 3) { if (comp(t, 0, sa[left]).second == tlen) return find_range(left, left, right, tlen); if (comp(t, 0, sa[right]).second == tlen) return find_range(left, right, right, tlen); return make_pair(-1, -1); } med = left + right - med; ret = comp(t, min(leftlen, rightlen), sa[med]); if (ret.second == tlen) return find_range(left, med, right, tlen); return make_pair(-1, -1); } }; // Usage: // SuffixArray sa(S); // LCPArray lcp(sa); // StringSearch search(lcp); #line 5 "verify/verify-yosupo-string/yosupo-zalgo-suffixarray.test.cpp" using namespace Nyaan; void Nyaan::solve(){ ins(S); SuffixArray sa(S); LCPArray lcp(sa); StringSearch search(lcp); rep(i,sz(S)){ cout << (i?" ":"") << search.ArbitaryLCP(0 , i); } out(); }