#define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_composite" // #include "../../template/template.hpp" // #include "../../math/affine-transformation.hpp" #include "../../modint/montgomery-modint.hpp" #include "../../segment-tree/rbst-segment-tree.hpp" // using namespace Nyaan; using mint = LazyMontgomeryModInt<998244353>; using A = Affine<mint>; A f(A a, A b) { return a * b; } A ti() { return A{}; } using Seg = RBSTSegmentTree<int, A, f, ti>; void Nyaan::solve() { inl(N, Q); V<A> a(N); rep(i, N) { inl(c, d); a[i] = {c, d}; } Seg seg{a}; rep(_, Q) { inl(cmd); if (cmd == 0) { inl(p, c, d); seg.set_val(p, {c, d}); } else { inl(l, r, x); out(seg.fold(l, r)(x)); } } }
#line 1 "verify/verify-yosupo-ds/yosupo-point-set-range-composite-rbstseg.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_composite" // #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 4 "verify/verify-yosupo-ds/yosupo-point-set-range-composite-rbstseg.test.cpp" // #line 2 "math/affine-transformation.hpp" template <typename mint> struct Affine { mint a, b; constexpr Affine() : a(1), b(0) {} constexpr Affine(mint _a, mint _b) : a(_a), b(_b) {} mint operator()(mint x) { return a * x + b; } // R(L(x)) friend Affine operator*(const Affine& l, const Affine& r) { return Affine(l.a * r.a, l.b * r.a + r.b); } bool operator==(const Affine& r) const { return a == r.a && b == r.b; } bool operator!=(const Affine& r) const { return a != r.a || b != r.b; } friend ostream& operator<<(ostream& os, const Affine& r) { os << "( " << r.a << ", " << r.b << " )"; return os; } }; /** * @brief アフィン変換 */ #line 2 "modint/montgomery-modint.hpp" template <uint32_t mod> struct LazyMontgomeryModInt { using mint = LazyMontgomeryModInt; using i32 = int32_t; using u32 = uint32_t; using u64 = uint64_t; static constexpr u32 get_r() { u32 ret = mod; for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret; return ret; } static constexpr u32 r = get_r(); static constexpr u32 n2 = -u64(mod) % mod; static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30"); static_assert((mod & 1) == 1, "invalid, mod % 2 == 0"); static_assert(r * mod == 1, "this code has bugs."); u32 a; constexpr LazyMontgomeryModInt() : a(0) {} constexpr LazyMontgomeryModInt(const int64_t &b) : a(reduce(u64(b % mod + mod) * n2)){}; static constexpr u32 reduce(const u64 &b) { return (b + u64(u32(b) * u32(-r)) * mod) >> 32; } constexpr mint &operator+=(const mint &b) { if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } constexpr mint &operator-=(const mint &b) { if (i32(a -= b.a) < 0) a += 2 * mod; return *this; } constexpr mint &operator*=(const mint &b) { a = reduce(u64(a) * b.a); return *this; } constexpr mint &operator/=(const mint &b) { *this *= b.inverse(); return *this; } constexpr mint operator+(const mint &b) const { return mint(*this) += b; } constexpr mint operator-(const mint &b) const { return mint(*this) -= b; } constexpr mint operator*(const mint &b) const { return mint(*this) *= b; } constexpr mint operator/(const mint &b) const { return mint(*this) /= b; } constexpr bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } constexpr bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } constexpr mint operator-() const { return