// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/point_add_rectangle_sum
#include "../../../src/ds/kdtree/lib.hpp"
using namespace tifa_libs;
i64 op(i64 x, i64 y) { return x + y; }
int main() {
std::cin.tie(nullptr)->std::ios::sync_with_stdio(false);
u32 n, q;
std::cin >> n >> q;
kdtree<i64, op> kdt(3000);
using point_t = decltype(kdt)::point;
point_t p1, p2;
i64 w;
flt_ (u32, i, 0, n) {
std::cin >> p1[0] >> p1[1] >> w;
kdt.insert(p1, w);
}
flt_ (u32, i, 0, q, opt) {
std::cin >> opt >> p1[0] >> p1[1];
if (!opt) {
std::cin >> w;
kdt.insert(p1, w);
} else {
std::cin >> p2[0] >> p2[1];
--p2[0], --p2[1];
std::cout << kdt.query(p1, p2) << '\n';
}
}
return 0;
}
#line 1 "test/cpv/library-checker-datastructure/point_add_rectangle_sum.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/point_add_rectangle_sum
#line 2 "src/ds/kdtree/lib.hpp"
#line 2 "src/util/alias/others/lib.hpp"
#line 2 "src/util/consts/lib.hpp"
#line 2 "src/util/alias/num/lib.hpp"
#line 2 "src/util/util/lib.hpp"
// https://github.com/Tiphereth-A/CP-lib
#include <bits/extc++.h>
// clang-format off
namespace tifa_libs {
#define CEXP constexpr
#define CEXPE constexpr explicit
#define CR const&
#define CP const*
#define PC *const
#define CPC const*const
#define TPN typename
#define NE noexcept
#define CNE const noexcept
#define ND [[nodiscard]]
#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t) * 2, __VA_ARGS__, __VA_ARGS__ CR>
// NOLINTNEXTLINE(misc-const-correctness)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)
#define retif_(cond, if_true, ...) if cond return if_true __VA_OPT__(; else return __VA_ARGS__)
#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif
using namespace std::ranges;
using namespace std::literals;
template <class T>
CEXP T abs(T x) NE { retif_((x < 0), -x, x); }
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/num/lib.hpp"
// clang-format off
namespace tifa_libs {
#define mk0_(w, t) using w = t; using c##w = const t
#define mk_(w, t) mk0_(w, t); CEXP w operator""_##w(unsigned long long x) NE { return (w)x; }
mk_(i8, int8_t) mk_(u8, uint8_t) mk_(i16, int16_t) mk_(u16, uint16_t) mk_(i32, int32_t) mk_(u32, uint32_t) mk_(i64, int64_t) mk_(u64, uint64_t) mk_(isz, ssize_t) mk_(usz, size_t) mk_(chr, char) mk_(schr, signed char) mk_(uchr, unsigned char) mk_(sint, signed) mk_(uint, unsigned);
mk0_(i128, __int128_t); mk0_(u128, __uint128_t); mk0_(f32, float); mk0_(f64, double); mk0_(f128, long double);
#undef mk0_
#undef mk_
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/consts/lib.hpp"
// clang-format off
namespace tifa_libs {
using std::numbers::pi_v;
template <std::floating_point FP>
inline FP eps_v = std::sqrt(std::numeric_limits<FP>::epsilon());
template <std::floating_point FP>
CEXP void set_eps(FP v) NE { eps_v<FP> = v; }
CEXP u32 TIME = ((__TIME__[0] & 15) << 20) | ((__TIME__[1] & 15) << 16) | ((__TIME__[3] & 15) << 12) | ((__TIME__[4] & 15) << 8) | ((__TIME__[6] & 15) << 4) | (__TIME__[7] & 15);
CEXP auto STR2U16 = [] { std::array<u32, 65536> table{}; table.fill(-1_u32); flt_ (u32, i, 48, 58) flt_ (u32, j, 48, 58) table[i << 8 | j] = (j & 15) * 10 + (i & 15); return table; }();
inline const auto fn_0 = [](auto&&...) NE {};
inline const auto fn_is0 = [](auto x) NE { return x == 0; };
