cp-library
競技プログラミング用 C++ ライブラリ
test/li_chao_tree_segment.test.cpp
test/li_chao_tree_segment.test.cpp · GitHub で見る
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コード
#define PROBLEM "https://judge.yosupo.jp/problem/segment_add_get_min"
#include "../data_structure/li_chao_tree.hpp"
#include "../components/radix_sort.hpp"
#include <bit>
#include <algorithm>
#include <cstdint>
#include "../components/fast_io.hpp"
#include <tuple>
#include <utility>
#include <vector>
using namespace std;
int main() {
FastInput input;
FastOutput output;
int n = 0, q = 0;
input.read(n), input.read(q);
struct Segment {
int64_t l, r, a, b;
};
vector<Segment> initial(n);
for (auto &[l, r, a, b] : initial) input.read(l), input.read(r), input.read(a), input.read(b);
struct Query {
int type, index;
Segment f;
};
vector<Query> queries(q);
vector<uint64_t> points;
points.reserve(2 * initial.size() + 2 * queries.size());
auto endpoint = [&](int64_t value, unsigned tag) { points.push_back((uint64_t(uint32_t(value) ^ (1U << 31)) << 32) | tag); };
for (int i = 0; i < n; ++i) { endpoint(initial[i].l, 4U * i); endpoint(initial[i].r, 4U * i + 1); }
for (auto &query : queries) {
input.read(query.type), input.read(query.f.l);
unsigned tag = 4U * unsigned(n + (&query - queries.data()));
if (query.type == 0) {
input.read(query.f.r), input.read(query.f.a), input.read(query.f.b);
endpoint(query.f.l, tag), endpoint(query.f.r, tag + 1);
} else endpoint(query.f.l, tag + 2);
}
if (none_of(queries.begin(), queries.end(), [](const Query &query) { return query.type == 1; })) return 0;
stable_radix_sort<11>(points, [](uint64_t point) { return uint32_t(point >> 32); });
vector<int64_t> xs;
xs.reserve(q);
for (size_t first = 0; first < points.size();) {
size_t last = first + 1;
while (last < points.size() && uint32_t(points[last] >> 32) == uint32_t(points[first] >> 32)) ++last;
bool queried = false;
for (size_t i = first; i < last; ++i) {
unsigned tag = uint32_t(points[i]), owner = tag / 4;
if ((tag & 3) == 2) { queries[owner - n].index = int(xs.size()); queried = true; }
else {
auto &segment = owner < unsigned(n) ? initial[owner] : queries[owner - n].f;
(tag & 1 ? segment.r : segment.l) = int(xs.size());
}
}
if (queried) xs.push_back(bit_cast<int32_t>(uint32_t(points[first] >> 32) ^ (1U << 31)));
first = last;
}
LiChaoTree<int64_t, false, int64_t> tree(std::move(xs));
for (auto [l, r, a, b] : initial) tree.add_segment_index(int(l), int(r), a, b);
for (auto query : queries) {
if (query.type == 0) tree.add_segment_index(int(query.f.l), int(query.f.r), query.f.a, query.f.b);
else {
auto value = tree.query_index(query.index);
if (value) output.println(*value);
else output.write("INFINITY\n");
}
}
}
#line 1 "test/li_chao_tree_segment.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/segment_add_get_min"
#line 1 "data_structure/li_chao_tree.hpp"
#include <algorithm>
#include <bit>
#include <cassert>
#include <cstddef>
#include <cstdint>
#include <limits>
#include <optional>
#include <type_traits>
#include <utility>
#include <vector>
template <class T = std::int64_t, bool maximize = false, class R = std::conditional_t<std::is_integral_v<T>, std::conditional_t<(sizeof(T) < 8), std::int64_t, __int128_t>, T>>
class LiChaoTree {
