#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3035"
#include <algorithm>
#include <climits>
#include <iostream>
#include <map>
#include "Mylib/AlgebraicStructure/Monoid/max.cpp"
#include "Mylib/AlgebraicStructure/Monoid/min.cpp"
#include "Mylib/AlgebraicStructure/Monoid/sum.cpp"
#include "Mylib/AlgebraicStructure/Monoid/with_count.cpp"
#include "Mylib/AlgebraicStructure/MonoidAction/add_max_with_count.cpp"
#include "Mylib/AlgebraicStructure/MonoidAction/add_min_with_count.cpp"
#include "Mylib/DataStructure/SegmentTree/lazy_segment_tree.cpp"
#include "Mylib/IO/input_tuples.cpp"
#include "Mylib/IO/input_vector.cpp"
namespace hl = haar_lib;
using sum = hl::sum_monoid<int64_t>;
using max_with_count = hl::with_count<hl::max_monoid<int64_t>>;
using min_with_count = hl::with_count<hl::min_monoid<int64_t>>;
using add_max_with_count = hl::add_max_with_count<sum, max_with_count>;
using add_min_with_count = hl::add_min_with_count<sum, min_with_count>;
int main() {
std::cin.tie(0);
std::ios::sync_with_stdio(false);
int H, W, Q;
std::cin >> H >> W >> Q;
auto A = hl::input_vector<int64_t>(H);
auto B = hl::input_vector<int64_t>(W);
auto seg_h_max = hl::lazy_segment_tree<add_max_with_count>(H);
auto seg_h_min = hl::lazy_segment_tree<add_min_with_count>(H);
auto seg_w_max = hl::lazy_segment_tree<add_max_with_count>(W);
auto seg_w_min = hl::lazy_segment_tree<add_min_with_count>(W);
seg_h_max.init_with_vector(A);
seg_h_min.init_with_vector(A);
seg_w_max.init_with_vector(B);
seg_w_min.init_with_vector(B);
for (auto [type] : hl::input_tuples<int>(Q)) {
switch (type) {
case 1: {
int a, b, v;
std::cin >> a >> b >> v;
--a;
seg_h_max.update(a, b, v);
seg_h_min.update(a, b, v);
break;
}
case 2: {
int c, d, v;
std::cin >> c >> d >> v;
--c;
seg_w_max.update(c, d, v);
seg_w_min.update(c, d, v);
break;
}
case 3: {
int64_t a, b, c, d;
std::cin >> a >> b >> c >> d;
--a, --c;
std::map<int64_t, int64_t> m;
auto x = std::vector{seg_h_max.fold(a, b), seg_h_min.fold(a, b)};
auto y = std::vector{seg_w_max.fold(c, d), seg_w_min.fold(c, d)};
if (x[0].value == x[1].value) x.pop_back();
if (y[0].value == y[1].value) y.pop_back();
int64_t M = LLONG_MAX;
for (auto p : x) {
for (auto q : y) {
M = std::min(M, *p.value * *q.value);
}
}
if (M == 0) {
int64_t p = 0;
for (auto e : x)
if (e.value == 0) p += e.count;
int64_t q = 0;
for (auto e : y)
if (e.value == 0) q += e.count;
m[0] = (b - a) * q + (d - c) * p - p * q;
} else {
for (auto p : x) {
for (auto q : y) {
m[*p.value * *q.value] += p.count * q.count;
}
}
}
std::cout << m.begin()->first << " " << m.begin()->second << "\n";
break;
}
case 4: {
int64_t a, b, c, d;
std::cin >> a >> b >> c >> d;
--a, --c;
std::map<int64_t, int64_t> m;
auto x = std::vector{seg_h_max.fold(a, b), seg_h_min.fold(a, b)};
auto y = std::vector{seg_w_max.fold(c, d), seg_w_min.fold(c, d)};
if (x[0].value == x[1].value) x.pop_back();
if (y[0].value == y[1].value) y.pop_back();
int64_t M = LLONG_MIN;
for (auto p : x) {
for (auto q : y) {
M = std::max(M, *p.value * *q.value);
}
}
if (M == 0) {
int64_t p = 0;
for (auto e : x)
if (e.value == 0) p += e.count;
int64_t q = 0;
for (auto e : y)
if (e.value == 0) q += e.count;
m[0] = (b - a) * q + (d - c) * p - p * q;
} else {
for (auto p : x) {
for (auto q : y) {
m[*p.value * *q.value] += p.count * q.count;
}
}
}
std::cout << m.rbegin()->first << " " << m.rbegin()->second << "\n";
break;
}
}
}
return 0;
}
#line 1 "test/aoj/3035/main.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3035"
#include <algorithm>
#include <climits>
#include <iostream>