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/others/lib.hpp"
namespace tifa_libs {
template <class T>
struct chash {
CEXP static u64 C = u64(pi_v<f128> * 2e18) | 71;
CEXP u64 operator()(T x) CNE { return __builtin_bswap64(((u64)x ^ TIME) * C); }
};
// clang-format off
#define mk_(w, t) using w = t; using c##w = const t;
mk_(strn, std::string) mk_(strnv, std::string_view)
#undef mk_
template <class T> struct edge_t { T w; u32 u, v; CEXP auto operator<=>(edge_t CR) const = default; }; template <class T> using cedge_t = const edge_t<T>;
template <class T> struct pt3 { T _0, _1, _2; CEXP auto operator<=>(pt3 CR) const = default; }; template <class T> using cpt3 = const pt3<T>;
template <class T> struct pt4 { T _0, _1, _2, _3; CEXP auto operator<=>(pt4 CR) const = default; }; template <class T> using cpt4 = const pt4<T>;
#define mkT_(w, t, ...) template <class T> using w = t __VA_OPT__(, ) __VA_ARGS__; template <class T> using c##w = const t __VA_OPT__(, ) __VA_ARGS__;
mkT_(ptt, std::pair<T, T>) mkT_(alc, std::pmr::polymorphic_allocator<T>) mkT_(vec, std::vector<T>) mkT_(vvec, vec<vec<T>>) mkT_(v3ec, vvec<vec<T>>) mkT_(vecpt, vec<ptt<T>>) mkT_(vvecpt, vvec<ptt<T>>) mkT_(ptvec, ptt<vec<T>>) mkT_(ptvvec, ptt<vvec<T>>)
#undef mkT_
template <class T> using itl = std ::initializer_list<T>;
template <class T, usz ext = std::dynamic_extent> using spn = std::span<T const, ext>;
template <class T, usz N> using arr = std::array<T, N>; template <class T, usz N> using carr = std::array<const T, N>;
template <class U, class T> using vecp = vec<std::pair<U, T>>; template <class U, class T> using vvecp = vvec<std::pair<U, T>>;
template <class U, class T> using vvecp = vvec<std::pair<U, T>>; template <class U, class T> using vvvecp = vvec<vvec<std::pair<U, T>>>;
#ifdef PB_DS_ASSOC_CNTNR_HPP
template <class T, class C = std::less<T>> using set = __gnu_pbds::tree<T, __gnu_pbds::null_type, C>;
template <class K, class V, class C = std::less<K>> using map = __gnu_pbds::tree<K, V, C>;
// hset<u64> s({}, {}, {}, {}, {1<<16});
template <class T, class HF = chash<T>> using hset = __gnu_pbds::gp_hash_table<T, __gnu_pbds::null_type, HF>;
// hmap<u64, int> s({}, {}, {}, {}, {1<<16});
template <class K, class V, class HF = chash<K>> using hmap = __gnu_pbds::gp_hash_table<K, V, HF>;
#else
using std::set, std::map;
template <class T, class HF = chash<T>> using hset = std::unordered_set<T, HF>;
template <class K, class V, class HF = chash<K>> using hmap = std::unordered_map<K, V, HF>;
#endif
#ifdef PB_DS_PRIORITY_QUEUE_HPP
template <class T, class C = std::less<T>> using pq = __gnu_pbds::priority_queue<T, C>;
#else
template <class T, class C = std::less<T>> using pq = std::priority_queue<T, vec<T>, C>;
#endif
template <class T> using pqg = pq<T, std::greater<T>>;
// clang-format on
#define mk1_(V, A, T) using V##A = V<T>;
#define mk_(V, A, T) mk1_(V, A, T) mk1_(c##V, A, T)
#define mk(A, T) mk_(edge_t, A, T) mk_(ptt, A, T) mk_(pt3, A, T) mk_(pt4, A, T) mk_(vec, A, T) mk_(vvec, A, T) mk_(v3ec, A, T) mk_(vecpt, A, T) mk_(vvecpt, A, T) mk_(ptvec, A, T) mk_(ptvvec, A, T) mk1_(spn, A, T) mk1_(itl, A, T)
mk(b, bool) mk(c, chr) mk(i, i32) mk(u, u32) mk(ii, i64) mk(uu, u64) mk(t, isz) mk(z, usz) mk(f, f32) mk(d, f64) mk(s, strn);
