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#include "string/range_update_range_hash.hpp"
range_update_range_hash<base_num, mint>::from(s)
s
base_num
mint
base_num = 1, mint = modint2305843009213693951
prod(l, r)
s[l..r]
all_prod()
apply(l, r, x)
x
set(p, x)
s[p]
get(p)
lcp(l1, r1, l2, r2)
s[l1..r1]
s[l2..r2]
cmp(l1, r1, l2, r2)
s1 = s[l1..r1]
s2 = s[l2..r2]
s1 < s2 ? -1 : s1 == s2 ? 0 : 1
prod
all_prod
apply
set
get
lcp
cmp
#pragma once #include <algorithm> #include <array> #include <random> #include "atcoder/lazysegtree.hpp" #include "math/modint2305843009213693951.hpp" #include "math/pow_sum_table.hpp" #include "math/pow_table.hpp" template <int base_num = 1, typename mint = modint2305843009213693951> struct range_update_range_hash { public: range_update_range_hash() { } range_update_range_hash(const std::vector<int>& a) : n(a.size()) { std::vector<S> v(n); for (int i = 0; i < n; i++) { for (int base_id = 0; base_id < base_num; base_id++) { v[i].hash[base_id] = a[i]; } v[i].size = 1; v[i].is_e = false; } segt = atcoder::lazy_segtree<S, op, e, F, mapping, composition, id>(v); } template <typename Iterable> static range_update_range_hash from(const Iterable& s) { std::vector<int> a; for (auto&& e : s) a.push_back(int(e)); return range_update_range_hash(a); } template <typename T> void set(int p, T x) { segt.set(p, int(x)); } std::array<mint, base_num> get(int p) { return segt.get(p).hash; } std::array<mint, base_num> prod(int l, int r) { return segt.prod(l, r).hash; } std::array<mint, base_num> all_prod() { return segt.all_prod(); } template <typename T> void apply(int l, int r, T x) { segt.apply(l, r, {int(x), false}); } int lcp(int l1, int r1, int l2, int r2) { int len = std::min(r1 - l1, r2 - l2); int ok = 0, ng = len + 1; while (ng - ok > 1) { int mid = (ok + ng) / 2; bool f = prod(l1, l1 + mid) == prod(l2, l2 + mid); (f ? ok : ng) = mid; } return ok; } int cmp(int l1, int r1, int l2, int r2) { int x = std::min({lcp(l1, r1, l2, r2), r1 - l1, r2 - l2}); if (l1 + x == r1 && l2 + x != r2) return -1; if (l1 + x == r1 && l2 + x == r2) return 0; if (l1 + x != r1 && l2 + x == r2) return 1; return get(l1 + x)[0].val() < get(l2 + x)[0].val() ? -1 : 1; } private: static inline std::array<mint, base_num> gen_bases() { static std::mt19937_64 rng(std::random_device{}()); std::array<mint, base_num> bases; for (int i = 0; i < base_num; i++) { while (true) { uint64_t k = std::uniform_int_distribution<uint64_t>( 1, mint::mod - 1)(rng); if (std::gcd(k, mint::mod - 1) != 1) continue; uint64_t b = mint(r).pow(k).val(); if (b <= A) continue; bases[i] = b; break; } } return bases; } static inline std::array<pow_mod_sums<mint>, base_num> init_pow_sums( const std::array<mint, base_num>& bases) { std::array<pow_mod_sums<mint>, base_num> pow_sums; for (int i = 0; i < base_num; i++) { pow_sums[i] = pow_mod_sums<mint>(bases[i], 0); } return pow_sums; } static inline std::array<pow_mods<mint>, base_num> init_pows( const std::array<mint, base_num>& bases) { std::array<pow_mods<mint>, base_num> pows; for (int i = 0; i < base_num; i++) { pows[i] = pow_mods<mint>(bases[i], 0); } return pows; } static inline std::array<mint, base_num> bases = gen_bases(); static inline std::array<pow_mod_sums<mint>, base_num> pow_sums = init_pow_sums(bases); static inline std::array<pow_mods<mint>, base_num> pows = init_pows(bases); int n; static constexpr uint64_t r = 37; static constexpr uint64_t A = 2147483647; struct S { std::array<mint, base_num> hash; int size; bool is_e; }; static S op(S a, S b) { if (a.is_e) return