This documentation is automatically generated by online-judge-tools/verification-helper
#include "ds/offline_query/rectangle_add_point_sum.hpp"
#include "ds/fenwicktree/fenwicktree.hpp"
template <typename AbelGroup, typename XY, bool SMALL_X = false>
struct Rectangle_Add_Point_Sum {
using G = typename AbelGroup::value_type;
vector<tuple<XY, XY, XY, G>> rect;
vector<tuple<int, XY, XY>> point;
Rectangle_Add_Point_Sum() {}
void add_query(XY x1, XY x2, XY y1, XY y2, G g) {
rect.eb(y1, x1, x2, g), rect.eb(y2, x2, x1, g);
}
void sum_query(XY x, XY y) { point.eb(len(point), x, y); }
vector<G> calc() {
int N = rect.size(), Q = point.size();
if (N == 0 || Q == 0) return vector<G>(Q, AbelGroup::unit());
// X 方向の座圧
int NX = 0;
if (!SMALL_X) {
sort(all(point),
[&](auto &x, auto &y) -> bool { return get<1>(x) < get<1>(y); });
vc<XY> keyX;
keyX.reserve(Q);
for (auto &&[i, a, b]: point) {
if (len(keyX) == 0 || keyX.back() != a) { keyX.eb(a); }
a = len(keyX) - 1;
}
for (auto &&[y, x1, x2, g]: rect) x1 = LB(keyX, x1), x2 = LB(keyX, x2);
NX = len(keyX);
}
if (SMALL_X) {
XY mx = infty<XY>;
for (auto &&[i, x, y]: point) chmin(mx, x);
for (auto &&[i, x, y]: point) x -= mx, chmax(NX, x + 1);
for (auto &&[y, x1, x2, g]: rect) {
x1 -= mx, x2 -= mx;
x1 = max(0, min<int>(x1, NX)), x2 = max(0, min<int>(x2, NX));
}
}
sort(all(point),
[&](auto &x, auto &y) -> bool { return get<2>(x) < get<2>(y); });
sort(all(rect),
[&](auto &x, auto &y) -> bool { return get<0>(x) < get<0>(y); });
FenwickTree<AbelGroup> bit(NX);
vc<G> res(Q, AbelGroup::unit());
int j = 0;
FOR(i, Q) {
auto [q, x, y] = point[i];
while (j < N && get<0>(rect[j]) <= y) {
auto [yy, x1, x2, g] = rect[j++];
bit.add(x1, g), bit.add(x2, AbelGroup::inverse(g));
}
res[q] = bit.sum(x + 1);
}
return res;
}
};
#line 2 "alg/monoid/add.hpp"
template <typename E>
struct Monoid_Add {
using X = E;
using value_type = X;
static constexpr X op(const X &x, const X &y) noexcept { return x + y; }
static constexpr X inverse(const X &x) noexcept { return -x; }
static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; }
static constexpr X unit() { return X(0); }
static constexpr bool commute = true;
};
#line 3 "ds/fenwicktree/fenwicktree.hpp"
template <typename Monoid>
struct FenwickTree {
using G = Monoid;
using MX = Monoid;
using E = typename G::value_type;
int n;
vector<E> dat;
E total;
FenwickTree() {}
FenwickTree(int n) { build(n); }
template <typename F>
FenwickTree(int n, F f) {
build(n, f);
}
FenwickTree(const vc<E>& v) { build(v); }
void build(int m) {
n = m;
dat.assign(m, G::unit());
total = G::unit();
}
void build(const vc<E>& v) {
build(len(v), [&](int i) -> E { return v[i]; });
}
template <typename F>
void build(int m, F f) {
n = m;
dat.clear();
dat.reserve(n);
total = G::unit();
FOR(i, n) { dat.eb(f(i)); }
for (int i = 1; i <= n; ++i) {
int j = i + (i & -i);
if (j <= n) dat[j - 1] = G::op(dat[i - 1], dat[j - 1]);
}
total = prefix_sum(m);
}
E prod_all() { return total; }
E sum_all() { return total; }
E sum(int k) { return prefix_sum(k); }
E prod(int k) { return prefix_prod(k); }
E prefix_sum(int k) { return prefix_prod(k); }
E prefix_prod(int k) {
chmin(k, n);
E ret = G::unit();
for (; k > 0; k -= k & -k) ret = G::op(ret, dat[k - 1]);
return ret;
}
E sum(int L, int R) { return prod(L, R); }
E prod(int L, int R) {
chmax(L, 0), chmin(R, n);
if (L == 0) return prefix_prod(R);
assert(0 <= L && L <= R && R <= n);
E pos = G::unit(), neg = G::unit();
while (L < R) { pos = G::op(pos, dat[R - 1]), R -= R & -R; }
while (R < L) { neg = G::op(neg, dat[L - 1]), L -= L & -L; }
return G::op(pos, G::inverse(neg));
}
vc<E> get_all() {
vc<E> res(n);
FOR(i, n) res[i] = prod(i, i + 1);