static_assert((std::is_integral_v<T> && std::is_signed_v<T> && sizeof(T) <= 8) || std::is_floating_point_v<T>);
struct Line {
T a, b;
template <class V>
V eval(T x) const { return V(R(a) * R(x) + R(b)); }
};
int n = 0, base = 1;
bool wide = false, dense = false;
std::vector<T> xs;
std::vector<Line> lines;
std::vector<std::uint8_t> state;
template <class V>
static bool better(V a, V b) {
if constexpr (maximize) return a > b;
else return a < b;
}
template <class V>
void insert(int k, int l, int width, Line f) {
for (;;) {
Line &g = lines[k];
if (!(state[k] & 1)) {
g = f;
state[k] = 3;
return;
}
if (f.a == g.a) {
if (better(f.b, g.b)) g = f;
return;
}
int half = width >> 1, m = l + half;
if (better(f.template eval<V>(xs[m]), g.template eval<V>(xs[m]))) std::swap(f, g);
if (!half) return;
bool right = better(f.a, g.a);
int edge = right ? l + width - 1 : l;
if (!better(f.template eval<V>(xs[edge]), g.template eval<V>(xs[edge]))) return;
k = k * 2 + right;
if (right) l = m;
width = half;
}
}
template <class V>
void insert_segment(int k, int l, int r, int ql, int qr, Line f) {
if (ql <= l && r <= qr) {
insert<V>(k, l, r - l, f);
return;
}
if (state[k] & 1) {
const Line &g = lines[k];
if (f.a == g.a) {
if (!better(f.b, g.b)) return;
} else {
int edge = better(f.a, g.a) ? std::min(r, qr) - 1 : std::max(l, ql);
if (!better(f.template eval<V>(xs[edge]), g.template eval<V>(xs[edge]))) return;
}
}
state[k] |= 2;
int m = (l + r) >> 1;
if (ql < m) insert_segment<V>(k * 2, l, m, ql, qr, f);
if (m < qr) insert_segment<V>(k * 2 + 1, m, r, ql, qr, f);
}
void check(Line f, int l, int r) {
if constexpr (std::is_integral_v<T> && std::is_same_v<R, __int128_t>) {
if (!wide) {
R a = f.template eval<R>(xs[l]), b = f.template eval<R>(xs[r - 1]);
wide = a != R(std::int64_t(a)) || b != R(std::int64_t(b));
}
}
}
template <class F>
decltype(auto) dispatch(F f) const {
if constexpr (std::is_integral_v<T> && std::is_same_v<R, __int128_t>) {
if (!wide) return f.template operator()<std::int64_t>();
}
return f.template operator()<R>();
}
int lower(T x) const {
if (n <= 1) return n && xs[0] < x;
if constexpr (std::is_integral_v<T>)
if (dense) return int(std::clamp<__int128_t>(__int128_t(x) - xs[0], 0, n));
int i = 0;
for (int step = base >> 1; step; step >>= 1) i += int(xs[i + step - 1] < x) * step;
return std::min(n, i + int(xs[i] < x));
}
template <class V>
std::optional<R> query_impl(int i) const {
assert(0 <= i && i < n);
V result = maximize ? std::numeric_limits<V>::lowest() : std::numeric_limits<V>::max();
bool found = false;
for (int k = 1, bit = base >> 1;; bit >>= 1) {
if (!state[k]) break;
if (state[k] & 1) {
V value = lines[k].template eval<V>(xs[i]);
if ((std::is_floating_point_v<V> && !found) || better(value, result)) result = value;
found = true;
}
if (!bit) break;
k = k * 2 + bool(i & bit);
}
if (found) return result;
return std::nullopt;
}
public:
using value_type = R;
explicit LiChaoTree(std::vector<T> coordinates = {}) { build(std::move(coordinates)); }
void build(std::vector<T> coordinates) {
if (!std::is_sorted(coordinates.begin(), coordinates.end())) std::sort(coordinates.begin(), coordinates.end());
coordinates.erase(std::unique(coordinates.begin(), coordinates.end()), coordinates.end());
assert(coordinates.size() <= std::size_t(1) << 29);