#include <map>
#line 3 "Mylib/AlgebraicStructure/Monoid/max.cpp"
#include <optional>
namespace haar_lib {
template <typename T>
struct max_monoid {
using value_type = std::optional<T>;
value_type operator()() const { return {}; }
value_type operator()(const value_type &a, const value_type &b) const {
if (not a) return b;
if (not b) return a;
return {std::max(*a, *b)};
}
};
} // namespace haar_lib
#line 4 "Mylib/AlgebraicStructure/Monoid/min.cpp"
namespace haar_lib {
template <typename T>
struct min_monoid {
using value_type = std::optional<T>;
value_type operator()() const { return {}; }
value_type operator()(const value_type &a, const value_type &b) const {
if (not a) return b;
if (not b) return a;
return {std::min(*a, *b)};
}
};
} // namespace haar_lib
#line 2 "Mylib/AlgebraicStructure/Monoid/sum.cpp"
namespace haar_lib {
template <typename T>
struct sum_monoid {
using value_type = T;
value_type operator()() const { return 0; }
value_type operator()(value_type a, value_type b) const { return a + b; }
};
} // namespace haar_lib
#line 2 "Mylib/AlgebraicStructure/Monoid/with_count.cpp"
#include <cstdint>
#include <utility>
namespace haar_lib {
namespace with_count_impl {
template <typename T>
struct internal_value {
T value;
int64_t count;
internal_value() : value(T()), count(0) {}
internal_value(T value) : value(value), count(1) {}
internal_value(T value, int64_t count) : value(value), count(count) {}
};
} // namespace with_count_impl
template <typename Monoid>
struct with_count {
using value_type = with_count_impl::internal_value<typename Monoid::value_type>;
const static Monoid M;
value_type operator()() const {
return {M(), 0};
}
value_type operator()(const value_type &a, const value_type &b) const {
if (a.value == b.value) return {a.value, a.count + b.count};
if (M(a.value, b.value) == a.value) return a;
return b;
}
};
} // namespace haar_lib
#line 2 "Mylib/AlgebraicStructure/MonoidAction/add_max_with_count.cpp"
namespace haar_lib {
template <typename MonoidUpdate, typename MonoidGet>
struct add_max_with_count {
using monoid_get = MonoidGet;
using monoid_update = MonoidUpdate;
using value_type_get = typename MonoidGet::value_type;
using value_type_update = typename MonoidUpdate::value_type;
value_type_get operator()(const value_type_get &a, const value_type_update &b, int) const {
return {a.value ? a.value.value() + b : a.value, a.count};
}
};
} // namespace haar_lib
#line 2 "Mylib/AlgebraicStructure/MonoidAction/add_min_with_count.cpp"
namespace haar_lib {
template <typename MonoidUpdate, typename MonoidGet>
struct add_min_with_count {
using monoid_get = MonoidGet;
using monoid_update = MonoidUpdate;
using value_type_get = typename MonoidGet::value_type;
using value_type_update = typename MonoidUpdate::value_type;
value_type_get operator()(const value_type_get &a, const value_type_update &b, int) const {
return {a.value ? a.value.value() + b : a.value, a.count};
}
};
} // namespace haar_lib
#line 2 "Mylib/DataStructure/SegmentTree/lazy_segment_tree.cpp"
#include <cassert>
#include <vector>
namespace haar_lib {
template <typename Monoid>
class lazy_segment_tree {
public:
using monoid_get = typename Monoid::monoid_get;
using monoid_update = typename Monoid::monoid_update;
using value_type_get = typename monoid_get::value_type;
using value_type_update = typename monoid_update::value_type;
private:
Monoid M_;
monoid_get M_get_;
monoid_update M_update_;
int depth_, size_, hsize_;
std::vector<value_type_get> data_;
std::vector<value_type_update> lazy_;
