結果
| 問題 |
No.3214 small square
|
| ユーザー |
 zawakasu
|
| 提出日時 | 2025-07-26 02:01:21 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 804 ms / 3,000 ms |
| コード長 | 15,439 bytes |
| コンパイル時間 | 3,250 ms |
| コンパイル使用メモリ | 172,848 KB |
| 実行使用メモリ | 55,956 KB |
| 最終ジャッジ日時 | 2025-07-26 02:01:54 |
| 合計ジャッジ時間 | 25,463 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 40 |
ソースコード
#include <iostream>
#include <iomanip>
#include <cassert>
#include <vector>
#include <algorithm>
#include <utility>
#include <numeric>
#include <tuple>
#include <ranges>
namespace ranges = std::ranges;
namespace views = std::views;
// #include "Src/Number/IntegerDivision.hpp"
// #include "Src/Utility/BinarySearch.hpp"
#include <cstdint>
#include <cstddef>
namespace zawa {
using i16 = std::int16_t;
using i32 = std::int32_t;
using i64 = std::int64_t;
using i128 = __int128_t;
using u8 = std::uint8_t;
using u16 = std::uint16_t;
using u32 = std::uint32_t;
using u64 = std::uint64_t;
using usize = std::size_t;
} // namespace zawa
#include <iterator>
#include <limits>
namespace zawa {
template <class T>
class CompressedSequence {
public:
static constexpr u32 NotFound = std::numeric_limits<u32>::max();
CompressedSequence() = default;
template <class InputIterator>
CompressedSequence(InputIterator first, InputIterator last) : comped_(first, last), f_{} {
std::sort(comped_.begin(), comped_.end());
comped_.erase(std::unique(comped_.begin(), comped_.end()), comped_.end());
comped_.shrink_to_fit();
f_.reserve(std::distance(first, last));
for (auto it{first} ; it != last ; it++) {
f_.emplace_back(std::distance(comped_.begin(), std::lower_bound(comped_.begin(), comped_.end(), *it)));
}
}
CompressedSequence(const std::vector<T>& A) : CompressedSequence(A.begin(), A.end()) {}
inline usize size() const noexcept {
return comped_.size();
}
u32 operator[](const T& v) const {
return std::distance(comped_.begin(), std::lower_bound(comped_.begin(), comped_.end(), v));
}
u32 upper_bound(const T& v) const {
return std::distance(comped_.begin(), std::upper_bound(comped_.begin(), comped_.end(), v));
}
u32 find(const T& v) const {
u32 i = std::distance(comped_.begin(), std::lower_bound(comped_.begin(), comped_.end(), v));
return i == comped_.size() or comped_[i] != v ? NotFound : i;
}
bool contains(const T& v) const {
u32 i = std::distance(comped_.begin(), std::lower_bound(comped_.begin(), comped_.end(), v));
return i < comped_.size() and comped_[i] == v;
}
u32 at(const T& v) const {
u32 res = find(v);
assert(res != NotFound);
return res;
}
inline u32 map(u32 i) const noexcept {
assert(i < f_.size());
return f_[i];
}
inline T inverse(u32 i) const noexcept {
assert(i < size());
return comped_[i];
}
inline std::vector<T> comped() const noexcept {
return comped_;
}
private:
std::vector<T> comped_;
std::vector<u32> f_;
};
} // namespace zawa
// #include "Src/Sequence/RunLengthEncoding.hpp"
// #include "Src/Algebra/Group/AdditiveGroup.hpp"
// #include "Src/DataStructure/FenwickTree/FenwickTree.hpp"
// #include "Src/DataStructure/SegmentTree/SegmentTree.hpp"
// #include "Src/DataStructure/DisjointSetUnion/DisjointSetUnion.hpp"
