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#define PROBLEM "https://judge.yosupo.jp/problem/range_affine_range_sum" #include <bits/stdc++.h> using namespace std; #include "../LazySegTree.h" #include "../../Math/modint.h" #include "../../buffered_reader.h" using modular = ModInt<998244353>; struct Node { modular sum, sz; }; struct Lazy { modular a, b; }; Node op(Node l, Node r) { return Node { l.sum + r.sum, l.sz + r.sz }; } Node e() { return Node{0, 0}; } Node apply(Lazy f, Node node) { return Node{ f.a * node.sum + f.b * node.sz, node.sz }; } Lazy combine(Lazy g, Lazy f) { return Lazy { f.a * g.a, g.a * f.b + g.b }; } Lazy id() { return Lazy{1, 0}; } int32_t main() { ios::sync_with_stdio(0); cin.tie(0); int n, q; cin >> n >> q; vector<Node> nodes(n); for (auto& node : nodes) { cin >> node.sum; node.sz = 1; } LazySegTree<Node, op, e, Lazy, apply, combine, id> st(nodes); while (q--) { int typ; cin >> typ; if (typ == 0) { int l, r; Lazy f; cin >> l >> r >> f.a >> f.b; st.apply(l, r, f); } else { int l, r; cin >> l >> r; cout << st.prod(l, r).sum << '\n'; } } return 0; }
#line 1 "DataStructure/test/segment_tree_rangeaffinerangesum.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/range_affine_range_sum" #include <bits/stdc++.h> using namespace std; #line 1 "DataStructure/LazySegTree.h" // Lazy Segment Tree, copied from AtCoder {{{ // Source: https://github.com/atcoder/ac-library/blob/master/atcoder/lazysegtree.hpp // Doc: https://atcoder.github.io/ac-library/master/document_en/lazysegtree.html // // Notes: // - Index of elements from 0 // - Range queries are [l, r-1] // - composition(f, g) should return f(g()) // // Tested: // - https://oj.vnoi.info/problem/qmax2 // - https://oj.vnoi.info/problem/lites // - (range set, add, mult, sum) https://oj.vnoi.info/problem/segtree_itmix // - (range add (i-L)*A + B, sum) https://oj.vnoi.info/problem/segtree_itladder // - https://atcoder.jp/contests/practice2/tasks/practice2_l // - https://judge.yosupo.jp/problem/range_affine_range_sum int ceil_pow2(int n) { int x = 0; while ((1U << x) < (unsigned int)(n)) x++; return x; } template< class S, // node data type S (*op) (S, S), // combine 2 nodes S (*e) (), // identity element class F, // lazy propagation tag S (*mapping) (F, S), // apply tag F on a node F (*composition) (F, F), // combine 2 tags F (*id)() // identity tag > struct LazySegTree { LazySegTree() : LazySegTree(0) {} explicit LazySegTree(int n) : LazySegTree(vector<S>(n, e())) {} explicit LazySegTree(const vector<S>& v) : _n((int) v.size()) { log = 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); } } // 0 <= p < n 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); } // 0 <= p < n S get(int p) { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); return d[p]; } // Get product in range [l, r-1] // 0 <= l <= r <= n // For empty segment (l == r) -> return e() 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]; } // 0 <= p < n 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); } // Apply f on all elements in range [l, r-1] // 0 <= l <= r <= n 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); } } // Binary search on SegTree to find largest r: // f(op(a[l] .. a[r-1])) = true (assuming empty array is always true) // f(op(a[l] .. a[r])) = false (assuming op(..., a[n]), which is out of bound, is always false) 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; } // Binary search on SegTree to find smallest l: // f(op(a[l] .. a[r-1])) = true (assuming empty array is always true) // f(op(a[l-1] .. a[r-1])) = false (assuming op(a[-1], ..), which is out of bound, is always false) 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; vector<S> d; 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(); } }; // }}} // Examples {{{ // https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_D // https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_E // https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_F // https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_G // https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_H // https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_I // supports: // - set a(l -> r) to val; val > NOT_SET // - add a(l -> r) += val // - find sum a(l -> r) // - find min a(l -> r) struct RangeSetAddMinSumOps { struct S { long long sum, min, sz; }; static S op(S l, S r) { return S { l.sum + r.sum, min(l.min, r.min), l.sz + r.sz }; } static S e() { return S {0LL, INT_MAX, 0}; } static const long long NOT_SET = -1000111000; struct F { long long set, add; }; static S mapping(F f, S s) { if (f.set == NOT_SET) { return S { s.sum + f.add * s.sz, s.min + f.add, s.sz, }; } return S { (f.set + f.add) * s.sz, f.set + f.add, s.sz, }; } static F composition(F f, F g) { if (f.set == NOT_SET) { return F { g.set, g.add + f.add }; } return f; } static F id() { return F { NOT_SET, 0 }; } }; // }}} #line 1 "Math/modint.h" // ModInt {{{ template<int MD> struct ModInt { using ll = long long; int x; constexpr ModInt() : x(0) {} constexpr ModInt(ll v) { _set(v % MD + MD); } constexpr static int mod() { return MD; } constexpr explicit