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#define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_composite" #include "../../template/template.hpp" #include "../../structure/develop/splay-tree-base.hpp" #include "../../structure/develop/reversible-splay-tree.hpp" #include "../../math/combinatorics/mod-int.hpp" using mint = ModInt< 998244353 >; int main() { int N, Q; cin >> N >> Q; using pi = pair< mint, mint >; auto f = [](const pi &a, const pi &b) -> pi { return {a.first * b.first, a.second * b.first + b.second}; }; auto s = [](const pi &a) { return a; }; RST< pi > seg(f, s, pi(1, 0)); vector< pi > V(N); for(int i = 0; i < N; i++) { cin >> V[i].first >> V[i].second; } auto root = seg.build(V); for(int i = 0; i < Q; i++) { int t; cin >> t; if(t == 0) { int p; mint a, b; cin >> p >> a >> b; root = seg.set_element(root, p, pi(a, b)); } else { int l, r; mint x; cin >> l >> r >> x; auto ret = seg.query(root, l, r); cout << ret.first * x + ret.second << "\n"; } } }
#line 1 "test/verify/yosupo-point-set-range-composite-3.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_composite" #line 1 "template/template.hpp" #include<bits/stdc++.h> using namespace std; using int64 = long long; const int mod = 1e9 + 7; const int64 infll = (1LL << 62) - 1; const int inf = (1 << 30) - 1; struct IoSetup { IoSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); } } iosetup; template< typename T1, typename T2 > ostream &operator<<(ostream &os, const pair< T1, T2 >& p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator>>(istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T > ostream &operator<<(ostream &os, const vector< T > &v) { for(int i = 0; i < (int) v.size(); i++) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template< typename T > istream &operator>>(istream &is, vector< T > &v) { for(T &in : v) is >> in; return is; } template< typename T1, typename T2 > inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template< typename T1, typename T2 > inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); } template< typename T = int64 > vector< T > make_v(size_t a) { return vector< T >(a); } template< typename T, typename... Ts > auto make_v(size_t a, Ts... ts) { return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...)); } template< typename T, typename V > typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) { t = v; } template< typename T, typename V > typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) { for(auto &e : t) fill_v(e, v); } template< typename F > struct FixPoint : F { explicit FixPoint(F &&f) : F(forward< F >(f)) {} template< typename... Args > decltype(auto) operator()(Args &&... args) const { return F::operator()(*this, forward< Args >(args)...); } }; template< typename F > inline decltype(auto) MFP(F &&f) { return FixPoint< F >{forward< F >(f)}; } #line 4 "test/verify/yosupo-point-set-range-composite-3.test.cpp" #line 1 "structure/develop/splay-tree-base.hpp" /** * @brief Splay-Tree-Base(Splay木) */ template< typename Node > struct SplayTreeBase { public: using NP = Node *; bool is_root(const NP &t) const { return !t->p || (t->p->l != t && t->p->r != t); } inline size_t count(const NP &t) const { return t ? t->sz : 0; } void splay(NP t) { push(t); while(!is_root(t)) { auto *q = t->p; if(!is_root(t)) { push(q), push(t); if(q->l == t) rotr(t); else rotl(t); } else { auto *r = q->p; push(r), push(q), push(t); if(r->l == q) { if(q->l == t) rotr(q), rotr(t); else rotl(t), rotr(t); } else { if(q->r == t) rotl(q), rotl(t); else rotr(t), rotl(t); } } } } NP erase(NP t) { splay(t); Node *x = t->l, *y = t->r; delete t; if(!x) { t = y; if(t) t->p = nullptr; } else if(!y) { t = x; t->p = nullptr; } else { x->p = nullptr; t = get_right(x); splay(t); t->r = y; y->p = t; } return t; } NP splay_front(NP t) { splay(t); while(t->l) t = t->l; splay(t); return t; } NP splay_back(NP t) { splay(t); while(t->r) t = t->r; splay(t); return t; } pair< NP, NP > split(NP t, int k) { if(!t) return {nullptr, nullptr}; push(t); if(k <= count(t->l)) { auto x = split(t->l, k); t->l = x.second; t->p = nullptr; if(x.second) x.second->p = t; return {x.first, update(t)}; } else { auto x = split(t->r, k - count(t->l) - 1); t->r = x.first; t->p = nullptr; if(x.first) x.first->p = t; return {update(t), x.second}; } } template< typename... Args > NP merge(NP p, Args... args) { return merge(p, merge(args...)); } NP merge(NP l, NP r) { if(!l && !r) return nullptr; if(!l) return splay(r), r; if(!r) return splay(l), l; splay(l), splay(r); l = splay_back(l); l->r = r; r->p = l; update(l); return l; } tuple< NP, NP, NP > split3(NP t, int a, int b) { splay(t); auto x = split(t, a); auto y = split(x.second, b - a); return make_tuple(x.first, y.first, y.second); } virtual void push(NP t) = 0; virtual Node *update(NP t) = 0; private: void rotr(NP t) { auto *x = t->p, *y = x->p; if((x->l = t->r)) t->r->p = x; t->r = x, x->p = t; update(x), update(t); if((t->p = y)) { if(y->l == x) y->l = t; if(y->r == x) y->r = t; update(y); } } void rotl(NP t) { auto *x = t->p, *y = x->p; if((x->r = t->l)) t->l->p = x; t->l = x, x->p = t; update(x), update(t); if((t->p = y)) { if(y->l == x) y->l = t; if(y->r == x) y->r = t; update(y); } } NP build(int l, int r, const vector< NP > &v) { if(l + 1 >= r) return v[l]; return merge(build(l, (l + r) >> 1, v), build((l + r) >> 1, r, v)); } protected: NP build_node(const vector< NP > &v) { return build(0, v.size(), v); } NP insert_node(NP t, int k, NP v) { splay(t); auto x = split(t, k); return merge(x.first, v, x.second); } NP erase_node(NP t, int k) { splay(t); auto x = split(t, k); auto y = split(x.second, 1); delete y.first; return merge(x.first, y.second); } }; #line 1 "structure/develop/reversible-splay-tree.hpp" /** * @brief Reversible-Splay-Tree(反転可能Splay木) */ template< typename Tp > struct ReversibleSplayTreeNode { using T = Tp; ReversibleSplayTreeNode *l, *r, *p; T key, sum; bool rev; size_t sz; ReversibleSplayTreeNode() : ReversibleSplayTreeNode(Tp()) {} ReversibleSplayTreeNode(const T &key) : key(key), sum(key), rev(false), l(nullptr), r(nullptr), p(nullptr), sz(1) {} }; template< typename Np > struct ReversibleSplayTree : SplayTreeBase< Np > { public: using Node = Np; using T = typename Node::T; using F = function< T(T, T) >; using S = function< T(T) >; using super = SplayTreeBase< Node >; using NP = typename super::NP; explicit ReversibleSplayTree(const F &f, const S &s, const T &M1) : f(f), s(s), M1(M1) {} using super::splay; using super::split; using super::count; using super::merge; using super::build_node; using super::insert_node; inline const T &sum(const NP t) { return t ? t->sum : M1; } NP alloc(const T &x) { return new Node(x); } T query(NP &t, int a, int b) { splay(t); auto x = split(t, a); auto y = split(x.second, b - a); auto ret = sum(y.first); t = merge(x.first, y.first, y.second); return ret; } NP build(const vector< T > &v) { vector< NP > vs(v.size()); for(int i = 0; i < v.size(); i++) vs[i] = alloc(v[i]); return build_node(vs); } void toggle(NP t) { swap(t->l, t->r); t->sum = s(t->sum); t->rev ^= true; } NP update(NP t) override { t->sz = 1; t->sum = t->key; if(t->l) t->sz += t->l->sz, t->sum = f(t->l->sum, t->sum); if(t->r) t->sz += t->r->sz, t->sum = f(t->sum, t->r->sum); return t; } void push(NP t) override { if(t->rev) { if(t->l) toggle(t->l); if(t->r) toggle(t->r); t->rev = false; } } NP insert(NP t, int k, const T &x) { return insert_node(t, k, alloc(x)); } NP set_element(NP t, int k, const T &x) { splay(t); return imp_set_element(t, k, x); } pair< NP , NP > split_lower_bound(NP t, const T &key) { if(!t) return {nullptr, nullptr}; push(t); if(key <= t->key) { auto x = split_lower_bound(t->l, key); t->l = x.second; t->p = nullptr; if(x.second) x.second->p = t; return {x.first, update(t)}; } else { auto x = split_lower_bound(t->r, key); t->r = x.first; t->p = nullptr; if(x.first) x.first->p = t; return {update(t), x.second}; } } private: const T M1; const F f; const S s; NP imp_set_element(NP t, int k, const T &x) { push(t); if(k < count(t->l)) { return imp_set_element(t->l, k, x); } else if(k == count(t->l)) { t->key = x; splay(t); return t; } else { return imp_set_element(t->r, k - count(t->l) - 1, x); } } }; template< typename T > using RST = ReversibleSplayTree< ReversibleSplayTreeNode< T > >; #line 7 "test/verify/yosupo-point-set-range-composite-3.test.cpp" #line 1 "math/combinatorics/mod-int.hpp" template< int mod > struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (int) (1LL * x * p.x % mod); return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inverse(); return *this; } ModInt operator-() const { return ModInt(-x); } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inverse() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(int64_t n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); } static int get_mod() { return mod; } }; using modint = ModInt< mod >; #line 9 "test/verify/yosupo-point-set-range-composite-3.test.cpp" using mint = ModInt< 998244353 >; int main() { int N, Q; cin >> N >> Q; using pi = pair< mint, mint >; auto f = [](const pi &a, const pi &b) -> pi { return {a.first * b.first, a.second * b.first + b.second}; }; auto s = [](const pi &a) { return a; }; RST< pi > seg(f, s, pi(1, 0)); vector< pi > V(N); for(int i = 0; i < N; i++) { cin >> V[i].first >> V[i].second; } auto root = seg.build(V); for(int i = 0; i < Q; i++) { int t; cin >> t; if(t == 0) { int p; mint a, b; cin >> p >> a >> b; root = seg.set_element(root, p, pi(a, b)); } else { int l, r; mint x; cin >> l >> r >> x; auto ret = seg.query(root, l, r); cout << ret.first * x + ret.second << "\n"; } } }