#include <concepts>
namespace zawa {
namespace concepts {
template <class T>
concept Semigroup = requires {
typename T::Element;
{ T::operation(std::declval<typename T::Element>(), std::declval<typename T::Element>()) } -> std::same_as<typename T::Element>;
};
} // namespace concepts
} // namespace zawa
namespace zawa {
namespace concepts {
template <class T>
concept Identitiable = requires {
typename T::Element;
{ T::identity() } -> std::same_as<typename T::Element>;
};
template <class T>
concept Monoid = Semigroup<T> and Identitiable<T>;
} // namespace
} // namespace zawa
namespace zawa {
namespace concepts {
template <class T>
concept MonoidWithAction = requires {
requires Monoid<typename T::ValueMonoid>;
requires Monoid<typename T::OperatorMonoid>;
{ T::mapping(
std::declval<typename T::ValueMonoid::Element>(),
std::declval<typename T::OperatorMonoid::Element>()
) } -> std::same_as<typename T::ValueMonoid::Element>;
};
} // namespace concepts
} // namespace zawa
#include <bit>
namespace zawa {
template <concepts::MonoidWithAction S>
class LazySegmentTree {
public:
using VM = S::ValueMonoid;
using V = typename VM::Element;
using OM = S::OperatorMonoid;
using O = typename OM::Element;
LazySegmentTree() = default;
explicit LazySegmentTree(usize n)
: m_n{n}, m_sz{1u << (std::bit_width(n))}, m_dat(m_sz << 1, VM::identity()), m_lazy(m_sz << 1, OM::identity()) {}
explicit LazySegmentTree(const std::vector<V>& a)
: m_n{a.size()}, m_sz{1u << (std::bit_width(a.size()))}, m_dat(m_sz << 1, VM::identity()), m_lazy(m_sz << 1, OM::identity()) {
std::ranges::copy(a, m_dat.begin() + inner_size());
for (usize i = inner_size() ; --i ; ) recalc(i);
}
[[nodiscard]] inline usize size() const noexcept {
return m_n;
}
[[nodiscard]] V operator[](usize i) {
assert(i < size());
return get(i, 1, 0, inner_size());
}
[[nodiscard]] V get(usize i) {
return (*this)[i];
}
[[nodiscard]] V product(usize l, usize r) {
assert(l <= r and r <= size());
return product(l, r, 1, 0, inner_size());
}
void operation(usize l, usize r, const O& o) {
assert(l <= r and r <= size());
return operation(l, r, o, 1, 0, inner_size());
}
void assign(usize i, const V& v) {
assert(i < size());
assign(i, v, 1, 0, inner_size());
}
void operation(usize i, const O& o) {
assert(i < size());
operation(i, o, 1, 0, inner_size());
}
private:
using NodeInfo = std::tuple<usize, usize, usize>;
public:
template <class F>
requires std::predicate<F, V>
usize maxRight(usize l, F f) {
assert(l <= size());
if (!f(VM::identity())) return l;
if (l == size()) return size();
std::vector<NodeInfo> ranges;
partition_range(l, size(), ranges, 1, 0, inner_size());
V prod = VM::identity();
for (auto [nd, nl, nr] : ranges) {
if (!f(VM::operation(prod, m_dat[nd]))) {
return maxRight(f, prod, nd, nl, nr);
}
else {
prod = VM::operation(prod, m_dat[nd]);
}
}
return size();
}
template <class F>
requires std::predicate<F, V>
usize minLeft(usize r, F f) {
assert(r <= size());
if (!f(VM::identity())) return r;
if (!r) return 0;
std::vector<NodeInfo> ranges;
partition_range(0, r, ranges, 1, 0, inner_size());
V prod = VM::identity();
for (auto [nd, nl, nr] : ranges | std::views::reverse) {