operator bool() const { return x != 0; } constexpr ModInt operator + (const ModInt& a) const { return ModInt()._set((ll) x + a.x); } constexpr ModInt operator - (const ModInt& a) const { return ModInt()._set((ll) x - a.x + MD); } constexpr ModInt operator * (const ModInt& a) const { return ModInt()._set((ll) x * a.x % MD); } constexpr ModInt operator / (const ModInt& a) const { return ModInt()._set((ll) x * a.inv().x % MD); } constexpr ModInt operator - () const { return ModInt()._set(MD - x); } constexpr ModInt& operator += (const ModInt& a) { return *this = *this + a; } constexpr ModInt& operator -= (const ModInt& a) { return *this = *this - a; } constexpr ModInt& operator *= (const ModInt& a) { return *this = *this * a; } constexpr ModInt& operator /= (const ModInt& a) { return *this = *this / a; } friend constexpr ModInt operator + (ll a, const ModInt& b) { return ModInt()._set(a % MD + b.x); } friend constexpr ModInt operator - (ll a, const ModInt& b) { return ModInt()._set(a % MD - b.x + MD); } friend constexpr ModInt operator * (ll a, const ModInt& b) { return ModInt()._set(a % MD * b.x % MD); } friend constexpr ModInt operator / (ll a, const ModInt& b) { return ModInt()._set(a % MD * b.inv().x % MD); } constexpr bool operator == (const ModInt& a) const { return x == a.x; } constexpr bool operator != (const ModInt& a) const { return x != a.x; } friend std::istream& operator >> (std::istream& is, ModInt& other) { ll val; is >> val; other = ModInt(val); return is; } constexpr friend std::ostream& operator << (std::ostream& os, const ModInt& other) { return os << other.x; } constexpr ModInt pow(ll k) const { ModInt ans = 1, tmp = x; while (k) { if (k & 1) ans *= tmp; tmp *= tmp; k >>= 1; } return ans; } constexpr ModInt inv() const { if (x < 1000111) { _precalc(1000111); return invs[x]; } int a = x, b = MD, ax = 1, bx = 0; while (b) { int q = a/b, t = a%b; a = b; b = t; t = ax - bx*q; ax = bx; bx = t; } assert(a == 1); if (ax < 0) ax += MD; return ax; } static std::vector<ModInt> factorials, inv_factorials, invs; constexpr static void _precalc(int n) { if (factorials.empty()) { factorials = {1}; inv_factorials = {1}; invs = {0}; } if (n > MD) n = MD; int old_sz = factorials.size(); if (n <= old_sz) return; factorials.resize(n); inv_factorials.resize(n); invs.resize(n); for (int i = old_sz; i < n; ++i) factorials[i] = factorials[i-1] * i; inv_factorials[n-1] = factorials.back().pow(MD - 2); for (int i = n - 2; i >= old_sz; --i) inv_factorials[i] = inv_factorials[i+1] * (i+1); for (int i = n-1; i >= old_sz; --i) invs[i] = inv_factorials[i] * factorials[i-1]; } static int get_primitive_root() { static int primitive_root = 0; if (!primitive_root) { primitive_root = [&]() { std::set<int> fac; int v = MD - 1; for (ll i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i; if (v > 1) fac.insert(v); for (int g = 1; g < MD; g++) { bool ok = true; for (auto i : fac) if (ModInt(g).pow((MD - 1) / i) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } static ModInt C(int n, int k) { _precalc(n + 1); return factorials[n] * inv_factorials[k] * inv_factorials[n-k]; } private: // Internal, DO NOT USE. // val must be in [0, 2*MD) constexpr inline __attribute__((always_inline)) ModInt& _set(ll v) { x = v >= MD ? v - MD : v; return *this; } }; template <int MD> std::vector<ModInt<MD>> ModInt<MD>::factorials = {1}; template <int MD> std::vector<ModInt<MD>> ModInt<MD>::inv_factorials = {1}; template <int MD> std::vector<ModInt<MD>> ModInt<MD>::invs = {0}; // }}} #line 1 "buffered_reader.h" // Buffered reader {{{ namespace IO { const int BUFSIZE = 1<<14; char buf[BUFSIZE + 1], *inp = buf; bool reacheof; char get_char() { if (!*inp && !reacheof) { memset(buf, 0, sizeof buf); int tmp = fread(buf, 1, BUFSIZE, stdin); if (tmp != BUFSIZE) reacheof = true; inp = buf; } return *inp++; } template<typename T> T get() { int neg = 0; T res = 0; char c = get_char(); while (!std::isdigit(c) && c != '-' && c != '+') c = get_char(); if (c == '+') { neg = 0; } else if (c == '-') { neg = 1; } else res = c - '0'; c = get_char(); while (std::isdigit(c)) { res = res * 10 + (c - '0'); c = get_char(); } return neg ? -res : res; } }; // Helper methods int ri() { return IO::get<int>(); } // }}} #line 9 "DataStructure/test/segment_tree_rangeaffinerangesum.test.cpp" using modular = ModInt<998244353>; struct Node { modular sum, sz; }; struct Lazy { modular a, b; }; Node op(Node l, Node r) { return Node { l.sum + r.sum, l.sz + r.sz }; } Node e() { return Node{0, 0}; } Node apply(Lazy f, Node node) { return Node{ f.a * node.sum + f.b * node.sz, node.sz }; } Lazy combine(Lazy g, Lazy f) { return Lazy { f.a * g.a, g.a * f.b + g.b }; } Lazy id() { return Lazy{1, 0}; } int32_t main() { ios::sync_with_stdio(0); cin.tie(0); int n, q; cin >> n >> q; vector<Node> nodes(n); for (auto& node : nodes) { cin >> node.sum; node.sz = 1; } LazySegTree<Node, op, e, Lazy, apply, combine, id> st(nodes); while (q--) { int typ; cin >> typ; if (typ == 0) { int l, r; Lazy f; cin >> l >> r >> f.a >> f.b; st.apply(l, r, f); } else { int l, r; cin >> l >> r; cout << st.prod(l, r).sum << '\n'; } } return 0; }