n = static_cast<int>(coordinates.size());
if constexpr (std::is_integral_v<T>) dense = n && __int128_t(coordinates.back()) - coordinates[0] == n - 1;
base = int(std::bit_ceil(unsigned(std::max(1, n))));
xs = std::move(coordinates);
if (n) xs.resize(base, xs.back());
lines.resize(base * 2);
state.assign(base * 2, 0);
wide = false;
}
int size() const { return n; }
void clear() {
std::fill(state.begin(), state.end(), 0);
wide = false;
}
T coordinate(int i) const {
assert(0 <= i && i < n);
return xs[i];
}
int index(T x) const {
int i = lower(x);
assert(i < n && xs[i] == x);
return i;
}
void add_line(T a, T b) {
if (n) {
Line f{a, b};
check(f, 0, n);
dispatch([&]<class V>() { insert<V>(1, 0, base, f); });
}
}
void add_segment_index(int l, int r, T a, T b) {
assert(0 <= l && l <= r && r <= n);
if (l < r) {
Line f{a, b};
check(f, l, r);
dispatch([&]<class V>() { insert_segment<V>(1, 0, base, l, r == n ? base : r, f); });
}
}
void add_segment(T l, T r, T a, T b) {
assert(l <= r);
int left = lower(l);
int right = lower(r);
add_segment_index(left, right, a, b);
}
std::optional<R> query_index(int i) const {
return dispatch([&]<class V>() { return query_impl<V>(i); });
}
std::optional<R> query(T x) const { return query_index(index(x)); }
};
#line 1 "components/radix_sort.hpp"
#line 5 "components/radix_sort.hpp"
#include <array>
#line 11 "components/radix_sort.hpp"
template <int Bits, class T, class Key>
void stable_radix_sort(std::vector<T> &values, Key &&key) {
static_assert(1 <= Bits && Bits <= 16);
constexpr unsigned buckets = 1U << Bits, mask = buckets - 1;
using K = std::remove_cvref_t<decltype(key(std::declval<const T &>()))>;
static_assert(std::is_integral_v<K> && std::is_unsigned_v<K> && sizeof(K) <= sizeof(std::uint64_t));
if (values.size() < 2) return;
if (values.size() < 256) {
std::stable_sort(values.begin(), values.end(), [&](const T &a, const T &b) { return key(a) < key(b); });
return;
}
std::uint64_t first = key(values.front()), previous = first, varying = 0;
bool sorted = true;
for (std::size_t i = 1; i < values.size(); ++i) {
std::uint64_t current = key(values[i]);
varying |= first ^ current;
sorted &= previous <= current;
previous = current;
}
if (sorted) return;
std::vector<T> scratch(values.size());
using Counts = std::conditional_t<(Bits <= 11), std::array<std::size_t, buckets>, std::vector<std::size_t>>;
Counts count = [] {
if constexpr (Bits <= 11) return Counts{};
else return Counts(buckets);
}();
for (int shift = 0; shift < 64; shift += Bits) {
if (!((varying >> shift) & mask)) continue;
std::fill(count.begin(), count.end(), 0);
for (const auto &value : values) ++count[(static_cast<std::uint64_t>(key(value)) >> shift) & mask];
std::size_t sum = 0;
for (auto &x : count) {
auto n = x;
x = sum, sum += n;
}
for (auto &&value : values) scratch[count[(static_cast<std::uint64_t>(key(value)) >> shift) & mask]++] = std::move(value);
values.swap(scratch);
}
}
template <class T, class Key>
void stable_radix_sort(std::vector<T> &values, Key key) {
stable_radix_sort<8>(values, std::move(key));
}
namespace radix_sort_detail {
template <int Bits = 8, class T, class Key>
void sort_by_key(std::vector<T> &values, Key key) {
using K = std::remove_cvref_t<decltype(key(std::declval<const T &>()))>;