return res;
}
void add(int k, E x) { multiply(k, x); }
void multiply(int k, E x) {
static_assert(G::commute);
total = G::op(total, x);
for (++k; k <= n; k += k & -k) dat[k - 1] = G::op(dat[k - 1], x);
}
void set(int k, E x) { add(k, G::op(G::inverse(prod(k, k + 1)), x)); }
template <class F>
int max_right(const F check, int L = 0) {
assert(check(G::unit()));
E s = G::unit();
int i = L;
// 2^k 進むとダメ
int k = [&]() {
while (1) {
if (i % 2 == 1) { s = G::op(s, G::inverse(dat[i - 1])), i -= 1; }
if (i == 0) { return topbit(n) + 1; }
int k = lowbit(i) - 1;
if (i + (1 << k) > n) return k;
E t = G::op(s, dat[i + (1 << k) - 1]);
if (!check(t)) { return k; }
s = G::op(s, G::inverse(dat[i - 1])), i -= i & -i;
}
}();
while (k) {
--k;
if (i + (1 << k) - 1 < len(dat)) {
E t = G::op(s, dat[i + (1 << k) - 1]);
if (check(t)) { i += (1 << k), s = t; }
}
}
return i;
}
// check(i, x)
template <class F>
int max_right_with_index(const F check, int L = 0) {
assert(check(L, G::unit()));
E s = G::unit();
int i = L;
// 2^k 進むとダメ
int k = [&]() {
while (1) {
if (i % 2 == 1) { s = G::op(s, G::inverse(dat[i - 1])), i -= 1; }
if (i == 0) { return topbit(n) + 1; }
int k = lowbit(i) - 1;
if (i + (1 << k) > n) return k;
E t = G::op(s, dat[i + (1 << k) - 1]);
if (!check(i + (1 << k), t)) { return k; }
s = G::op(s, G::inverse(dat[i - 1])), i -= i & -i;
}
}();
while (k) {
--k;
if (i + (1 << k) - 1 < len(dat)) {
E t = G::op(s, dat[i + (1 << k) - 1]);
if (check(i + (1 << k), t)) { i += (1 << k), s = t; }
}
}
return i;
}
template <class F>
int min_left(const F check, int R) {
assert(check(G::unit()));
E s = G::unit();
int i = R;
// false になるところまで戻る
int k = 0;
while (i > 0 && check(s)) {
s = G::op(s, dat[i - 1]);
k = lowbit(i);
i -= i & -i;
}
if (check(s)) {
assert(i == 0);
return 0;
}
// 2^k 進むと ok になる
// false を維持して進む
while (k) {
--k;
E t = G::op(s, G::inverse(dat[i + (1 << k) - 1]));
if (!check(t)) { i += (1 << k), s = t; }
}
return i + 1;
}
int kth(E k, int L = 0) {
return max_right([&k](E x) -> bool { return x <= k; }, L);
}
};
#line 2 "ds/offline_query/rectangle_add_point_sum.hpp"
template <typename AbelGroup, typename XY, bool SMALL_X = false>
struct Rectangle_Add_Point_Sum {
using G = typename AbelGroup::value_type;
vector<tuple<XY, XY, XY, G>> rect;
vector<tuple<int, XY, XY>> point;
Rectangle_Add_Point_Sum() {}
void add_query(XY x1, XY x2, XY y1, XY y2, G g) {
rect.eb(y1, x1, x2, g), rect.eb(y2, x2, x1, g);
}
void sum_query(XY x, XY y) { point.eb(len(point), x, y); }
vector<G> calc() {
int N = rect.size(), Q = point.size();
if (N == 0 || Q == 0) return vector<G>(Q, AbelGroup::unit());
// X 方向の座圧
int NX = 0;
if (!SMALL_X) {
sort(all(point),
[&](auto &x, auto &y) -> bool { return get<1>(x) < get<1>(y); });
vc<XY> keyX;
keyX.reserve(Q);
for (auto &&[i, a, b]: point) {
if (len(keyX) == 0 || keyX.back() != a) { keyX.eb(a); }
a = len(keyX) - 1;
}
for (auto &&[y, x1, x2, g]: rect) x1 = LB(keyX, x1), x2 = LB(keyX, x2);
NX = len(keyX);
}
if (SMALL_X) {
XY mx = infty<XY>;
for (auto &&[i, x, y]: point) chmin(mx, x);
for (auto &&[i, x, y]: point) x -= mx, chmax(NX, x + 1);
for (auto &&[y, x1, x2, g]: rect) {
x1 -= mx, x2 -= mx;
x1 = max(0, min<int>(x1, NX)), x2 = max(0, min<int>(x2, NX));
}
}
sort(all(point),
[&](auto &x, auto &y) -> bool { return get<2>(x) < get<2>(y); });
sort(all(rect),
[&](auto &x, auto &y) -> bool { return get<0>(x) < get<0>(y); });
FenwickTree<AbelGroup> bit(NX);
vc<G> res(Q, AbelGroup::unit());
int j = 0;
FOR(i, Q) {
auto [q, x, y] = point[i];
while (j < N && get<0>(rect[j]) <= y) {
auto [yy, x1, x2, g] = rect[j++];
bit.add(x1, g), bit.add(x2, AbelGroup::inverse(g));
}
res[q] = bit.sum(x + 1);
}
return res;
}
};