#undef mk
#undef mk_
#undef mk1_
} // namespace tifa_libs
#line 2 "src/util/traits/math/lib.hpp"
// clang-format off
#line 4 "src/util/traits/math/lib.hpp"
namespace tifa_libs {
template <class T> concept char_c = std::same_as<T, char> || std::same_as<T, signed char> || std::same_as<T, unsigned char>;
#pragma GCC diagnostic ignored "-Wpedantic"
template <class T> concept s128_c = std::same_as<T, __int128_t> || std::same_as<T, __int128>;
template <class T> concept u128_c = std::same_as<T, __uint128_t> || std::same_as<T, unsigned __int128>;
template <class T> concept i128_c = s128_c<T> || u128_c<T>;
#pragma GCC diagnostic warning "-Wpedantic"
template <class T> concept imost64_c = std::integral<T> && sizeof(T) * __CHAR_BIT__ <= 64;
template <class T> concept smost64_c = imost64_c<T> && std::signed_integral<T>;
template <class T> concept umost64_c = imost64_c<T> && std::unsigned_integral<T>;
template <class T> concept int_c = i128_c<T> || imost64_c<T>;
template <class T> concept sint_c = s128_c<T> || smost64_c<T>;
template <class T> concept uint_c = u128_c<T> || umost64_c<T>;
template <class T> concept arithm_c = std::is_arithmetic_v<T> || int_c<T>;
template <class T> concept mint_c = requires(T x) { {x.mod()} -> uint_c; {x.val()} -> uint_c; };
template <class T> concept dft_c = requires(T x, std::vector<TPN T::data_t> v, u32 n) { {x.size()} -> std::same_as<u32>; x.bzr(n); x.dif(v, n); x.dit(v, n); };
template <class T> concept ntt_c = dft_c<T> && requires(T x) { T::max_size; T::G; };
template <class T> struct to_sint : std::make_signed<T> {};
template <> struct to_sint<u128> { using type = i128; };
template <> struct to_sint<i128> { using type = i128; };
template <class T> using to_sint_t = TPN to_sint<T>::type;
template <class T> struct to_uint : std::make_unsigned<T> {};
template <> struct to_uint<u128> { using type = u128; };
template <> struct to_uint<i128> { using type = u128; };
template <class T> using to_uint_t = TPN to_uint<T>::type;
template <arithm_c T> struct to_bigger : std::make_unsigned<T> {};
#define _(w,ww) template <> struct to_bigger<w> { using type = ww; }
#define _2(w,ww) _(i##w,i##ww); _(u##w,u##ww);
_2(8, 16); _2(16, 32); _2(32, 64); _2(64, 128); _(f32, f64); _(f64, f128);
#undef _2
#undef _
template <class T> using to_bigger_t = TPN to_bigger<T>::type;
template <arithm_c T> CEXP T inf_v = [] {
if CEXP(sint_c<T>) return T(to_uint_t<T>(-1) / 4 - 1);
else if CEXP(uint_c<T>) return T(-1) / 2 - 1;
else return std::numeric_limits<T>::max() / 2 - 1;
}();
} // namespace tifa_libs
// clang-format on
#line 2 "src/ds/bt_trv/lib.hpp"
#line 2 "src/util/traits/ds/lib.hpp"
// clang-format off
#line 4 "src/util/traits/ds/lib.hpp"
namespace tifa_libs {
// tree pointer (for DS)
template <class P> concept tp_ds_c = requires(P p) { p->ch; std::is_array_v<decltype(p->ch)>; std::rank_v<decltype(p->ch)> == 1; };
// binary tree pointer (for DS)
template <class P> concept tp2_ds_c = tp_ds_c<P> && std::extent_v<decltype(std::declval<P>()->ch)> == 2;
template <class T> concept dsu_c = requires(T dsu, u32 x, u32 y) { {dsu.find(x)} -> std::same_as<i32>; {dsu.size()} -> std::same_as<u32>; {dsu.size(x)} -> std::same_as<u32>; {dsu.same(x, y)} -> std::same_as<bool>; {dsu.merge(x, y)} -> std::same_as<bool>; };
