cp-library
競技プログラミング用 C++ ライブラリ
test/kinetic_tournament.test.cpp
test/kinetic_tournament.test.cpp · GitHub で見る
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コード
#define PROBLEM "https://judge.yosupo.jp/problem/range_add_range_min"
#include "../data_structure/kinetic_tournament.hpp"
#include "../components/fast_io.hpp"
int main() {
FastInput in;
FastOutput out;
int n = 0, q = 0;
in.read(n); in.read(q);
std::vector<std::int64_t> values(n), slopes(n);
for (auto &value : values) in.read(value);
KineticTournament<std::int64_t, false> tree(slopes, values);
for (int i = 0; i < q; ++i) {
int type = 0, l = 0, r = 0;
in.read(type); in.read(l); in.read(r);
if (!type) { std::int64_t value = 0; in.read(value); tree.add(l, r, value); }
else out.println(tree.prod(l, r)->value);
}
}
#line 1 "test/kinetic_tournament.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_add_range_min"
#line 1 "data_structure/kinetic_tournament.hpp"
#line 1 "data_structure/segtree_beats.hpp"
#include <algorithm>
#include <bit>
#include <cassert>
#include <cstddef>
#include <limits>
#include <utility>
#include <vector>
template <class S, auto op, auto e, class F, auto mapping, auto composition, auto id>
class SegtreeBeats {
int n_ = 0, base_ = 1, log_ = 0;
std::vector<S> data_;
std::vector<F> lazy_;
std::vector<unsigned char> dirty_;
void check([[maybe_unused]] int l, [[maybe_unused]] int r) const {
assert(0 <= l && l <= r && r <= n_);
}
void pull(int k) { data_[k] = op(data_[2 * k], data_[2 * k + 1]); }
void all_apply(int k, const F &f) {
if (k < base_) {
lazy_[k] = dirty_[k] ? composition(f, lazy_[k]) : f;
dirty_[k] = 1;
}
if (mapping(f, data_[k])) return;
assert(k < base_);
push(k);
pull(k);
}
void push(int k) {
if (!dirty_[k]) return;
all_apply(2 * k, lazy_[k]);
all_apply(2 * k + 1, lazy_[k]);
dirty_[k] = 0;
}
void push_path(int k) {
for (int h = log_; h; --h) push(k >> h);
}
void push_range(int l, int r) {
for (int h = log_; h; --h) {
if (((l >> h) << h) != l) push(l >> h);
if (((r >> h) << h) != r) push((r - 1) >> h);
}
}
void pull_range(int l, int r) {
for (int h = 1; h <= log_; ++h) {
if (((l >> h) << h) != l) pull(l >> h);
if (((r >> h) << h) != r) pull((r - 1) >> h);
}
}
public:
SegtreeBeats() : SegtreeBeats(0) {}
explicit SegtreeBeats(int n, const S &value = e()) {
assert(0 <= n && n <= std::numeric_limits<int>::max() / 4);
build(std::vector<S>(n, value));
}
explicit SegtreeBeats(const std::vector<S> &a) { build(a); }
void build(const std::vector<S> &a) {
assert(a.size() <= std::size_t(std::numeric_limits<int>::max() / 4));
n_ = static_cast<int>(a.size());
base_ = static_cast<int>(std::bit_ceil(static_cast<unsigned>(std::max(1, n_))));
log_ = std::countr_zero(static_cast<unsigned>(base_));
data_.assign(2 * base_, e());
lazy_.assign(base_, id());
dirty_.assign(base_, 0);
std::copy(a.begin(), a.end(), data_.begin() + base_);
for (int k = base_ - 1; k; --k) pull(k);
}
int size() const { return n_; }
bool empty() const { return !n_; }
S all_prod() const { return data_[1]; }
S get(int p) {
assert(0 <= p && p < n_);
int k = p + base_;
push_path(k);
return data_[k];
}
void set(int p, const S &value) {
assert(0 <= p && p < n_);
int k = p + base_;
push_path(k);
data_[k] = value;
while (k >>= 1) pull(k);
}
S prod(int l, int r) {
check(l, r);
if (l == r) return e();
l += base_, r += base_;
push_range(l, r);
S left = e(), right = e();
while (l < r) {
if (l & 1) left = op(std::move(left), data_[l++]);
if (r & 1) right = op(data_[--r], std::move(right));
l >>= 1, r >>= 1;
}
return op(std::move(left), std::move(right));
}
void apply(const F &f) { if (n_) all_apply(1, f); }
void apply(int p, const F &f) {
assert(0 <= p && p < n_);
int k = p + base_;
push_path(k);
all_apply(k, f);
while (k >>= 1) pull(k);
}
void apply(int l, int r, const F &f) {
check(l, r);
if (l == r) return;
l += base_, r += base_;
push_range(l, r);
int first = l, last = r;
while (l < r) {
if (l & 1) all_apply(l++, f);
if (r & 1) all_apply(--r, f);