if constexpr (std::is_integral_v<K> && !std::is_same_v<K, bool> && sizeof(K) <= 8 && std::is_default_constructible_v<T>) {
using U = std::make_unsigned_t<K>;
constexpr U sign = std::is_signed_v<K> ? U(1) << (sizeof(K) * 8 - 1) : U(0);
stable_radix_sort<Bits>(values, [&](const T &value) { return U(U(key(value)) ^ sign); });
} else std::sort(values.begin(), values.end(), [&](const T &a, const T &b) { return key(a) < key(b); });
}
}
#line 1 "components/fast_io.hpp"
#line 8 "components/fast_io.hpp"
#include <charconv>
#line 11 "components/fast_io.hpp"
#include <cstdio>
#include <cstring>
#include <memory>
#include <stdexcept>
#include <string>
#include <string_view>
#line 18 "components/fast_io.hpp"
#if defined(__unix__) || defined(__APPLE__)
#include <sys/mman.h>
#include <sys/stat.h>
#include <unistd.h>
#endif
namespace fast_io_detail { struct BulkInput; struct BulkOutput; }
class FastInput {
friend struct fast_io_detail::BulkInput;
static constexpr std::size_t capacity = 1 << 16;
FILE *file = nullptr;
std::unique_ptr<char[]> buffer;
const char *current = "", *end = current;
std::string scratch;
void *mapping = nullptr;
std::size_t mapped_size = 0;
bool refill() {
if (!file) return false;
std::size_t n = std::fread(buffer.get(), 1, capacity, file);
current = buffer.get();
end = current + n;
return n;
}
static const char *scan(const char *p, const char *end) {
while (end - p >= 8) {
std::uint64_t x;
std::memcpy(&x, p, 8);
if ((x - 0x2121212121212121ULL) & ~x & 0x8080808080808080ULL) break;
p += 8;
}
while (p != end && static_cast<unsigned char>(*p) > ' ') ++p;
return p;
}
public:
explicit FastInput(FILE *input = stdin) {
#if defined(__unix__) || defined(__APPLE__)
struct stat status;
int fd = fileno(input);
auto offset = ftello(input);
if (fd >= 0 && offset >= 0 && !fstat(fd, &status) && S_ISREG(status.st_mode) && status.st_size > offset) {
mapped_size = status.st_size;
mapping = mmap(nullptr, mapped_size, PROT_READ, MAP_PRIVATE, fd, 0);
if (mapping != MAP_FAILED) {
current = static_cast<const char *>(mapping) + offset;
end = static_cast<const char *>(mapping) + mapped_size;
return;
}
mapping = nullptr;
}
#endif
file = input;
buffer = std::make_unique_for_overwrite<char[]>(capacity);
}
explicit FastInput(std::string_view input) : current(input.empty() ? "" : input.data()), end(current + input.size()) {}
FastInput(const FastInput &) = delete;
FastInput &operator=(const FastInput &) = delete;
~FastInput() {
#if defined(__unix__) || defined(__APPLE__)
if (mapping) munmap(mapping, mapped_size);
#endif
}
std::string_view token() {
while (true) {
while (current != end && static_cast<unsigned char>(*current) <= ' ') ++current;
if (current != end) break;
if (!refill()) return {};
}
const char *begin = current;
current = scan(current, end);
if (current != end || !file) return {begin, std::size_t(current - begin)};
scratch.assign(begin, end);
while (refill()) {
current = scan(current, end);
scratch.append(buffer.get(), std::size_t(current - buffer.get()));
if (current != end) break;
}
return scratch;
}
template <class T>
bool read(T &value) {
if constexpr (std::is_integral_v<T> && !std::is_same_v<T, bool>) {
while (true) {
while (current != end && static_cast<unsigned char>(*current) <= ' ') ++current;
if (current != end) break;