mint() - mint(*this); } constexpr mint operator+() const { return mint(*this); } constexpr mint pow(u64 n) const { mint ret(1), mul(*this); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } constexpr mint inverse() const { int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0; while (y > 0) { t = x / y; x -= t * y, u -= t * v; tmp = x, x = y, y = tmp; tmp = u, u = v, v = tmp; } return mint{u}; } friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); } friend istream &operator>>(istream &is, mint &b) { int64_t t; is >> t; b = LazyMontgomeryModInt<mod>(t); return (is); } constexpr u32 get() const { u32 ret = reduce(a); return ret >= mod ? ret - mod : ret; } static constexpr u32 get_mod() { return mod; } }; #line 2 "segment-tree/rbst-segment-tree.hpp" #line 2 "internal/internal-type-traits.hpp" #line 4 "internal/internal-type-traits.hpp" using namespace std; namespace internal { template <typename T> using is_broadly_integral = typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>, true_type, false_type>::type; template <typename T> using is_broadly_signed = typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>, true_type, false_type>::type; template <typename T> using is_broadly_unsigned = typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>, true_type, false_type>::type; #define ENABLE_VALUE(x) \ template <typename T> \ constexpr bool x##_v = x<T>::value; ENABLE_VALUE(is_broadly_integral); ENABLE_VALUE(is_broadly_signed); ENABLE_VALUE(is_broadly_unsigned); #undef ENABLE_VALUE #define ENABLE_HAS_TYPE(var) \ template <class, class = void> \ struct has_##var : false_type {}; \ template <class T> \ struct has_##var<T, void_t<typename T::var>> : true_type {}; \ template <class T> \ constexpr auto has_##var##_v = has_##var<T>::value; #define ENABLE_HAS_VAR(var) \ template <class, class = void> \ struct has_##var : false_type {}; \ template <class T> \ struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \ template <class T> \ constexpr auto has_##var##_v = has_##var<T>::value; } // namespace internal #line 4 "segment-tree/rbst-segment-tree.hpp" ENABLE_HAS_VAR(lazy); ENABLE_HAS_VAR(shift); template <typename Node, typename I, typename T, typename E, T (*f)(T, T), T (*g)(T, E), E (*h)(E, E), T (*ti)(), E (*ei)()> struct RBSTSegmentTreeBase { protected: using Ptr = Node *; template <typename... Args> static Ptr _my_new(Args... args) { return new Node(args...); } static void _my_del(Ptr t) { delete t; } static int _count(const Ptr t) { return t ? t->cnt : 0; } static T _sum(const Ptr &t) { return t ? t->sum : ti(); } static uint64_t _rng() { static uint64_t x_ = 88172645463325252ULL; return x_ ^= x_ << 7, x_ ^= x_ >> 9, x_ & 0xFFFFFFFFull; } static Ptr _merge(Ptr l, Ptr r) { if (!l || !r) return l ? l : r; if (int((_rng() * (l->cnt + r->cnt)) >> 32) < l->cnt) { _push(l); l->r = _merge(l->r, r); return _update(l); } else { _push(r); r->l = _merge(l, r->l); return _update(r); } } static Ptr _build(int l, int r, const vector<pair<I, T>> &dat) { if (l == r) return nullptr; if (l + 1 == r) return _my_new(dat[l].first, dat[l].second); int m = (l + r) / 2; return _merge(_build(l, m, dat), _build(m, r, dat)); }; static void _push([[maybe_unused]] Ptr t) { if