l >>= 1, r >>= 1;
}
pull_range(first, last);
}
template <class Predicate>
int max_right(int l, Predicate predicate) {
assert(0 <= l && l <= n_ && predicate(e()));
if (l == n_) return n_;
int k = l + base_;
push_path(k);
S value = e();
do {
while (!(k & 1)) k >>= 1;
S next = op(value, data_[k]);
if (!predicate(next)) {
while (k < base_) {
push(k);
k *= 2;
next = op(value, data_[k]);
if (predicate(next)) value = std::move(next), ++k;
}
return std::min(k - base_, n_);
}
value = std::move(next);
++k;
} while ((k & -k) != k);
return n_;
}
template <class Predicate>
int min_left(int r, Predicate predicate) {
assert(0 <= r && r <= n_ && predicate(e()));
if (!r) return 0;
int k = r + base_;
push_path(k - 1);
S value = e();
do {
--k;
while (k > 1 && (k & 1)) k >>= 1;
S next = op(data_[k], value);
if (!predicate(next)) {
while (k < base_) {
push(k);
k = 2 * k + 1;
next = op(data_[k], value);
if (predicate(next)) value = std::move(next), --k;
}
return k + 1 - base_;
}
value = std::move(next);
} while ((k & -k) != k);
return 0;
}
std::vector<S> values() {
for (int k = 1; k < base_; ++k) push(k);
return std::vector<S>(data_.begin() + base_, data_.begin() + base_ + n_);
}
};
#line 1 "components/kinetic_tournament_monoid.hpp"
#line 6 "components/kinetic_tournament_monoid.hpp"
#include <cstdint>
#line 8 "components/kinetic_tournament_monoid.hpp"
#include <type_traits>
namespace kinetic_tournament_detail {
template<class T, bool maximize> struct Monoid {
static_assert(std::is_integral_v<T> && std::is_signed_v<T> && sizeof(T) <= 8);
using W = __int128_t;
using U = std::uint64_t;
static constexpr U never = std::numeric_limits<U>::max();
struct Node { T value = 0, slope = 0; U remaining = never; int index = -1; };
struct Tag { W steps = 0, add = 0; };
static Node identity() { return {}; }
static Tag tag_identity() { return {}; }
static bool better(const Node &a, const Node &b) {
if (a.index == -1) return false;
if (b.index == -1) return true;
if (a.value != b.value) return maximize ? a.value > b.value : a.value < b.value;
return maximize ? a.index > b.index : a.index < b.index;
}
static Node op(Node a, Node b) {
if (a.index == -1) return b;
if (b.index == -1) return a;
bool left = better(a, b);
Node result = left ? a : b;
result.remaining = std::min(a.remaining, b.remaining);
if (left == maximize && a.slope < b.slope) {
U gap = U(a.value) - U(b.value);
U difference = U(b.slope) - U(a.slope);
assert(gap > 0);
result.remaining = std::min(result.remaining, (gap - 1) / difference);
}
return result;
}
static bool mapping(Tag tag, Node &node) {
if (node.index == -1) return true;
if (node.remaining != never && tag.steps > W(node.remaining)) return false;
W value = W(node.value) + tag.steps * node.slope + tag.add;
assert(std::numeric_limits<T>::lowest() <= value && value <= std::numeric_limits<T>::max());
node.value = T(value);
if (node.remaining != never) node.remaining -= U(tag.steps);
return true;
}
static Tag composition(Tag a, Tag b) { return {a.steps + b.steps, a.add + b.add}; }
};
}
#line 6 "data_structure/kinetic_tournament.hpp"
#include <optional>
template<class T = std::int64_t, bool maximize = true> class KineticTournament {
using M = kinetic_tournament_detail::Monoid<T, maximize>;
using Node = typename M::Node;
SegtreeBeats<Node, M::op, M::identity, typename M::Tag, M::mapping, M::composition, M::tag_identity> tree_;
std::vector<T> slopes_;
std::vector<unsigned char> active_;
int count_ = 0;
void check([[maybe_unused]] int i) const { assert(0 <= i && i < size()); }
void check([[maybe_unused]] int l, [[maybe_unused]] int r) const { assert(0 <= l && l <= r && r <= size()); }
public:
struct Result { int index; T value; };
using value_type = T;
KineticTournament() = default;
explicit KineticTournament(const std::vector<T> &slopes, T value = 0) { build(slopes, value); }
KineticTournament(const std::vector<T> &slopes, const std::vector<T> &values) { build(slopes, values); }
