#define PROBLEM "https://judge.yosupo.jp/problem/rectangle_sum" #include "../../template/template.hpp" #include "../../data-structure-2d/rectangle-sum.hpp" using namespace Nyaan; void Nyaan::solve() { ini(N, Q); vl xs(N), ys(N), ws(N); in3(xs, ys, ws); auto f = [](ll u, ll v) { return u + v; }; RectangleSum<ll, ll, decltype(f)> rect(xs, ys, ws, f); rep(_, Q) { inl(l, d, r, u); out(rect.rect_sum(l, d, r, u)); } }
#line 1 "verify/verify-yosupo-ds/yosupo-rectangle-sum.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/rectangle_sum" #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 2 "data-structure-2d/rectangle-sum.hpp" #line 2 "segment-tree/persistent-segment-tree.hpp" template <typename T, typename F, int NODES = 20000000> struct PersistentSegmentTree { using ll = long long; struct Node { T data; Node *l, *r; Node() {} Node(const T &_data) : data(_data), l(nullptr), r(nullptr) {} }; Node *pool; int pid; ll N; const F f; const T ID; Node *nil; vector<Node *> roots; PersistentSegmentTree(const vector<T> &v, const F &f_, const T &ID_) : pid(0), f(f_), ID(ID_), nil(nullptr) { pool = new Node[NODES]; nil = my_new(ID); nil->l = nil->r = nil; roots.reserve(262144); roots.push_back(build(v)); } PersistentSegmentTree(const ll &N_, const F &f_, const T &ID_) : pid(0), N(N_), f(f_), ID(ID_), nil(nullptr) { pool = new Node[NODES]; nil = my_new(ID); nil->l = nil->r = nil; roots.reserve(262144); roots.push_back(nil); } Node *my_new(const T &data) { pool[pid].data = data; pool[pid].l = pool[pid].r = nil; return &(pool[pid++]); } Node *merge(Node *l, Node *r) { pool[pid].data = f(l->data, r->data); pool[pid].l = l; pool[pid].r = r; return &(pool[pid++]); } Node *build(const vector<T> &v) { N = (ll)v.size(); return build(0, (ll)v.size(), v); } Node *build(ll l, ll r, const vector<T> &v) { if (l + 1 == r) return my_new(v[l]); ll m = (l + r) >> 1; return merge(build(l, m, v), build(m, r, v)); } private: Node *update_(ll a, const T &x, Node *n, ll l, ll r) { if (l + 1 == r) return my_new(x); ll m = (l + r) >> 1; if (a < m) return merge(update_(a, x, n->l, l, m), n->r); return merge(n->l, update_(a, x, n->r, m, r)); } Node *add_(ll a, const T &x, Node *n, ll l, ll r) { if (l + 1 == r) return my_new(f(x, n->data)); ll m = (l + r) >> 1; if (a < m) return merge(add_(a, x, n->l, l, m), n->r); return merge(n->l, add_(a, x, n->r, m, r)); } T query_(ll a, ll b, Node *n, ll l, ll r) { if (n == nil) return ID; if (r <= a or b <= l) return ID; if (a <= l and r <= b) return n->data; ll m = (l + r) >> 1; return f(query_(a, b, n->l, l, m), query_(a, b, n->r, m, r)); } public: Node *update(Node *n, ll k, const T &x) { Node *root = update_(k, x, n, 0, N); roots.push_back(root); return root; } Node *update(int t, ll k, const T &x) { Node *root = update_(k, x, roots[t], 0, N); roots.push_back(root); return root; } Node *update(ll k, const T &x) { Node *root = update_(k, x, roots.back(), 0, N); roots.push_back(root); return root; } Node *add(Node *n, ll k, const T &x) { Node *root = add_(k, x, n, 0, N); roots.push_back(root); return root; } Node *add(int t, ll k, const T &x) { Node *root = add_(k, x, roots[t], 0, N); roots.push_back(root); return root; } Node *add(ll k, const T &x) { Node *root = add_(k, x, roots.back(), 0, N); roots.push_back(root); return root; } T query(Node *n, ll a, ll b) { return query_(a, b, n, 0, N); } T query(int t, ll a, ll b) { return query_(a, b, roots[t], 0, N); } T query(ll a, ll b) { return query_(a, b, roots.back(), 0, N); } Node *new_tree() { return nil; } }; /** * @brief 永続セグメント木 * @docs docs/segment-tree/persistent-segtree.md */ #line 6 "data-structure-2d/rectangle-sum.hpp" template <typename T, typename U, typename F> struct RectangleSum { PersistentSegmentTree<U, F> seg; vector<T> xs, ys; vector<U> ws; vector<int> ord; RectangleSum(const vector<T> &xs_, const vector<T> &ys_, const vector<U> &ws_, const F &f) : seg({(int)xs_.size() + 1, f, U(0)}) { int N = xs_.size(); xs.reserve(N); ys.reserve(N); ws.reserve(N); ord.resize(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), [&](int i, int j) { return xs_[i] < xs_[j]; }); for (auto &i : ord) { xs.push_back(xs_[i]); ys.push_back(ys_[i]); ws.push_back(ws_[i]); } iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), [&](int i, int j) { return ys[i] < ys[j]; }); vector<T> ys2; ys2.reserve(N); for (auto &i : ord) { seg.add(i, ws[i]); ys2.push_back(ys[i]); } ys.swap(ys2); } // [ [x1, 0], [x2, y] ) U rect_sum(T x1, T x2, T y) { int l = lower_bound(begin(xs), end(xs), x1) - begin(xs); int r = lower_bound(begin(xs), end(xs), x2) - begin(xs); int u = lower_bound(begin(ys), end(ys), y) - begin(ys); return seg.query(u, l, r); } // [ [x1, y1], [x2, y2] ) U rect_sum(T x1, T y1, T x2, T y2) { if (x1 >= x2 || y1 >= y2) return U(0); int l = lower_bound(begin(xs), end(xs), x1) - begin(xs); int r = lower_bound(begin(xs), end(xs), x2) - begin(xs); int d = lower_bound(begin(ys), end(ys), y1) - begin(ys); int u = lower_bound(begin(ys), end(ys), y2) - begin(ys); return seg.query(u, l, r) - seg.query(d, l, r); } }; /* * @brief 矩形和(永続セグメント木) */ #line 5 "verify/verify-yosupo-ds/yosupo-rectangle-sum.test.cpp" using namespace Nyaan; void Nyaan::solve() { ini(N, Q); vl xs(N), ys(N), ws(N); in3(xs, ys, ws); auto f = [](ll u, ll v) { return u + v; }; RectangleSum<ll, ll, decltype(f)> rect(xs, ys, ws, f); rep(_, Q) { inl(l, d, r, u); out(rect.rect_sum(l, d, r, u)); } }