} // namespace tifa_libs
// clang-format on
#line 4 "src/ds/bt_trv/lib.hpp"
namespace tifa_libs {
template <tp2_ds_c pointer, class F>
requires requires(pointer p, F&& f) { f(p); }
CEXP void pre_order(pointer p, F&& f) NE {
if (p) f(p), pre_order(p->ch[0], std::forward<F>(f)), pre_order(p->ch[1], std::forward<F>(f));
}
template <tp2_ds_c pointer, class F>
requires requires(pointer p, F f) { f(p); }
CEXP void in_order(pointer p, F&& f) NE {
if (p) in_order(p->ch[0], std::forward<F>(f)), f(p), in_order(p->ch[1], std::forward<F>(f));
}
template <tp2_ds_c pointer, class F>
requires requires(pointer p, F f) { f(p); }
CEXP void post_order(pointer p, F&& f) NE {
if (p) post_order(p->ch[0], std::forward<F>(f)), post_order(p->ch[1], std::forward<F>(f)), f(p);
}
template <tp_ds_c pointer, class F>
requires requires(pointer p, u32 level, F f) { f(p, level); }
CEXP void level_order(pointer p, F&& f) NE {
if (!p) return;
u32 level = 0;
std::queue<pointer> q({p});
while (!q.empty()) {
flt_ (u32, i, 0, (u32)q.size()) {
auto now = q.front();
q.pop(), f(now, level);
for (auto&& s : now->ch) q.push(s);
}
++level;
}
}
template <tp_ds_c pointer, class Alloc>
CEXP void dealloc_subtree(pointer p, Alloc& alloc) NE {
if (!p) return;
for (auto&& s : p->ch) dealloc_subtree(s, alloc);
alloc.deallocate(p, 1);
}
template <tp_ds_c pointer>
CEXP pointer most(pointer p, bool dir) NE {
if (!p) return nullptr;
while (p->ch[dir]) p = p->ch[dir];
return p;
}
template <tp2_ds_c pointer>
CEXP auto leftmost(pointer p) NE { return most(p, 0); }
template <tp2_ds_c pointer>
CEXP auto rightmost(pointer p) NE { return most(p, 1); }
} // namespace tifa_libs
#line 6 "src/ds/kdtree/lib.hpp"
namespace tifa_libs {
template <class T, auto op, arithm_c Coord = i32, u32 K = 2, bool remove_empty_node = false>
class kdtree {
static_assert(K);
struct TIFA;
public:
using point = arr<Coord, K>;
private:
using pointer = TIFA*;
using const_pointer = const TIFA*;
struct TIFA {
// NOLINTNEXTLINE(modernize-avoid-c-arrays)
pointer ch[2];
T sum, val;
point min, max, coord;
template <u32 k>
requires /**/ (k < K)
static CEXP bool cmp(const_pointer l, const_pointer r) { return l->coord[k] < r->coord[k]; }
};
const T E;
cu32 B;
u32 cnt{0};
CEXP pointer newnode(cT_(point) p, cT_(T) val) {
pointer x = alloc.allocate(1);
x->ch[0] = x->ch[1] = nullptr, x->sum = x->val = val;
flt_ (u32, i, 0, K) x->min[i] = x->max[i] = x->coord[i] = p[i];
return x;
}
CEXP void pushup(pointer x) NE {
auto [l, r] = x->ch;
x->sum = x->val;
if (l) {
x->sum = op(x->sum, l->sum);
flt_ (u32, i, 0, K) x->max[i] = max(l->max[i], x->max[i]);
flt_ (u32, i, 0, K) x->min[i] = min(l->min[i], x->min[i]);
}
if (r) {
x->sum = op(x->sum, r->sum);
flt_ (u32, i, 0, K) x->max[i] = max(r->max[i], x->max[i]);
flt_ (u32, i, 0, K) x->min[i] = min(r->min[i], x->min[i]);
}
}
template <u32 k>
requires /**/ (k < K)
CEXP void build(pointer& x, vec<pointer>& h, u32 l, u32 r) NE {
if (l >= r) return;
u32 mid = l + (r - l) / 2;
nth_element(begin(h) + l, begin(h) + mid, begin(h) + r, TIFA::template cmp<k>);
x = h[mid], x->sum = x->val;
flt_ (u32, i, 0, K) x->min[i] = x->max[i] = x->coord[i];