KineticTournament(const std::vector<T> &slopes, const std::vector<std::optional<T>> &values) { build(slopes, values); }
KineticTournament(const std::vector<T> &slopes, std::nullopt_t) { build(slopes, std::nullopt); }
KineticTournament(const KineticTournament &) = default;
KineticTournament &operator=(const KineticTournament &) = default;
KineticTournament(KineticTournament &&other) : KineticTournament() { swap(other); }
KineticTournament &operator=(KineticTournament &&other) {
if (this != &other) { KineticTournament next(std::move(other)); swap(next); }
return *this;
}
void swap(KineticTournament &other) noexcept {
std::swap(tree_, other.tree_);
slopes_.swap(other.slopes_); active_.swap(other.active_); std::swap(count_, other.count_);
}
void build(const std::vector<T> &slopes, const std::vector<std::optional<T>> &values) {
assert(slopes.size() == values.size() && slopes.size() <= std::size_t(std::numeric_limits<int>::max() / 4));
assert(std::is_sorted(slopes.begin(), slopes.end()));
slopes_ = slopes;
active_.assign(slopes.size(), 0);
count_ = 0;
std::vector<Node> nodes(slopes.size());
for (int i = 0; i < size(); ++i) if (values[i]) {
nodes[i] = {*values[i], slopes_[i], M::never, i};
active_[i] = 1; ++count_;
}
tree_.build(nodes);
}
void build(const std::vector<T> &slopes, const std::vector<T> &values) { build(slopes, std::vector<std::optional<T>>(values.begin(), values.end())); }
void build(const std::vector<T> &slopes, T value = 0) { build(slopes, std::vector<std::optional<T>>(slopes.size(), value)); }
void build(const std::vector<T> &slopes, std::nullopt_t) { build(slopes, std::vector<std::optional<T>>(slopes.size())); }
int size() const { return static_cast<int>(slopes_.size()); }
int active_size() const { return count_; }
bool empty() const { return count_ == 0; }
const std::vector<T> &slopes() const { return slopes_; }
void clear() { tree_.build(std::vector<Node>(size())); std::fill(active_.begin(), active_.end(), 0); count_ = 0; }
void set(int i, T value) {
check(i);
tree_.set(i, Node{value, slopes_[i], M::never, i});
count_ += !active_[i]; active_[i] = 1;
}
bool erase(int i) {
check(i);
if (!active_[i]) return false;
tree_.set(i, M::identity());
active_[i] = 0; --count_;
return true;
}
std::optional<T> get(int i) { check(i); return active_[i] ? std::optional<T>(tree_.get(i).value) : std::nullopt; }
void apply(int l, int r, T a, T b = 0) {
check(l, r); assert(a >= 0);
if (l == r || (!a && !b)) return;
if (!l && r == size()) tree_.apply({a, b});
else tree_.apply(l, r, {a, b});
}
void add(int l, int r, T value) { apply(l, r, 0, value); }
void advance(int l, int r, T steps = 1) { apply(l, r, steps, 0); }
void all_apply(T a, T b = 0) { apply(0, size(), a, b); }
std::optional<Result> prod(int l, int r) {
check(l, r);
if (!l && r == size()) return all_prod();
auto node = tree_.prod(l, r);
return node.index == -1 ? std::nullopt : std::optional<Result>(Result{node.index, node.value});
}
std::optional<Result> all_prod() const {
auto node = tree_.all_prod();
return node.index == -1 ? std::nullopt : std::optional<Result>(Result{node.index, node.value});
}
std::vector<std::optional<T>> values() {
auto nodes = tree_.values();
std::vector<std::optional<T>> result(size());
for (int i = 0; i < size(); ++i) if (active_[i]) result[i] = nodes[i].value;
return result;
}
};
#line 1 "components/fast_io.hpp"
#line 5 "components/fast_io.hpp"
#include <array>
#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 4 "test/kinetic_tournament.test.cpp"
int main() {
FastInput in;
FastOutput out;
int n = 0, q = 0;
in.read(n); in.read(q);
std::vector<std::int64_t> values(n), slopes(n);
for (auto &value : values) in.read(value);
KineticTournament<std::int64_t, false> tree(slopes, values);
for (int i = 0; i < q; ++i) {
int type = 0, l = 0, r = 0;
in.read(type); in.read(l); in.read(r);
if (!type) { std::int64_t value = 0; in.read(value); tree.add(l, r, value); }
else out.println(tree.prod(l, r)->value);
}
}