b; if (b.is_e) return a; for (int base_id = 0; base_id < base_num; base_id++) { b.hash[base_id] += a.hash[base_id] * pows[base_id][b.size]; } b.size += a.size; return b; } static S e() { return {std::array<mint, base_num>(), 0, true}; } struct F { int f; bool is_id; }; static S mapping(F f, S x) { if (!f.is_id) { for (int base_id = 0; base_id < base_num; base_id++) { x.hash[base_id] = f.f * pow_sums[base_id][x.size]; } } return x; } static F composition(F f, F g) { return (f.is_id ? g : f); } static F id() { return {0, true}; } atcoder::lazy_segtree<S, op, e, F, mapping, composition, id> segt; };
#line 2 "string/range_update_range_hash.hpp" #include <algorithm> #include <array> #include <random> #line 1 "atcoder/lazysegtree.hpp" #line 5 "atcoder/lazysegtree.hpp" #include <cassert> #include <iostream> #include <vector> #line 1 "atcoder/internal_bit.hpp" #ifdef _MSC_VER #include <intrin.h> #endif namespace atcoder { namespace internal { // @param n `0 <= n` // @return minimum non-negative `x` s.t. `n <= 2**x` int ceil_pow2(int n) { int x = 0; while ((1U << x) < (unsigned int)(n)) x++; return x; } // @param n `1 <= n` // @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0` constexpr int bsf_constexpr(unsigned int n) { int x = 0; while (!(n & (1 << x))) x++; return x; } // @param n `1 <= n` // @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0` int bsf(unsigned int n) { #ifdef _MSC_VER unsigned long index; _BitScanForward(&index, n); return index; #else return __builtin_ctz(n); #endif } } // namespace internal } // namespace atcoder #line 10 "atcoder/lazysegtree.hpp" namespace atcoder { template <class S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S), F (*composition)(F, F), F (*id)()> struct lazy_segtree { public: lazy_segtree() : lazy_segtree(0) {} explicit lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {} explicit lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) { log = internal::ceil_pow2(_n); size = 1 << log; d = std::vector<S>(2 * size, e()); lz = std::vector<F>(size, id()); for (int i = 0; i < _n; i++) d[size + i] = v[i]; for (int i = size - 1; i >= 1; i--) { update(i); } } void set(int p, S x) { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); d[p] = x; for (int i = 1; i <= log; i++) update(p >> i); } S get(int p) { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); return d[p]; } S prod(int l, int r) { assert(0 <= l && l <= r && r <= _n); if (l == r) return e(); l += size; r += size; for (int i = log; i >= 1; i--) { if (((l >> i) << i) != l) push(l >> i); if (((r >> i) << i) != r) push((r - 1) >> i); } S sml = e(), smr = e(); while (l < r) { if (l & 1) sml = op(sml, d[l++]); if (r & 1) smr = op(d[--r], smr); l >>= 1; r >>= 1; } return op(sml, smr); } S all_prod() { return d[1]; } void apply(int p, F f) { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); d[p] = mapping(f, d[p]); for (int i = 1; i <= log; i++) update(p >> i); } void apply(int l, int r, F f) { assert(0 <= l && l <= r && r <= _n); if (l == r) return; l += size; r += size; for (int i = log; i >= 1; i--) { if (((l >> i) << i) != l) push(l >> i); if (((r >> i) << i) != r) push((r - 1) >> i); } { int l2 = l, r2 = r; while (l < r) { if (l & 1) all_apply(l++, f); if (r & 1) all_apply(--r, f); l >>= 1; r >>= 1; } l = l2; r = r2; } for (int i = 1; i <= log; i++) { if (((l >> i) << i) != l) update(l >> i); if (((r >> i) << i) != r) update((r - 1) >> i); } } template <bool (*g)(S)> int max_right(int l) { return max_right(l, [](S x) { return g(x); }); } template <class G> int