build<(k + 1) % K>(x->ch[0], h, l, mid), build<(k + 1) % K>(x->ch[1], h, mid + 1, r);
pushup(x);
}
CEXP void rebuild(pointer& x) NE {
vec<pointer> h;
auto flatten = [&](auto&& f, pointer& x) -> void {
if (!x) return;
if CEXP (remove_empty_node) {
auto _ = x->val == E;
if (!_) h.push_back(x);
f(f, x->ch[0]), f(f, x->ch[1]);
if (_) alloc.deallocate(x, 1);
} else h.push_back(x), f(f, x->ch[0]), f(f, x->ch[1]);
x = nullptr;
};
flatten(flatten, x), build<0>(x, h, 0, (u32)h.size());
}
template <bool use_set, u32 k>
requires /**/ (k < K)
CEXP bool ins_set_(pointer& x, cT_(point) p, cT_(T) val) NE {
if (!x) {
x = newnode(p, val);
return true;
}
bool f;
if (p == x->coord) {
f = false;
if CEXP (!use_set) x->val = op(x->val, val), x->sum = op(x->sum, val);
else {
x->val = val, x->sum = val;
if (x->ch[0]) x->sum = op(x->sum, x->ch[0]->sum);
if (x->ch[1]) x->sum = op(x->sum, x->ch[1]->sum);
}
} else f = ins_set_<use_set, (k + 1) % K>(x->ch[p[k] >= x->coord[k]], p, val);
pushup(x);
return f;
}
CEXP bool check_range(const_pointer x, cT_(point) L, cT_(point) R) CNE {
flt_ (u32, i, 0, K)
if (x->min[i] < L[i] || R[i] < x->max[i]) return false;
return true;
}
CEXP bool check_point(const_pointer x, cT_(point) L, cT_(point) R) CNE {
flt_ (u32, i, 0, K)
if (x->coord[i] < L[i] || R[i] < x->coord[i]) return false;
return true;
}
CEXP bool check(const_pointer x, cT_(point) L, cT_(point) R) CNE {
if (!x) return false;
flt_ (u32, i, 0, K)
if (R[i] < x->min[i] || x->max[i] < L[i]) return false;
return true;
}
CEXP void query_(const_pointer x, cT_(point) L, cT_(point) R, T& ans) CNE {
if (!x) return;
if (check_range(x, L, R)) {
ans = op(ans, x->sum);
return;
}
if (check_point(x, L, R)) ans = op(ans, x->val);
if (check(x->ch[0], L, R)) query_(x->ch[0], L, R, ans);
if (check(x->ch[1], L, R)) query_(x->ch[1], L, R, ans);
}
public:
pointer root{nullptr};
// threshold = $O\left(\sqrt{n\log n}\right)$
CEXPE kdtree(u32 rebuild_threshold, cT_(T) e = T{}) NE : E{e}, B{rebuild_threshold} { assert(rebuild_threshold > 1); }
kdtree(kdtree CR) = delete;
kdtree& operator=(kdtree CR) = delete;
CEXP ~kdtree() NE { dealloc_subtree(root, alloc); }
CEXP void insert(cT_(point) coord, cT_(T) val) NE {
if ((cnt += ins_set_<false, 0>(root, coord, val)) == B) cnt = 0, rebuild(root);
}
CEXP void set(cT_(point) coord, cT_(T) val) NE {
if ((cnt += ins_set_<true, 0>(root, coord, val)) == B) cnt = 0, rebuild(root);
}
//! [L, R]
CEXP T query(cT_(point) L, cT_(point) R) CNE {
T ans{E};
query_(root, L, R, ans);
return ans;
}
private:
alc<TIFA> alloc;
};
} // namespace tifa_libs
#line 3 "test/cpv/library-checker-datastructure/point_add_rectangle_sum.cpp"
using namespace tifa_libs;
i64 op(i64 x, i64 y) { return x + y; }
int main() {
std::cin.tie(nullptr)->std::ios::sync_with_stdio(false);
u32 n, q;
std::cin >> n >> q;
kdtree<i64, op> kdt(3000);
using point_t = decltype(kdt)::point;
point_t p1, p2;
i64 w;
flt_ (u32, i, 0, n) {
std::cin >> p1[0] >> p1[1] >> w;
kdt.insert(p1, w);
}
flt_ (u32, i, 0, q, opt) {
std::cin >> opt >> p1[0] >> p1[1];
if (!opt) {
std::cin >> w;
kdt.insert(p1, w);
} else {
std::cin >> p2[0] >> p2[1];
--p2[0], --p2[1];
std::cout << kdt.query(p1, p2) << '\n';
}
}
return 0;
}
test/cpv/library-checker-datastructure/point_add_rectangle_sum.cpp