constexpr (has_lazy_v<Node>) { if (!t) return; if (t->lazy != ei()) { if (t->l) _propagate(t->l, t->lazy); if (t->r) _propagate(t->r, t->lazy); t->lazy = ei(); } } if constexpr (has_shift_v<Node>) { if (!t) return; if (t->shift != I{}) { if (t->l) _shift(t->l, t->shift); if (t->r) _shift(t->r, t->shift); t->shift = I{}; } } } static void _propagate([[maybe_unused]] Ptr t, [[maybe_unused]] const E &x) { if constexpr (has_lazy_v<Node>) { if (!t) return; t->lazy = h(t->lazy, x); t->val = g(t->val, x); t->sum = g(t->sum, x); } } static void _shift([[maybe_unused]] Ptr t, [[maybe_unused]] const I &sh) { if constexpr (has_shift_v<Node>) { if (!t) return; t->key += sh, t->shift += sh; } } static Ptr _update(Ptr t) { if (!t) return t; t->cnt = 1; t->sum = t->val; if (t->l) t->cnt += t->l->cnt, t->sum = f(t->l->sum, t->sum); if (t->r) t->cnt += t->r->cnt, t->sum = f(t->sum, t->r->sum); return t; } // key が k であるノードを探す, なければ nullptr static Ptr _find(Ptr t, I k) { while (t) { _push(t); if (k == t->key) return t; t = k < t->key ? t->l : t->r; } return nullptr; } static void _erase(Ptr &t, I k) { if (!t) return; _push(t); if (k == t->key) { Ptr tl = t->l, tr = t->r; _my_del(t); t = _merge(tl, tr); } else if (k < t->key) { _erase(t->l, k); _update(t); } else { _erase(t->r, k); _update(t); } } // [k 未満, k 以上] static pair<Ptr, Ptr> _split_by_key(Ptr t, I k) { if (!t) return {nullptr, nullptr}; _push(t); if (k == t->key) { Ptr tl = t->l; t->l = nullptr; return {tl, _update(t)}; } else if (k < t->key) { auto s = _split_by_key(t->l, k); t->l = s.second; return {s.first, _update(t)}; } else { auto s = _split_by_key(t->r, k); t->r = s.first; return {_update(t), s.second}; } } // [k 未満, k, k 超過] static array<Ptr, 3> _split_by_key3(Ptr t, I k) { if (!t) return {{nullptr, nullptr, nullptr}}; _push(t); if (k == t->key) { Ptr tl = t->l, tr = t->r; t->l = t->r = nullptr; return {{tl, _update(t), tr}}; } else if (k < t->key) { auto s = _split_by_key3(t->l, k); t->l = s[2]; return {{s[0], s[1], _update(t)}}; } else { auto s = _split_by_key3(t->r, k); t->r = s[0]; return {{_update(t), s[1], s[2]}}; } } // (-inf, i] の prod について check(prod) の (true / false) で切る template <typename C> static pair<Ptr, Ptr> _split_max_right(Ptr t, const C &check, T prod = ti()) { assert(check(prod)); if (!t) return {nullptr, nullptr}; _push(t); T p1 = f(prod, _sum(t->l)); if (check(p1)) { prod = p1; } else { auto s = _split_max_right(t->l, check, prod); t->l = s.second; return {s.first, _update(t)}; } prod = f(prod, t->val); if (!check(prod)) { Ptr tl = t->l; t->l = nullptr; return {tl, _update(t)}; } p1 = f(prod, _sum(t->r)); if (check(p1)) { return {t, nullptr}; } else { auto s = _split_max_right(t->r, check, prod); t->r = s.first; return {_update(t), s.second}; } } // [i, inf) の prod について check(prod) の (false / true) で切る template <typename C> static pair<Ptr, Ptr> _split_min_left(Ptr t, const C &check, T prod = ti()) { assert(check(prod)); if (!t) return {nullptr, nullptr}; _push(t); T p1 = f(_sum(t->r), prod); if (check(p1)) { prod = p1; } else { auto s = _split_min_left(t->r, check, prod); t->r = s.first; return {_update(t), s.second}; } prod = f(t->val, prod); if (!check(prod)) { Ptr tr = t->r; t->r = nullptr; return {_update(t), tr}; } p1 = f(_sum(t->l), prod); if (check(p1)) { return {nullptr, t}; } else { auto s = _split_min_left(t->l, check, prod); t->l = s.second; return {s.first, _update(t)}; } } // [l, inf) である地点に apply static void _apply_left(Ptr t, I l, const E &e) { if (!t) return; _push(t); if (t->key < l) { _apply_left(t->r, l, e); } else if (t->key == l) { t->val = g(t->val, e); _propagate(t->r, e); } else { _apply_left(t->l, l, e); t->val = g(t->val, e); _propagate(t->r, e); } _update(t); } // [-inf, r) である地点に apply static void _apply_right(Ptr t, I r, const E &e) { if (!t) return; _push(t); if (t->key < r) { _propagate(t->l, e); t->val = g(t->val, e); _apply_right(t->r, r, e); } else if (t->key == r) { _propagate(t->l, e); } else { _apply_right(t->l, r, e); } _update(t); } // [l, r) に apply static void _apply(Ptr t, I l, I r, const E &e) { if (!t) return; _push(t); if (t->key < l) { _apply(t->r, l, r, e); } else if (t->key == l) { t->val = g(t->val, e); _apply_right(t->r, r, e); } else if (t->key < r) { _apply_left(t->l, l, e); t->val = g(t->val, e); _apply_right(t->r, r, e); } else if (t->key == r) { _apply_left(t->l, l, e); } else { _apply(t->l, l, r, e); } _update(t); } // l 以上 static T _fold_left(Ptr t, I l) { if (!t) return ti(); _push(t); if (t->key < l) { return _fold_left(t->r, l); } else if (t->key == l) { return f(t->val, _fold_left(t->r, l)); } else { T tl = _fold_left(t->l, l); return f(f(tl, t->val), _sum(t->r)); } } // r 未満 static T _fold_right(Ptr t, I r) { if (!t) return ti(); _push(t); if (t->key < r) { T tr = _fold_right(t->r, r); return f(f(_sum(t->l), t->val), tr); } else if (t->key == r) { return _sum(t->l); } else { return _fold_right(t->l, r); } } static T _fold(Ptr t, I l, I r) { if (!t) return ti(); _push(t); if (t->key < l) { return _fold(t->r, l, r); } else if (t->key == l) { return f(t->val, _fold_right(t->r, r)); } else if (t->key < r) { T tl = _fold_left(t->l, l); T tr = _fold_right(t->r, r); return f(f(tl, t->val), tr); } else if (t->key == r) { return _fold_left(t->l, l); } else { return _fold(t->l, l, r); } } // t を根とする木の上で最小の key は? (t が空の場合は failed) static pair<I, T> _get_min_keyval(Ptr t, const I &failed) { if (!t) return {failed, ti()}; while (t->l) _push(t), t = t->l; return {t->key, t->val}; } // t を根とする木の上で最小の key は? (t が空の場合は failed) static pair<I, T> _get_max_keyval(Ptr t, const I &failed) { if (!t) return {failed, ti()}; while (t->r) _push(t), t = t->r; return {t->key, t->val}; } // t を根とする木のうち、[0, i の区間 fold が true になる最大の i は何か? // exclusive かつ (空 または[0,右]が真の場合) の場合は failed(inf) // inclusive かつ (空 または[0,0] が偽の場合) の場合は failed template <typename C, bool exclusive> static I _max_right(Ptr t, C check, const I &failed) { if (!t) return failed; _push(t); Ptr now = t; T prod_now = ti(); [[maybe_unused]] I prev = failed; while (true) { if (now->l != nullptr) { _push(now->l); auto pl = f(prod_now, now->l->sum); if (check(pl)) { prod_now = pl; } else { now = now->l; continue; } } auto pl = f(prod_now, now->val); if (!check(pl)) { if constexpr (exclusive) { return now->key; } else { return now->l ? _get_max_keyval(now->l, failed).first : prev; } } prod_now = pl; if (now->r == nullptr) { if constexpr (exclusive) { return failed; } else { return now->key; } } _push(now->r); if constexpr (!exclusive) prev = now->key; now = now->r; } } // t を根とする木のうち、i, inf) の区間 fold が true になる最小の i は何か? // inclusive かつ (空 または 存在しない) 場合は failed // exlucisve かつ (空 または [左, inf) が真) の場合は failed template <typename C, bool inclusive> static I _min_left(Ptr t, C check, const I &failed) { if (!t) return failed; _push(t); Ptr now = t; T prod_now = ti(); [[maybe_unused]] I prev = failed; while (true) { if (now->r != nullptr) { _push(now->r); auto pr = f(now->r->sum, prod_now); if (check(pr)) { prod_now = pr; } else { now = now->r; continue; } } auto pr = f(now->val, prod_now); if (!check(pr)) { if constexpr (inclusive) { return now->r ? _get_min_keyval(now->r, failed).first : prev; } else { return now->key; } } prod_now = pr; if (now->l == nullptr) { if constexpr (inclusive) { return now->key; } else { return failed; } } _push(now->l); if constexpr (inclusive) prev = now->key; now = now->l; } } static void _clear(Ptr t) { if (!t) return; if (t->l) _clear(t->l); if (t->r) _clear(t->r); _my_del(t); } static Ptr _deepcopy(Ptr t) { if (!t) return nullptr; Ptr u = _my_new(*t); if (u->l) u->l = _deepcopy(u->l); if (u->r) u->r = _deepcopy(u->r); return u; } static void _dump(Ptr t) { if (!t) return; _push(t); _dump(t->l); cerr << "## key = " << t->key << ","; cerr << "\tval = " << t->val << ", "; cerr << "\tsum = " << t->sum << ", "; cerr << "\tchild = "; cerr << "( "; if (t->l) cerr << t->l->key; if (!t->l) cerr << "nil"; cerr << ", "; if (t->r) cerr << t->r->key; if (!t->r) cerr << "nil"; cerr << " )" << endl; _dump(t->r); } static void _make_array(Ptr t, vector<pair<I, T>> &v) { if (!t) return; _push(t); if (t->l) _make_array(t->l, v); v.emplace_back(t->key, t->val); if (t->r) _make_array(t->r, v); } public: Ptr root; RBSTSegmentTreeBase() : root(nullptr) {} RBSTSegmentTreeBase(Ptr t) : root(t) {} RBSTSegmentTreeBase(const vector<T> xs, const vector<I> &vals = {}) { if (!vals.empty()) assert(xs.size() == vals.size()); int n = xs.size(); vector<pair<I, T>> dat(n); for (int i = 0; i < n; i++) dat[i] = {vals.empty() ? i : vals[i], xs[i]}; root = _build(0, n, dat); } RBSTSegmentTreeBase(RBSTSegmentTreeBase &&rhs) noexcept { root = rhs.root; } RBSTSegmentTreeBase(const RBSTSegmentTreeBase &rhs) { root = rhs.root; } ~RBSTSegmentTreeBase() = default; using RBST = RBSTSegmentTreeBase; RBST &operator=(RBST &&rhs) noexcept { root = rhs.root; return *this; } RBST &operator=(const RBST &rhs) { root = rhs.root; return *this; } RBST deepcopy() { return _deepcopy(root); } friend void swap(RBST &lhs, RBST &rhs) { swap(lhs.root, rhs.root); } void swap(RBST &rhs) { swap(root, rhs.root); } // destructive ordered _merge (max(lhs) < min(rhs)) friend RBST ordered_merge(RBST &lhs, RBST &rhs) { assert(lhs.get_max_key() < rhs.get_min_key()); return RBST{_merge(lhs.root, rhs.root)}; } // 1 点 値の書き換え void set_val(I i, T x) { auto s = _split_by_key3(root, i); if (s[1] == nullptr) { s[1] = _my_new(i, x); } else { s[1]->val = x; } root = _merge(_merge(s[0], _update(s[1])), s[2]); } // すでに要素が存在するときに値を set する。