max_right(int l, G g) { assert(0 <= l && l <= _n); assert(g(e())); if (l == _n) return _n; l += size; for (int i = log; i >= 1; i--) push(l >> i); S sm = e(); do { while (l % 2 == 0) l >>= 1; if (!g(op(sm, d[l]))) { while (l < size) { push(l); l = (2 * l); if (g(op(sm, d[l]))) { sm = op(sm, d[l]); l++; } } return l - size; } sm = op(sm, d[l]); l++; } while ((l & -l) != l); return _n; } template <bool (*g)(S)> int min_left(int r) { return min_left(r, [](S x) { return g(x); }); } template <class G> int min_left(int r, G g) { assert(0 <= r && r <= _n); assert(g(e())); if (r == 0) return 0; r += size; for (int i = log; i >= 1; i--) push((r - 1) >> i); S sm = e(); do { r--; while (r > 1 && (r % 2)) r >>= 1; if (!g(op(d[r], sm))) { while (r < size) { push(r); r = (2 * r + 1); if (g(op(d[r], sm))) { sm = op(d[r], sm); r--; } } return r + 1 - size; } sm = op(d[r], sm); } while ((r & -r) != r); return 0; } private: int _n, size, log; std::vector<S> d; std::vector<F> lz; void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); } void all_apply(int k, F f) { d[k] = mapping(f, d[k]); if (k < size) lz[k] = composition(f, lz[k]); } void push(int k) { all_apply(2 * k, lz[k]); all_apply(2 * k + 1, lz[k]); lz[k] = id(); } }; } // namespace atcoder #line 2 "math/modint2305843009213693951.hpp" #include <cstdint> struct modint2305843009213693951 { using mint = modint2305843009213693951; public: static constexpr uint64_t mod = 2305843009213693951; modint2305843009213693951() : _v(0) { } modint2305843009213693951(uint64_t v) : _v(fast_mod(v)) { } static constexpr uint64_t fast_mod(uint64_t v) { uint64_t u = v >> 61; uint64_t d = v & mod; uint64_t x = u + d; if (x > mod) x -= mod; return x; } uint64_t val() const { return _v; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= mod) _v -= mod; return *this; } mint& operator-=(const mint& rhs) { _v -= rhs._v; if (_v >= mod) _v += mod; return *this; } mint& operator*=(const mint& rhs) { static constexpr uint64_t mask31 = (uint64_t(1) << 31) - 1; static constexpr uint64_t mask30 = (uint64_t(1) << 30) - 1; uint64_t au = _v >> 31; uint64_t ad = _v & mask31; uint64_t bu = rhs._v >> 31; uint64_t bd = rhs._v & mask31; uint64_t m = ad * bu + au * bd; uint64_t mu = m >> 30; uint64_t md = m & mask30; _v = fast_mod((au * bu << 1) + mu + (md << 31) + ad * bd); return *this; } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(uint64_t n) const { mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: uint64_t _v; }; #line 2 "math/pow_sum_table.hpp" template <typename mint> struct pow_mod_sums { pow_mod_sums() { } pow_mod_sums(mint base, int n) : base(base) { ensure(n); } // sum(pow[0..i]) const mint& operator[](int i) const { ensure(i); return pow_sums[i]; } void ensure(int n) const { int sz = pow_sums.size(); if (sz > n) return; pow_sums.resize(n + 1); pows.resize(n + 1); for (int i = sz; i <= n; i++) { pows[i] = base * pows[i - 1]; pow_sums[i] = pow_sums[i - 1] + pows[i - 1]; } } private: mutable std::vector<mint> pow_sums{0}; mutable std::vector<mint> pows{1}; mint base; static constexpr int mod = mint::mod; }; #line 3 "math/pow_table.hpp" template <typename mint> struct pow_mods { pow_mods() { } pow_mods(mint base, int n) : base(base) { ensure(n); } const mint& operator[](int i) const { ensure(i); return pows[i]; } void ensure(int n) const { int sz = pows.size(); if (sz > n) return; pows.resize(n + 1); for (int i = sz; i <= n; i++) pows[i] = base * pows[i - 1]; } private: mutable std::vector<mint> pows{1}; mint base; static constexpr int mod = mint::mod; }; #line 