if (!refill()) return false;
}
if constexpr (std::is_unsigned_v<T> && sizeof(T) == 4 && std::endian::native == std::endian::little) {
if (end - current >= 11) {
std::uint64_t x;
std::memcpy(&x, current, 8);
if (!(((x + 0x4646464646464646ULL) | (x - 0x3030303030303030ULL)) & 0x8080808080808080ULL)) {
x &= 0x0f0f0f0f0f0f0f0fULL;
x = (x * 10 + (x >> 8)) & 0x00ff00ff00ff00ffULL;
x = (x * 100 + (x >> 16)) & 0x0000ffff0000ffffULL;
std::uint64_t v = std::uint32_t(x * 10000 + (x >> 32));
int n = 8;
for (; n < 10 && static_cast<unsigned char>(current[n]) - unsigned('0') < 10; ++n)
v = v * 10 + (current[n] - '0');
if (static_cast<unsigned char>(current[n]) <= ' ' && v <= 0xffffffffULL) {
current += n;
value = T(v);
return true;
}
}
}
}
T parsed{};
auto result = std::from_chars(current, end, parsed);
if (result.ec == std::errc{} && (result.ptr != end ? static_cast<unsigned char>(*result.ptr) <= ' ' : !file)) {
current = result.ptr;
value = parsed;
return true;
}
}
auto s = token();
if (s.empty()) return false;
if constexpr (std::is_same_v<T, bool>) {
assert(s == "0" || s == "1");
value = s[0] == '1';
} else if constexpr (std::is_integral_v<T>) {
auto result = std::from_chars(s.data(), s.data() + s.size(), value);
assert(result.ec == std::errc{} && result.ptr == s.data() + s.size());
(void)result;
} else value = T(s);
return true;
}
};
class FastOutput {
friend struct fast_io_detail::BulkOutput;
inline static constexpr auto quads = [] {
std::array<std::array<char, 4>, 10000> table{};
for (int i = 0; i < 10000; ++i)
table[i] = {char('0' + i / 1000), char('0' + i / 100 % 10), char('0' + i / 10 % 10), char('0' + i % 10)};
return table;
}();
FILE *file;
std::unique_ptr<char[]> buffer = std::make_unique_for_overwrite<char[]>(1 << 16);
std::size_t capacity = 1 << 16, length = 0;
char *reserve(std::size_t n) {
if (n > capacity - length) {
if (!flush()) throw std::runtime_error("output failed");
if (n > capacity) {
std::size_t next = std::max(n, 2 * capacity);
buffer = std::make_unique_for_overwrite<char[]>(next);
capacity = next;
}
}
return buffer.get() + length;
}
public:
explicit FastOutput(FILE *output = stdout) : file(output) {}
FastOutput(const FastOutput &) = delete;
FastOutput &operator=(const FastOutput &) = delete;
~FastOutput() { flush(); }
bool flush() {
std::size_t offset = 0;
while (offset < length) {
auto n = std::fwrite(buffer.get() + offset, 1, length - offset, file);
if (!n) {
std::memmove(buffer.get(), buffer.get() + offset, length - offset);
length -= offset;
return false;
}
offset += n;
}
length = 0;
return std::fflush(file) == 0;
}
void write(char c) { *reserve(1) = c; ++length; }
void write(__uint128_t value) {
char digits[40];
char *end = digits + sizeof(digits), *begin = end;
do { *--begin = char('0' + value % 10); value /= 10; } while (value);
write(std::string_view(begin, end - begin));
}
void write(__int128_t value) {
__uint128_t magnitude = __uint128_t(value);
if (value < 0) write('-'), magnitude = 0 - magnitude;
write(magnitude);
}
void write(std::string_view s) {
char *out = reserve(s.size());
if (!s.empty()) std::memcpy(out, s.data(), s.size());
length += s.size();
}
template <class T> requires std::is_integral_v<T>
void write(T value) {
char *out = reserve(32);