void propagate(int i) {
if (lazy_[i] == M_update_()) return;
if (i < hsize_) {
lazy_[i << 1 | 0] = M_update_(lazy_[i], lazy_[i << 1 | 0]);
lazy_[i << 1 | 1] = M_update_(lazy_[i], lazy_[i << 1 | 1]);
}
const int len = hsize_ >> (31 - __builtin_clz(i));
data_[i] = M_(data_[i], lazy_[i], len);
lazy_[i] = M_update_();
}
void propagate_top_down(int i) {
std::vector<int> temp;
while (i > 1) {
i >>= 1;
temp.push_back(i);
}
for (auto it = temp.rbegin(); it != temp.rend(); ++it) propagate(*it);
}
void bottom_up(int i) {
while (i > 1) {
i >>= 1;
propagate(i << 1 | 0);
propagate(i << 1 | 1);
data_[i] = M_get_(data_[i << 1 | 0], data_[i << 1 | 1]);
}
}
public:
lazy_segment_tree() {}
lazy_segment_tree(int n) : depth_(n > 1 ? 32 - __builtin_clz(n - 1) + 1 : 1),
size_(1 << depth_),
hsize_(size_ / 2),
data_(size_, M_get_()),
lazy_(size_, M_update_()) {}
void update(int l, int r, const value_type_update &x) {
assert(0 <= l and l <= r and r <= hsize_);
propagate_top_down(l + hsize_);
if (r < hsize_) propagate_top_down(r + hsize_);
int L = l + hsize_, R = r + hsize_;
while (L < R) {
if (R & 1) {
--R;
lazy_[R] = M_update_(x, lazy_[R]);
propagate(R);
}
if (L & 1) {
lazy_[L] = M_update_(x, lazy_[L]);
propagate(L);
++L;
}
L >>= 1;
R >>= 1;
}
bottom_up(l + hsize_);
if (r < hsize_) bottom_up(r + hsize_);
}
void update(int i, const value_type_update &x) { update(i, i + 1, x); }
value_type_get fold(int l, int r) {
assert(0 <= l and l <= r and r <= hsize_);
propagate_top_down(l + hsize_);
if (r < hsize_) propagate_top_down(r + hsize_);
value_type_get ret_left = M_get_(), ret_right = M_get_();
int L = l + hsize_, R = r + hsize_;
while (L < R) {
if (R & 1) {
--R;
propagate(R);
ret_right = M_get_(data_[R], ret_right);
}
if (L & 1) {
propagate(L);
ret_left = M_get_(ret_left, data_[L]);
++L;
}
L >>= 1;
R >>= 1;
}
return M_get_(ret_left, ret_right);
}
value_type_get fold_all() {
return fold(0, hsize_);
}
value_type_get operator[](int i) { return fold(i, i + 1); }
template <typename T>
void init(const T &val) {
init_with_vector(std::vector<T>(hsize_, val));
}
template <typename T>
void init_with_vector(const std::vector<T> &val) {
data_.assign(size_, M_get_());
lazy_.assign(size_, M_update_());
for (int i = 0; i < (int) val.size(); ++i) data_[hsize_ + i] = (value_type_get) val[i];
for (int i = hsize_; --i > 0;) data_[i] = M_get_(data_[i << 1 | 0], data_[i << 1 | 1]);
}
};
} // namespace haar_lib
#line 2 "Mylib/IO/input_tuples.cpp"
#include <initializer_list>
#line 4 "Mylib/IO/input_tuples.cpp"
#include <tuple>
#line 6 "Mylib/IO/input_tuple.cpp"
namespace haar_lib {
template <typename T, size_t... I>
static void input_tuple_helper(std::istream &s, T &val, std::index_sequence<I...>) {
(void) std::initializer_list<int>{(void(s >> std::get<I>(val)), 0)...};
}
template <typename T, typename U>
std::istream &operator>>(std::istream &s, std::pair<T, U> &value) {
s >> value.first >> value.second;
return s;
}
template <typename... Args>
std::istream &operator>>(std::istream &s, std::tuple<Args...> &value) {
input_tuple_helper(s, value, std::make_index_sequence<sizeof...(Args)>());
return s;
}
} // namespace haar_lib
#line 8 "Mylib/IO/input_tuples.cpp"
namespace haar_lib {
template <typename... Args>
class InputTuples {
struct iter {
using value_type = std::tuple<Args...>;
value_type value;
bool fetched = false;
int N, c = 0;
value_type operator*() {
if (not fetched) {
std::cin >> value;
}
return value;
}
void operator++() {
++c;
fetched = false;
}
bool operator!=(iter &) const {
return c < N;
}
iter(int N) : N(N) {}
};