おそらく少し早い void set_val_fast(I i, T x) { static vector<Ptr> ps; ps.clear(); Ptr t = root; while (t) { _push(t); ps.push_back(t); if (i == t->key) break; t = i < t->key ? t->l : t->r; } if (!t) { set_val(i, x); return; } t->val = x; for (int j = ps.size() - 1; j >= 0; j--) _update(ps[j]); } // 1 点取得 T get_val(I i) { Ptr p = _find(root, i); return p ? p->val : ti(); } // 1 点 値の書き換え // func の返り値は void !!!!!!(参照された値を直接更新する) void apply_val(I i, const function<void(T &)> &func) { auto s = _split_by_key3(root, i); if (s[1] == nullptr) s[1] = _my_new(i); func(s[1]->val); root = _merge(_merge(s[0], _update(s[1])), s[2]); } // 1 点 値の書き換え 値が既に存在するときに早い // func の返り値は void !!!!!!(参照された値を直接更新する) void apply_val_fast(I i, const function<void(T &)> &func) { static vector<Ptr> ps; ps.clear(); Ptr t = root; while (t) { _push(t); ps.push_back(t); if (i == t->key) break; t = i < t->key ? t->l : t->r; } if (!t) { apply_val(i, func); return; } func(t->val); for (int j = ps.size() - 1; j >= 0; j--) _update(ps[j]); } // 頂点の削除 virtual void erase(I i) { _erase(root, i); } // 範囲作用 void apply(I l, I r, const E &e) { if (l >= r) return; _apply(root, l, r, e); } void apply_all(const E &e) { _propagate(root, e); } // 範囲取得 T fold(I l, I r) { if (l >= r) return ti(); return _fold(root, l, r); } T fold_all() { return _sum(root); } void shift(const I &sh) { _shift(root, sh); } // key 最小を取得 I get_min_key(I failed = -1) { return _get_min_keyval(root, failed).first; } // key 最大を取得 I get_max_key(I failed = -1) { return _get_max_keyval(root, failed).first; } // (key, val) 最小を取得 pair<I, T> get_min_keyval(I failed = -1) { return _get_min_keyval(root, failed); } // (key, val) 最大を取得 pair<I, T> get_max_keyval(I failed = -1) { return _get_max_keyval(root, failed); } // (key, val) 最小を pop pair<I, T> pop_min_keyval(I failed = -1) { assert(root != nullptr); auto kv = _get_min_keyval(root, failed); erase(kv.first); return kv; } // (key, val) 最大を取得 pair<I, T> pop_max_keyval(I failed = -1) { assert(root != nullptr); auto kv = _get_max_keyval(root, failed); erase(kv.first); return kv; } // n 未満の i のうち、[i, n) の区間 fold が true になる最小の i は何か? // (存在しない場合は failed を返す) template <typename C> I min_left(I n, C check, I failed) { assert(check(ti()) == true); auto [x, y] = _split_by_key(root, n); I res = _min_left<C, true>(x, check, failed); root = _merge(x, y); return res; } // n 未満の i のうち、(i, n) の区間 fold が true になる最小の i は何か? // (空だったり (左端, n) が 真の場合は minus_infty を返す) template <typename C> I min_left_exclusive(I n, C check, I minus_infty) { assert(check(ti()) == true); auto [x, y] = _split_by_key(root, n); I res = _min_left<C, false>(x, check, minus_infty); root = _merge(x, y); return res; } // n 以上の i のうち、[n, i) の区間 fold が true になる最大の i は何か? // (空だったり [n, 右端] が true の場合は infty を返す) template <typename C> I max_right(I n, C check, I infty) { assert(check(ti()) == true); auto [x, y] = _split_by_key(root, n); I res = _max_right<C, true>(y, check, infty); root = _merge(x, y); return res; } // n 以上の i のうち、[n, i] の区間 fold が true になる最大の i は何か? // (存在しない場合は failed を返す) template <typename C> I max_right_inclusive(I n, C check, I failed) { assert(check(ti()) == true); auto [x, y] = _split_by_key(root, n); I res = _max_right<C, false>(y, check, failed); root = _merge(x, y); return res; } // (key 未満, key 以上) で分割 // 呼び出し後のオブジェクトは空のセグ木になる pair<RBST, RBST> split_by_key(const I &key) { auto [x, y] = _split_by_key(root, key); root = nullptr; return make_pair(RBST{x}, RBST{y}); } // [i, inf) の区間積が (false, true) になる境界で分割 // 呼び出し後のオブジェクトは空のセグ木になる template <typename C> pair<RBST, RBST> split_min_left(const C &check) { assert(check(ti()) == true); auto [x, y] = _split_min_left(root, check); root = nullptr; return make_pair(RBST{x}, RBST{y}); } // (-inf, i] の区間積が (true, false) になる境界で分割 // 呼び出し後のオブジェクトは空のセグ木になる template <typename C> pair<RBST, RBST> split_max_right(const C &check) { assert(check(ti()) == true); auto [x, y] = _split_max_right(root, check); root = nullptr; return make_pair(RBST{x}, RBST{y}); } void clear() { _clear(root), root = nullptr; } int size() { return _count(root); } bool empty() { return !root; } void dump() { cerr << "***** dump start *****" << endl; _dump(root); cerr << "****** dump end ******" << endl; } // 列を配列に変換して返す vector<pair<I, T>> make_array() { vector<pair<I, T>> res; _make_array(root, res); return res; } }; namespace RBSTSegmentTreeImpl { bool _ei() { return false; } template <typename I, typename T, typename E, T (*f)(T, T), T (*g)(T, E), E (*h)(E, E), T (*ti)(), E (*ei)()> struct ShiftableLazySegNode { ShiftableLazySegNode *l, *r; I key, shift; T val, sum; E lazy; int cnt; ShiftableLazySegNode(const I &i, const T &t = ti()) : l(), r(), key(i), shift(I{}), val(t), sum(t), lazy(ei()), cnt(1) {} }; template <typename I, typename T, typename E, T (*f)(T, T), T (*g)(T, E), E (*h)(E, E), T (*ti)(), E (*ei)()> using RBSTShiftableLazySegmentTree = RBSTSegmentTreeBase<ShiftableLazySegNode<I, T, E, f, g, h, ti, ei>, I, T, E, f, g, h, ti, ei>; template <typename I, typename T, typename E, T (*f)(T, T), T (*g)(T, E), E (*h)(E, E), T (*ti)(), E (*ei)()> struct LazySegNode { LazySegNode *l, *r; I key; T val, sum; E lazy; int cnt; LazySegNode(const I &i, const T &t = ti()) : l(), r(), key(i), val(t), sum(t), lazy(ei()), cnt(1) {} }; template <typename I, typename T, typename E, T (*f)(T, T), T (*g)(T, E), E (*h)(E, E), T (*ti)(), E (*ei)()> using RBSTLazySegmentTree = RBSTSegmentTreeBase<LazySegNode<I, T, E, f, g, h, ti, ei>, I, T, E, f, g, h, ti, ei>; template <typename I, typename T, T (*f)(T, T), T (*ti)()> struct SegNode { SegNode *l, *r; I key; T val, sum; int cnt; SegNode(const I &i, const T &t = ti()) : l(), r(), key(i), val(t), sum(t), cnt(1) {} }; template <typename I, typename T, T (*f)(T, T), T (*ti)()> using RBSTSegmentTree = RBSTSegmentTreeBase<SegNode<I, T, f, ti>, I, T, bool, f, nullptr, nullptr, ti, _ei>; } // namespace RBSTSegmentTreeImpl using RBSTSegmentTreeImpl::RBSTLazySegmentTree; using RBSTSegmentTreeImpl::RBSTSegmentTree; using RBSTSegmentTreeImpl::RBSTShiftableLazySegmentTree; /** * @brief RBST-based Dynamic Lazy Segment Tree */ #line 8 "verify/verify-yosupo-ds/yosupo-point-set-range-composite-rbstseg.test.cpp" // using namespace Nyaan; using mint = LazyMontgomeryModInt<998244353>; using A = Affine<mint>; A f(A a, A b) { return a * b; } A ti() { return A{}; } using Seg = RBSTSegmentTree<int, A, f, ti>; void Nyaan::solve() { inl(N, Q); V<A> a(N); rep(i, N) { inl(c, d); a[i] = {c, d}; } Seg seg{a}; rep(_, Q) { inl(cmd); if (cmd == 0) { inl(p, c, d); seg.set_val(p, {c, d}); } else { inl(l, r, x); out(seg.fold(l, r)(x)); } } }