if constexpr (std::is_same_v<T, bool>) *out = '0' + value, ++length;
else if constexpr (std::is_unsigned_v<T> && sizeof(T) == 4) {
char *p = out;
if (value >= 100000000) {
auto high = value / 100000000, low = value % 100000000;
p = std::to_chars(p, p + 2, high).ptr;
std::memcpy(p, quads[low / 10000].data(), 4);
std::memcpy(p + 4, quads[low % 10000].data(), 4);
p += 8;
} else if (value >= 10000) {
p = std::to_chars(p, p + 4, value / 10000).ptr;
std::memcpy(p, quads[value % 10000].data(), 4);
p += 4;
} else p = std::to_chars(p, p + 4, value).ptr;
length += p - out;
} else length += std::to_chars(out, out + 32, value).ptr - out;
}
template <class T> requires requires(const T &value, char *out) { value.decimal_capacity(); value.to_chars(out); }
void write(const T &value) {
char *out = reserve(value.decimal_capacity());
length += value.to_chars(out) - out;
}
template <class T>
void println(const T &value) { write(value); write('\n'); }
};
#line 8 "test/li_chao_tree_segment.test.cpp"
#include <tuple>
#line 11 "test/li_chao_tree_segment.test.cpp"
using namespace std;
int main() {
FastInput input;
FastOutput output;
int n = 0, q = 0;
input.read(n), input.read(q);
struct Segment {
int64_t l, r, a, b;
};
vector<Segment> initial(n);
for (auto &[l, r, a, b] : initial) input.read(l), input.read(r), input.read(a), input.read(b);
struct Query {
int type, index;
Segment f;
};
vector<Query> queries(q);
vector<uint64_t> points;
points.reserve(2 * initial.size() + 2 * queries.size());
auto endpoint = [&](int64_t value, unsigned tag) { points.push_back((uint64_t(uint32_t(value) ^ (1U << 31)) << 32) | tag); };
for (int i = 0; i < n; ++i) { endpoint(initial[i].l, 4U * i); endpoint(initial[i].r, 4U * i + 1); }
for (auto &query : queries) {
input.read(query.type), input.read(query.f.l);
unsigned tag = 4U * unsigned(n + (&query - queries.data()));
if (query.type == 0) {
input.read(query.f.r), input.read(query.f.a), input.read(query.f.b);
endpoint(query.f.l, tag), endpoint(query.f.r, tag + 1);
} else endpoint(query.f.l, tag + 2);
}
if (none_of(queries.begin(), queries.end(), [](const Query &query) { return query.type == 1; })) return 0;
stable_radix_sort<11>(points, [](uint64_t point) { return uint32_t(point >> 32); });
vector<int64_t> xs;
xs.reserve(q);
for (size_t first = 0; first < points.size();) {
size_t last = first + 1;
while (last < points.size() && uint32_t(points[last] >> 32) == uint32_t(points[first] >> 32)) ++last;
bool queried = false;
for (size_t i = first; i < last; ++i) {
unsigned tag = uint32_t(points[i]), owner = tag / 4;
if ((tag & 3) == 2) { queries[owner - n].index = int(xs.size()); queried = true; }
else {
auto &segment = owner < unsigned(n) ? initial[owner] : queries[owner - n].f;
(tag & 1 ? segment.r : segment.l) = int(xs.size());
}
}
if (queried) xs.push_back(bit_cast<int32_t>(uint32_t(points[first] >> 32) ^ (1U << 31)));
first = last;
}
LiChaoTree<int64_t, false, int64_t> tree(std::move(xs));
for (auto [l, r, a, b] : initial) tree.add_segment_index(int(l), int(r), a, b);
for (auto query : queries) {
if (query.type == 0) tree.add_segment_index(int(query.f.l), int(query.f.r), query.f.a, query.f.b);
else {
auto value = tree.query_index(query.index);
if (value) output.println(*value);
else output.write("INFINITY\n");
}
}
}