if (!f(VM::operation(m_dat[nd], prod))) {
return minLeft(f, prod, nd, nl, nr);
}
else {
prod = VM::operation(prod, m_dat[nd]);
}
}
return 0;
}
private:
usize m_n{}, m_sz{};
std::vector<V> m_dat;
std::vector<O> m_lazy;
inline usize inner_size() const noexcept {
return m_sz;
}
void recalc(usize nd) {
// assert(nd < inner_size());
m_dat[nd] = VM::operation(m_dat[nd << 1 | 0], m_dat[nd << 1 | 1]);
}
void propagate(usize nd) {
// assert(nd < inner_size());
for (usize ch : {nd << 1 | 0, nd << 1 | 1}) {
m_dat[ch] = S::mapping(m_dat[ch], m_lazy[nd]);
m_lazy[ch] = OM::operation(m_lazy[ch], m_lazy[nd]);
}
m_lazy[nd] = OM::identity();
}
V product(usize ql, usize qr, usize nd, usize nl, usize nr) {
if (qr <= nl or nr <= ql) return VM::identity();
if (ql <= nl and nr <= qr) return m_dat[nd];
propagate(nd);
const usize m = (nl + nr) >> 1;
return VM::operation(
product(ql, qr, nd << 1 | 0, nl, m),
product(ql, qr, nd << 1 | 1, m, nr)
);
}
V get(usize i, usize nd, usize nl, usize nr) {
if (nd >= inner_size()) return m_dat[nd];
propagate(nd);
const usize m = (nl + nr) >> 1;
return i < m ? get(i, nd << 1 | 0, nl, m) : get(i, nd << 1 | 1, m, nr);
}
void operation(usize ql, usize qr, const O& o, usize nd, usize nl, usize nr) {
if (qr <= nl or nr <= ql) return;
if (ql <= nl and nr <= qr) {
m_dat[nd] = S::mapping(m_dat[nd], o);
m_lazy[nd] = OM::operation(m_lazy[nd], o);
return;
}
propagate(nd);
const usize m = (nl + nr) >> 1;
operation(ql, qr, o, nd << 1 | 0, nl, m);
operation(ql, qr, o, nd << 1 | 1, m, nr);
recalc(nd);
}
void operation(usize i, const O& o, usize nd, usize nl, usize nr) {
if (nl == i and i + 1 == nr) {
m_dat[nd] = S::mapping(m_dat[nd], o);
// 葉頂点なので、lazyへのopは不要
return;
}
propagate(nd);
const usize m = (nl + nr) >> 1;
i < m ? operation(i, o, nd << 1 | 0, nl, m) : operation(i, o, nd << 1 | 1, m, nr);
recalc(nd);
}
void assign(usize i, const V& v, usize nd, usize nl, usize nr) {
if (nl == i and i + 1 == nr) {
m_dat[nd] = v;
return;
}
propagate(nd);
const usize m = (nl + nr) >> 1;
i < m ? assign(i, v, nd << 1 | 0, nl, m) : assign(i, v, nd << 1 | 1, m, nr);
recalc(nd);
}
void partition_range(usize ql, usize qr, std::vector<NodeInfo>& res, usize nd, usize nl, usize nr) {
if (qr <= nl or nr <= ql) return;
if (ql <= nl and nr <= qr) {
res.emplace_back(nd, nl, nr);
return;
}
propagate(nd);
const usize m = (nl + nr) >> 1;
partition_range(ql, qr, res, nd << 1 | 0, nl, m);
partition_range(ql, qr, res, nd << 1 | 1, m, nr);
}
template <class F>
requires std::predicate<F, V>
usize maxRight(F f, const V& prod, usize nd, usize nl, usize nr) {
if (nd >= inner_size()) return nl;
propagate(nd);
const usize m = (nl + nr) >> 1, lch = nd << 1 | 0, rch = nd << 1 | 1;
return f(VM::operation(prod, m_dat[lch])) ?
maxRight(f, VM::operation(prod, m_dat[lch]), rch, m, nr) : maxRight(f, prod, lch, nl, m);
}
template <class F>
requires std::predicate<F, V>
usize minLeft(F f, const V& prod, usize nd, usize nl, usize nr) {
if (nd >= inner_size()) return nr;
propagate(nd);
const usize m = (nl + nr) >> 1, lch = nd << 1 | 0, rch = nd << 1 | 1;
return f(VM::operation(m_dat[rch], prod)) ?