10 "string/range_update_range_hash.hpp" template <int base_num = 1, typename mint = modint2305843009213693951> struct range_update_range_hash { public: range_update_range_hash() { } range_update_range_hash(const std::vector<int>& a) : n(a.size()) { std::vector<S> v(n); for (int i = 0; i < n; i++) { for (int base_id = 0; base_id < base_num; base_id++) { v[i].hash[base_id] = a[i]; } v[i].size = 1; v[i].is_e = false; } segt = atcoder::lazy_segtree<S, op, e, F, mapping, composition, id>(v); } template <typename Iterable> static range_update_range_hash from(const Iterable& s) { std::vector<int> a; for (auto&& e : s) a.push_back(int(e)); return range_update_range_hash(a); } template <typename T> void set(int p, T x) { segt.set(p, int(x)); } std::array<mint, base_num> get(int p) { return segt.get(p).hash; } std::array<mint, base_num> prod(int l, int r) { return segt.prod(l, r).hash; } std::array<mint, base_num> all_prod() { return segt.all_prod(); } template <typename T> void apply(int l, int r, T x) { segt.apply(l, r, {int(x), false}); } int lcp(int l1, int r1, int l2, int r2) { int len = std::min(r1 - l1, r2 - l2); int ok = 0, ng = len + 1; while (ng - ok > 1) { int mid = (ok + ng) / 2; bool f = prod(l1, l1 + mid) == prod(l2, l2 + mid); (f ? ok : ng) = mid; } return ok; } int cmp(int l1, int r1, int l2, int r2) { int x = std::min({lcp(l1, r1, l2, r2), r1 - l1, r2 - l2}); if (l1 + x == r1 && l2 + x != r2) return -1; if (l1 + x == r1 && l2 + x == r2) return 0; if (l1 + x != r1 && l2 + x == r2) return 1; return get(l1 + x)[0].val() < get(l2 + x)[0].val() ? -1 : 1; } private: static inline std::array<mint, base_num> gen_bases() { static std::mt19937_64 rng(std::random_device{}()); std::array<mint, base_num> bases; for (int i = 0; i < base_num; i++) { while (true) { uint64_t k = std::uniform_int_distribution<uint64_t>( 1, mint::mod - 1)(rng); if (std::gcd(k, mint::mod - 1) != 1) continue; uint64_t b = mint(r).pow(k).val(); if (b <= A) continue; bases[i] = b; break; } } return bases; } static inline std::array<pow_mod_sums<mint>, base_num> init_pow_sums( const std::array<mint, base_num>& bases) { std::array<pow_mod_sums<mint>, base_num> pow_sums; for (int i = 0; i < base_num; i++) { pow_sums[i] = pow_mod_sums<mint>(bases[i], 0); } return pow_sums; } static inline std::array<pow_mods<mint>, base_num> init_pows( const std::array<mint, base_num>& bases) { std::array<pow_mods<mint>, base_num> pows; for (int i = 0; i < base_num; i++) { pows[i] = pow_mods<mint>(bases[i], 0); } return pows; } static inline std::array<mint, base_num> bases = gen_bases(); static inline std::array<pow_mod_sums<mint>, base_num> pow_sums = init_pow_sums(bases); static inline std::array<pow_mods<mint>, base_num> pows = init_pows(bases); int n; static constexpr uint64_t r = 37; static constexpr uint64_t A = 2147483647; struct S { std::array<mint, base_num> hash; int size; bool is_e; }; static S op(S a, S b) { if (a.is_e) return b; if (b.is_e) return a; for (int base_id = 0; base_id < base_num; base_id++) { b.hash[base_id] += a.hash[base_id] * pows[base_id][b.size]; } b.size += a.size; return b; } static S e() { return {std::array<mint, base_num>(), 0, true}; } struct F { int f; bool is_id; }; static S mapping(F f, S x) { if (!f.is_id) { for (int base_id = 0; base_id < base_num; base_id++) { x.hash[base_id] = f.f * pow_sums[base_id][x.size]; } } return x; } static F composition(F f, F g) { return (f.is_id ? g : f); } static F id() { return {0, true}; } atcoder::lazy_segtree<S, op, e, F, mapping, composition, id> segt; };