int N;
public:
InputTuples(int N) : N(N) {}
iter begin() const { return iter(N); }
iter end() const { return iter(N); }
};
template <typename... Args>
auto input_tuples(int N) {
return InputTuples<Args...>(N);
}
} // namespace haar_lib
#line 4 "Mylib/IO/input_vector.cpp"
namespace haar_lib {
template <typename T>
std::vector<T> input_vector(int N) {
std::vector<T> ret(N);
for (int i = 0; i < N; ++i) std::cin >> ret[i];
return ret;
}
template <typename T>
std::vector<std::vector<T>> input_vector(int N, int M) {
std::vector<std::vector<T>> ret(N);
for (int i = 0; i < N; ++i) ret[i] = input_vector<T>(M);
return ret;
}
} // namespace haar_lib
#line 16 "test/aoj/3035/main.test.cpp"
namespace hl = haar_lib;
using sum = hl::sum_monoid<int64_t>;
using max_with_count = hl::with_count<hl::max_monoid<int64_t>>;
using min_with_count = hl::with_count<hl::min_monoid<int64_t>>;
using add_max_with_count = hl::add_max_with_count<sum, max_with_count>;
using add_min_with_count = hl::add_min_with_count<sum, min_with_count>;
int main() {
std::cin.tie(0);
std::ios::sync_with_stdio(false);
int H, W, Q;
std::cin >> H >> W >> Q;
auto A = hl::input_vector<int64_t>(H);
auto B = hl::input_vector<int64_t>(W);
auto seg_h_max = hl::lazy_segment_tree<add_max_with_count>(H);
auto seg_h_min = hl::lazy_segment_tree<add_min_with_count>(H);
auto seg_w_max = hl::lazy_segment_tree<add_max_with_count>(W);
auto seg_w_min = hl::lazy_segment_tree<add_min_with_count>(W);
seg_h_max.init_with_vector(A);
seg_h_min.init_with_vector(A);
seg_w_max.init_with_vector(B);
seg_w_min.init_with_vector(B);
for (auto [type] : hl::input_tuples<int>(Q)) {
switch (type) {
case 1: {
int a, b, v;
std::cin >> a >> b >> v;
--a;
seg_h_max.update(a, b, v);
seg_h_min.update(a, b, v);
break;
}
case 2: {
int c, d, v;
std::cin >> c >> d >> v;
--c;
seg_w_max.update(c, d, v);
seg_w_min.update(c, d, v);
break;
}
case 3: {
int64_t a, b, c, d;
std::cin >> a >> b >> c >> d;
--a, --c;
std::map<int64_t, int64_t> m;
auto x = std::vector{seg_h_max.fold(a, b), seg_h_min.fold(a, b)};
auto y = std::vector{seg_w_max.fold(c, d), seg_w_min.fold(c, d)};
if (x[0].value == x[1].value) x.pop_back();
if (y[0].value == y[1].value) y.pop_back();
int64_t M = LLONG_MAX;
for (auto p : x) {
for (auto q : y) {
M = std::min(M, *p.value * *q.value);
}
}
if (M == 0) {
int64_t p = 0;
for (auto e : x)
if (e.value == 0) p += e.count;
int64_t q = 0;
for (auto e : y)
if (e.value == 0) q += e.count;
m[0] = (b - a) * q + (d - c) * p - p * q;
} else {
for (auto p : x) {
for (auto q : y) {
m[*p.value * *q.value] += p.count * q.count;
}
}
}
std::cout << m.begin()->first << " " << m.begin()->second << "\n";
break;
}
case 4: {
int64_t a, b, c, d;
std::cin >> a >> b >> c >> d;
--a, --c;
std::map<int64_t, int64_t> m;
auto x = std::vector{seg_h_max.fold(a, b), seg_h_min.fold(a, b)};
auto y = std::vector{seg_w_max.fold(c, d), seg_w_min.fold(c, d)};
if (x[0].value == x[1].value) x.pop_back();
if (y[0].value == y[1].value) y.pop_back();
int64_t M = LLONG_MIN;
for (auto p : x) {
for (auto q : y) {
M = std::max(M, *p.value * *q.value);
}
}
if (M == 0) {
int64_t p = 0;
for (auto e : x)
if (e.value == 0) p += e.count;
int64_t q = 0;
for (auto e : y)
if (e.value == 0) q += e.count;
m[0] = (b - a) * q + (d - c) * p - p * q;
} else {
for (auto p : x) {
for (auto q : y) {
m[*p.value * *q.value] += p.count * q.count;
}
}
}
std::cout << m.rbegin()->first << " " << m.rbegin()->second << "\n";
break;
}
}
}
return 0;
}
test/aoj/3035/main.test.cpp
Max monoid
(Mylib/AlgebraicStructure/Monoid/max.cpp)