minLeft(f, VM::operation(m_dat[rch], prod), lch, nl, m) : minLeft(f, prod, rch, m, nr);
}
};
} // namespace zawa
using namespace zawa;
// #include "atcoder/modint"
// using mint = atcoder::modint998244353;
using namespace std;
#include <optional>
struct VM {
using Element = long long;
static Element identity() {
return 0LL;
}
static Element operation(Element L, Element R) {
return max(L, R);
}
};
struct OM {
using Element = long long;
static Element identity() {
return 0LL;
}
static Element operation(Element L, Element R) {
return L + R;
}
};
struct ACT {
using ValueMonoid = VM;
using OperatorMonoid = OM;
static VM::Element mapping(VM::Element v, OM::Element o) {
return v + o;
}
};
int N;
long long A, X[200020], Y[200020], V[200020];
long long solve() {
vector<long long> appx, appy;
for (int i = 0 ; i < N ; i++) {
const long long x = 2 * X[i], y = 2 * Y[i];
appx.push_back(x - 2 * A - 1);
appy.push_back(y - 2 * A - 1);
appx.push_back(x - 2 * A);
appy.push_back(y - 2 * A);
appx.push_back(x);
appy.push_back(y);
appx.push_back(x + 1);
appy.push_back(y + 1);
appx.push_back(x + 2 * A + 1);
}
CompressedSequence xs(appx), ys(appy);
vector<vector<int>> event(xs.size());
for (int i = 0 ; i < N ; i++) event[xs.at(2 * X[i])].push_back(i);
LazySegmentTree<ACT> seg(ys.size());
auto insert = [&](long long y, int v) -> void {
// cout << "inserted " << 2 * y << ' ' << v << endl;
seg.operation(ys[2 * (y - A)], ys.at(2 * y) + 1, v);
};
auto erase = [&](long long y, int v) -> void {
// cout << "erased " << 2 * y << ' ' << v << endl;
seg.operation(ys[2 * (y - A)], ys.at(2 * y) + 1, -v);
};
auto eval = [&]() -> long long {
return seg.product(0, seg.size());
};
int j = 0;
long long ans = 0LL;
for (int i = 0 ; i < ssize(event) ; ) {
while (xs.inverse(j) + 2 * A < xs.inverse(i)) {
for (int k : event[j]) erase(Y[k], V[k]);
// if (event[j].size()) cout << "erased " << xs.inverse(j) << endl;
// for (int k = 0 ; k < ssize(ys) ; k++) cout << seg[k] << ' ';
// cout << endl;
// ans = max(ans, eval());
j++;
}
while (i < ssize(xs) and xs.inverse(j) + 2 * A >= xs.inverse(i)) {
for (int k : event[i]) insert(Y[k], V[k]);
// if (event[i].size()) cout << "inserted " << xs.inverse(i) << endl;
i++;
}
// for (int k = 0 ; k < ssize(ys) ; k++) cout << seg[k] << ' ';
// cout << endl;
assert(i == ssize(xs) or xs.inverse(j) + 2 * A < xs.inverse(i));
ans = max(ans, eval());
}
for ( ; j < ssize(event) ; j++) {
for (int k : event[j]) erase(Y[k], V[k]);
// for (int k = 0 ; k < ssize(ys) ; k++) cout << seg[k] << ' ';
// cout << endl;
ans = max(ans, eval());
}
// for (int i = 0 ; i < ssize(ys) ; i++) cout << ys.inverse(i) << ' ';
// cout << endl;
return ans;
}
long long naive() {
long long L = (int)1e9, R = -L, D = (int)1e9, U = -D;
for (int i = 0 ; i < N ; i++) {
L = min(L, X[i]);
R = max(R, X[i]);
D = min(D, Y[i]);
U = max(U, Y[i]);
}
long long ans = 0;
for (long double x = L - A - 100 ; x <= R + A + 100 ; x += 0.5) {
for (long double y = D - A - 100 ; y <= R + A + 100 ; y += 0.5) {
long long cur = 0;
for (int i = 0 ; i < N ; i++) {
if (x <= X[i] and X[i] <= x + A and y <= Y[i] and Y[i] <= y + A) {
cur += V[i];
}
}
ans = max<long long>(ans, cur);
}
}
return ans;
}
#include <random>
std::mt19937 mt{std::random_device{}()};
int main() {
cin.tie(0);
cout.tie(0);
ios::sync_with_stdio(0);
#ifdef DEBUG
while (true) {
N = mt() % 200 + 1;
A = mt() % 20 + 1;
cout << "---------------------" << endl;
cout << N << ' ' << A << endl;
for (int i = 0 ; i < N ; i++) {
X[i] = mt() % 30 + 1;
Y[i] = mt() % 30 + 1;
V[i] = mt() % 51 - 25;
cout << X[i] << ' ' << Y[i] << ' ' << V[i] << endl;
}
long long my = solve(), ans = naive();
if (my != ans) {
cerr << ans << " but output " << my << endl;
exit(0);
}
}
#else
cin >> N >> A;
for (int i = 0 ; i < N ; i++) cin >> X[i] >> Y[i] >> V[i];
cout << solve() << endl;
#endif
}