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#define PROBLEM "https://judge.yosupo.jp/problem/static_rectangle_add_rectangle_sum" #include "../rectangle_add_rectangle_sum.hpp" #include "../../modint.hpp" #include <iostream> using namespace std; using mint = ModInt<998244353>; int main() { cin.tie(nullptr), ios::sync_with_stdio(false); RectangleAddRectangleSum<int, mint> rect_sum; const int bias = 500000000; int N, Q; cin >> N >> Q; while (N--) { int l, r, d, u; mint w; cin >> l >> d >> r >> u >> w; l -= bias; d -= bias; r -= bias; u -= bias; rect_sum.add_rectangle(l, r, d, u, w); } while (Q--) { int l, r, d, u; cin >> l >> d >> r >> u; l -= bias; d -= bias; r -= bias; u -= bias; rect_sum.add_query(l, r, d, u); } auto ret = rect_sum.solve(); for (auto x : ret) cout << x << '\n'; }
#line 1 "data_structure/test/rectangle_add_rectangle_sum.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/static_rectangle_add_rectangle_sum" #line 2 "segmenttree/binary_indexed_tree.hpp" #include <algorithm> #include <vector> // CUT begin // 0-indexed BIT (binary indexed tree / Fenwick tree) (i : [0, len)) template <class T> struct BIT { int n; std::vector<T> data; BIT(int len = 0) : n(len), data(len) {} void reset() { std::fill(data.begin(), data.end(), T(0)); } void add(int pos, T v) { // a[pos] += v pos++; while (pos > 0 and pos <= n) data[pos - 1] += v, pos += pos & -pos; } T sum(int k) const { // a[0] + ... + a[k - 1] T res = 0; while (k > 0) res += data[k - 1], k -= k & -k; return res; } T sum(int l, int r) const { return sum(r) - sum(l); } // a[l] + ... + a[r - 1] template <class OStream> friend OStream &operator<<(OStream &os, const BIT &bit) { T prv = 0; os << '['; for (int i = 1; i <= bit.n; i++) { T now = bit.sum(i); os << now - prv << ',', prv = now; } return os << ']'; } }; #line 4 "data_structure/rectangle_add_rectangle_sum.hpp" #include <tuple> #line 6 "data_structure/rectangle_add_rectangle_sum.hpp" // Static rectangle add rectangle sum // Calculate sums of rectangular weights inside the given rectangles // Complexity: O(q log q), q = # of rectangles / queries template <class Int, class T> class RectangleAddRectangleSum { struct AddQuery { Int xl, xr, yl, yr; T val; }; struct SumQuery { Int xl, xr, yl, yr; }; std::vector<AddQuery> add_queries; std::vector<SumQuery> sum_queries; public: RectangleAddRectangleSum() = default; // A[x][y] += val for (x, y) in [xl, xr) * [yl, yr) void add_rectangle(Int xl, Int xr, Int yl, Int yr, T val) { add_queries.push_back(AddQuery{xl, xr, yl, yr, val}); } // Get sum of A[x][y] for (x, y) in [xl, xr) * [yl, yr) void add_query(Int xl, Int xr, Int yl, Int yr) { sum_queries.push_back(SumQuery{xl, xr, yl, yr}); } std::vector<T> solve() const { std::vector<Int> ys; for (const auto &a : add_queries) { ys.push_back(a.yl); ys.push_back(a.yr); } std::sort(ys.begin(), ys.end()); ys.erase(std::unique(ys.begin(), ys.end()), ys.end()); const int Y = ys.size(); std::vector<std::tuple<Int, int, int>> ops; for (int q = 0; q < int(sum_queries.size()); ++q) { ops.emplace_back(sum_queries[q].xl, 0, q); ops.emplace_back(sum_queries[q].xr, 1, q); } for (int q = 0; q < int(add_queries.size()); ++q) { ops.emplace_back(add_queries[q].xl, 2, q); ops.emplace_back(add_queries[q].xr, 3, q); } std::sort(ops.begin(), ops.end()); BIT<T> b00(Y), b01(Y), b10(Y), b11(Y); std::vector<T> ret(sum_queries.size()); for (auto o : ops) { int qtype = std::get<1>(o), q = std::get<2>(o); if (qtype >= 2) { const AddQuery &query = add_queries.at(q); int i = std::lower_bound(ys.begin(), ys.end(), query.yl) - ys.begin(); int j = std::lower_bound(ys.begin(), ys.end(), query.yr) - ys.begin(); T x = std::get<0>(o); T yi = query.yl, yj = query.yr; if (qtype & 1) std::swap(i, j), std::swap(yi, yj); b00.add(i, x * yi * query.val); b01.add(i, -x * query.val); b10.add(i, -yi * query.val); b11.add(i, query.val); b00.add(j, -x * yj * query.val); b01.add(j, x * query.val); b10.add(j, yj * query.val); b11.add(j, -query.val); } else { const SumQuery &query = sum_queries.at(q); int i = std::lower_bound(ys.begin(), ys.end(), query.yl) - ys.begin(); int j = std::lower_bound(ys.begin(), ys.end(), query.yr) - ys.begin(); T x = std::get<0>(o); T yi = query.yl, yj = query.yr; if (qtype & 1) std::swap(i, j), std::swap(yi, yj); ret[q] += b00.sum(i) + b01.sum(i) * yi + b10.sum(i) * x + b11.sum(i) * x * yi; ret[q] -= b00.sum(j) + b01.sum(j) * yj + b10.sum(j) * x + b11.sum(j) * x * yj; } } return ret; } }; #line 2 "modint.hpp" #include <cassert> #include <iostream> #include <set> #line 6 "modint.hpp" template <int md> struct ModInt { using lint = long long; constexpr static int mod() { return md; } static int get_primitive_root() { static int primitive_root = 0; if (!primitive_root) { primitive_root = [&]() { std::set<int> fac; int v = md - 1; for (lint 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; } int val_; int val() const noexcept { return val_; } constexpr ModInt() : val_(0) {} constexpr ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; } constexpr ModInt(lint v) { _setval(v % md + md); } constexpr explicit operator bool() const { return val_ != 0; } constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val_ + x.val_); } constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val_ - x.val_ + md); } constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val_ * x.val_ % md); } constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val_ * x.inv().val() % md); } constexpr ModInt operator-() const { return ModInt()._setval(md - val_); } constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; } constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; } constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; } constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; } friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt(a) + x; } friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt(a) - x; } friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt(a) * x; } friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt(a) / x; } constexpr bool operator==(const ModInt &x) const { return val_ == x.val_; } constexpr bool operator!=(const ModInt &x) const { return val_ != x.val_; } constexpr bool operator<(const ModInt &x) const { return val_ < x.val_; } // To use std::map<ModInt, T> friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; return is >> t, x = ModInt(t), is; } constexpr friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val_; } constexpr ModInt pow(lint n) const { ModInt ans = 1, tmp = *this; while (n) { if (n & 1) ans *= tmp; tmp *= tmp, n >>= 1; } return ans; } static constexpr int cache_limit = std::min(md, 1 << 21); static std::vector<ModInt> facs, facinvs, invs; constexpr static void _precalculation(int N) { const int l0 = facs.size(); if (N > md) N = md; if (N <= l0) return; facs.resize(N), facinvs.resize(N), invs.resize(N); for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i; facinvs[N - 1] = facs.back().pow(md - 2); for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1); for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1]; } constexpr ModInt inv() const { if (this->val_ < cache_limit) { if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0}; while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return invs[this->val_]; } else { return this->pow(md - 2); } } constexpr ModInt fac() const { while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return facs[this->val_]; } constexpr ModInt facinv() const { while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return facinvs[this->val_]; } constexpr ModInt doublefac() const { lint k = (this->val_ + 1) / 2; return (this->val_ & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac()) : ModInt(k).fac() * ModInt(2).pow(k); } constexpr ModInt nCr(int r) const { if (r < 0 or this->val_ < r) return ModInt(0); return this->fac() * (*this - r).facinv() * ModInt(r).facinv(); } constexpr ModInt nPr(int r) const { if (r < 0 or this->val_ < r) return ModInt(0); return this->fac() * (*this - r).facinv(); } static ModInt binom(int n, int r) { static long long bruteforce_times = 0; if (r < 0 or n < r) return ModInt(0); if (n <= bruteforce_times or n < (int)facs.size()) return ModInt(n).nCr(r); r = std::min(r, n - r); ModInt ret = ModInt(r).facinv(); for (int i = 0; i < r; ++i) ret *= n - i; bruteforce_times += r; return ret; } // Multinomial coefficient, (k_1 + k_2 + ... + k_m)! / (k_1! k_2! ... k_m!) // Complexity: O(sum(ks)) template <class Vec> static ModInt multinomial(const Vec &ks) { ModInt ret{1}; int sum = 0; for (int k : ks) { assert(k >= 0); ret *= ModInt(k).facinv(), sum += k; } return ret * ModInt(sum).fac(); } // Catalan number, C_n = binom(2n, n) / (n + 1) // C_0 = 1, C_1 = 1, C_2 = 2, C_3 = 5, C_4 = 14, ... // https://oeis.org/A000108 // Complexity: O(n) static ModInt catalan(int n) { if (n < 0) return ModInt(0); return ModInt(n * 2).fac() * ModInt(n + 1).facinv() * ModInt(n).facinv(); } ModInt sqrt() const { if (val_ == 0) return 0; if (md == 2) return val_; if (pow((md - 1) / 2) != 1) return 0; ModInt b = 1; while (b.pow((md - 1) / 2) == 1) b += 1; int e = 0, m = md - 1; while (m % 2 == 0) m >>= 1, e++; ModInt x = pow((m - 1) / 2), y = (*this) * x * x; x *= (*this); ModInt z = b.pow(m); while (y != 1) { int j = 0; ModInt t = y; while (t != 1) j++, t *= t; z = z.pow(1LL << (e - j - 1)); x *= z, z *= z, y *= z; e = j; } return ModInt(std::min(x.val_, md - x.val_)); } }; template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1}; template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1}; template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0}; using ModInt998244353 = ModInt<998244353>; // using mint = ModInt<998244353>; // using mint = ModInt<1000000007>; #line 5 "data_structure/test/rectangle_add_rectangle_sum.test.cpp" using namespace std; using mint = ModInt<998244353>; int main() { cin.tie(nullptr), ios::sync_with_stdio(false); RectangleAddRectangleSum<int, mint> rect_sum; const int bias = 500000000; int N, Q; cin >> N >> Q; while (N--) { int l, r, d, u; mint w; cin >> l >> d >> r >> u >> w; l -= bias; d -= bias; r -= bias; u -= bias; rect_sum.add_rectangle(l, r, d, u, w); } while (Q--) { int l, r, d, u; cin >> l >> d >> r >> u; l -= bias; d -= bias; r -= bias; u -= bias; rect_sum.add_query(l, r, d, u); } auto ret = rect_sum.solve(); for (auto x : ret) cout << x << '\n'; }