#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/dynamic-segment-tree.hpp" using namespace Nyaan; using A = Affine<LazyMontgomeryModInt<998244353>>; A f(A a, A b) { return a * b; } A ti() { return A{}; } using Trie = DynamicSegmentTree<A, f, ti>; void Nyaan::solve() { inl(N, Q); Trie trie(N); rep(i, N) { inl(c, d); trie.set_val(i, {c, d}); } rep(_, Q) { inl(cmd); if (cmd == 0) { inl(p, c, d); trie.set_val(p, {c, d}); } else { inl(l, r, x); out(trie.fold(l, r)(x)); } } }
#line 1 "verify/verify-yosupo-ds/yosupo-point-set-range-composite-dynamic-segtree.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-dynamic-segtree.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/dynamic-segment-tree.hpp" template <typename T, typename E, T (*f)(T, T), T (*g)(T, E), E (*h)(E, E), T (*ti)(), E (*ei)()> struct DynamicLazySegmentTree { using ll = long long; struct Node; using Ptr = Node *; struct Node { Ptr l, r; T sum; E laz; Node() : l(nullptr), r(nullptr), sum(ti()), laz(ei()) {} }; Ptr root; ll Rmax; DynamicLazySegmentTree(ll n = 0) { Rmax = 2; while (Rmax <= n) Rmax *= 2; root = my_new(); } // get a[x] T get_val(ll x) { ll L = 0, R = Rmax; Ptr t = root; while (L + 1 < R) { push(t); ll M = (L + R) / 2; if (x < M) { if (!t->l) return ti(); t = t->l, R = M; } else { if (!t->r) return ti(); t = t->r, L = M; } } return t->sum; } // a[i] <- x void set_val(ll i, const T &x) { _set_val(root, 0, Rmax, i, x); } // apply x to a[l], a[l+1], ..., a[r-1] void apply(ll l, ll r, const E &x) { _apply(root, 0, Rmax, l, r, x); } // get sum(a[l], a[l+1], ..., a[r-1]) T fold(ll l, ll r) { return _fold(root, 0, Rmax, l, r); } // 破壊的。また、key が等しい要素がある場合は未定義 void merge(DynamicLazySegmentTree &rhs) { root = _merge(root, rhs.root); } private: DynamicLazySegmentTree(Ptr _root, ll _Rmax) : root(_root), Rmax(_Rmax) {} Ptr my_new() { return new Node{}; } void my_del(Ptr p) { delete p; } void propagate(Ptr t, const E &x) { assert(t != nullptr && x != ei()); t->laz = h(t->laz, x); t->sum = g(t->sum, x); } void push(Ptr t) { assert(t != nullptr); if (t->laz == ei()) return; if (!t->l) t->l = my_new(); if (!t->r) t->r = my_new(); propagate(t->l, t->laz); propagate(t->r, t->laz); t->laz = ei(); } void update(Ptr t) { assert(t->laz == ei()); t->sum = f(t->l ? t->l->sum : ti(), t->r ? t->r->sum : ti()); } void _set_val(Ptr t, ll L, ll R, ll i, const T &x) { assert(L <= i && i < R && t); if (L + 1 == R) { t->sum = x; return; } ll M = (L + R) / 2; push(t); if (i < M) { if (!t->l) t->l = my_new(); _set_val(t->l, L, M, i, x); } else { if (!t->r) t->r = my_new(); _set_val(t->r, M, R, i, x); } update(t); } void _apply(Ptr t, ll L, ll R, ll a, ll b, const E &x) { assert(a <= b && a < R && L < b && t); if (L == a and R == b) { propagate(t, x); if (L + 1 == R) t->laz = ei(); return; } ll M = (L + R) / 2; push(t); if (a < M) { if (!t->l) t->l = my_new(); _apply(t->l, L, M, a, min(b, M), x); } if (M < b) { if (!t->r) t->r = my_new(); _apply(t->r, M, R, max(a, M), b, x); } update(t); return; } T _fold(Ptr t, ll L, ll R, ll a, ll b) { assert(a <= b && a < R && L < b && t); if (L == a and R == b) return t->sum; ll M = (L + R) / 2; push(t); T v = ti(); if (a < M && t->l) v = f(_fold(t->l, L, M, a, min(b, M)), v); if (M < b && t->r) v = f(v, _fold(t->r, M, R, max(a, M), b)); return v; } Ptr _merge(Ptr t1, Ptr t2) { if (!t1 or !t2) return t1 ? t1 : t2; assert(t1->laz == ei() && t2->laz == ei()); t1->l = merge(t1->l, t2->l); t1->r = merge(t1->r, t2->r); update(t1), my_del(t2); return t1; } /* // [L, x), [x, R) で split pair<Ptr, Ptr> _split(Ptr t1, ll L, ll R, ll x) { if (!t1) return {nullptr, nullptr}; assert(t1->laz == ei()); Ptr t2 = my_new(); ll M = (L + R) / 2; } */ }; namespace DynamicSegmentTreeImpl { template <typename T> T g(T l, bool) { return l; } bool h(bool, bool) { return false; } bool ei() { return false; } template <typename T, T (*f)(T, T), T (*ti)()> using DynamicSegmentTree = DynamicLazySegmentTree<T, bool, f, g, h, ti, ei>; } // namespace DynamicSegmentTreeImpl using DynamicSegmentTreeImpl::DynamicSegmentTree; /** * @brief Dynamic Segment Tree */ #line 8 "verify/verify-yosupo-ds/yosupo-point-set-range-composite-dynamic-segtree.test.cpp" using namespace Nyaan; using A = Affine<LazyMontgomeryModInt<998244353>>; A f(A a, A b) { return a * b; } A ti() { return A{}; } using Trie = DynamicSegmentTree<A, f, ti>; void Nyaan::solve() { inl(N, Q); Trie trie(N); rep(i, N) { inl(c, d); trie.set_val(i, {c, d}); } rep(_, Q) { inl(cmd); if (cmd == 0) { inl(p, c, d); trie.set_val(p, {c, d}); } else { inl(l, r, x); out(trie.fold(l, r)(x)); } } }