cp-library
競技プログラミング用 C++ ライブラリ
test/sortable_segtree.test.cpp
test/sortable_segtree.test.cpp · GitHub で見る
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コード
#define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_sort_range_composite"
#include "../components/fast_io.hpp"
#include "../data_structure/sortable_segtree.hpp"
struct Affine { std::uint32_t a, b; };
Affine compose(Affine f, Affine g) {
return {std::uint32_t(std::uint64_t(g.a) * f.a % 998244353), std::uint32_t((std::uint64_t(g.a) * f.b + g.b) % 998244353)};
}
Affine identity() { return {1, 0}; }
int main() {
FastInput in;
FastOutput out;
int n = 0, q = 0;
in.read(n), in.read(q);
std::vector<std::pair<std::uint32_t, Affine>> a(n);
for (auto &[key, f] : a) in.read(key), in.read(f.a), in.read(f.b);
SortableSegtree<std::uint32_t, Affine, compose, identity> tree(a);
while (q--) {
int type = 0, l = 0, r = 0;
in.read(type), in.read(l);
if (type == 0) {
std::uint32_t key = 0, x = 0, y = 0;
in.read(key), in.read(x), in.read(y);
tree.set(l, key, {x, y});
} else {
in.read(r);
if (type == 1) {
std::uint32_t x = 0;
in.read(x);
auto f = tree.prod(l, r);
out.println((std::uint64_t(f.a) * x + f.b) % 998244353);
} else tree.sort(l, r, type == 3);
}
}
}
#line 1 "test/sortable_segtree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_sort_range_composite"
#line 1 "components/fast_io.hpp"
#include <algorithm>
#include <array>
#include <bit>
#include <cassert>
#include <charconv>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstring>
#include <memory>
#include <stdexcept>
#include <string>
#include <string_view>
#include <type_traits>
#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 1 "data_structure/sortable_segtree.hpp"
#line 1 "components/predecessor_set.hpp"
#line 1 "components/xor_select.hpp"
#line 7 "components/xor_select.hpp"
namespace xor_select_detail {
inline unsigned argmin(std::uint64_t word, unsigned key) {
assert(word && key < 64);
if (std::has_single_bit(word)) return std::countr_zero(word);
if ((word >> key) & 1) return key;
unsigned shift = key & 32;
word = std::rotl(word, shift);
auto exchange = [&](unsigned shift, std::uint64_t mask) {
word = ((word & mask) << shift) | ((word & ~mask) >> shift);
};
exchange(key & 16, 0x0000ffff0000ffffULL);
exchange(key & 8, 0x00ff00ff00ff00ffULL);
exchange(key & 4, 0x0f0f0f0f0f0f0f0fULL);
exchange(key & 2, 0x3333333333333333ULL);
exchange(key & 1, 0x5555555555555555ULL);
return std::countr_zero(word) ^ key;
}
}
#line 12 "components/predecessor_set.hpp"
#include <limits>
#include <span>
#line 15 "components/predecessor_set.hpp"
#include <utility>
#include <vector>
#if defined(__x86_64__) && (defined(__GNUC__) || defined(__clang__))
#include <immintrin.h>
#endif
namespace predecessor_set_detail {
inline void pack_scalar(const char *src, std::uint64_t *dst, std::size_t words) {
for (std::size_t i = 0; i < words; ++i) {
std::uint64_t word = 0;
if constexpr (std::endian::native == std::endian::little) {
for (int j = 0; j < 8; ++j) {
std::uint64_t x;
std::memcpy(&x, src + i * 64 + j * 8, 8);
assert((x & 0xfefefefefefefefeULL) == 0x3030303030303030ULL);
word |= ((x & 0x0101010101010101ULL) * 0x0102040810204080ULL >> 56) << (j * 8);
}
} else {
for (int j = 0; j < 64; ++j) {
assert(src[i * 64 + j] == '0' || src[i * 64 + j] == '1');
word |= std::uint64_t(src[i * 64 + j] - '0') << j;
}
}
dst[i] = word;
}
}
#if defined(__x86_64__) && (defined(__GNUC__) || defined(__clang__))
__attribute__((target("avx2"))) inline void pack_avx2(const char *src, std::uint64_t *dst, std::size_t words) {
const auto ones = _mm256_set1_epi8('1');
for (std::size_t i = 0; i < words; ++i) {
auto a = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(src + i * 64));
auto b = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(src + i * 64 + 32));
assert(_mm256_movemask_epi8(_mm256_cmpeq_epi8(_mm256_and_si256(a, _mm256_set1_epi8(-2)), _mm256_set1_epi8('0'))) == -1);
assert(_mm256_movemask_epi8(_mm256_cmpeq_epi8(_mm256_and_si256(b, _mm256_set1_epi8(-2)), _mm256_set1_epi8('0'))) == -1);
auto low = std::uint32_t(_mm256_movemask_epi8(_mm256_cmpeq_epi8(a, ones)));
auto high = std::uint32_t(_mm256_movemask_epi8(_mm256_cmpeq_epi8(b, ones)));
dst[i] = low | (std::uint64_t(high) << 32);
}
}
#endif
inline void pack(const char *src, std::uint64_t *dst, std::size_t words) {
#if defined(__x86_64__) && (defined(__GNUC__) || defined(__clang__))
if (words >= 4 && __builtin_cpu_supports("avx2")) return pack_avx2(src, dst, words);
#endif
pack_scalar(src, dst, words);
}
}
class PredecessorSet {
int n = 0, count = 0, height = 0;
std::array<int, 6> offset{}, length{};
std::array<int, 16> small{};
bool small_valid = false;
std::vector<std::uint64_t> data;
void mask_tail() {
int bits = n;
for (int h = 0; h < height; ++h) {
if (bits & 63) data[offset[h] + length[h] - 1] &= ~std::uint64_t(0) >> (64 - (bits & 63));
bits = length[h];
}
}
void rebuild() {
count = 0;
for (int i = 0; i < length[0]; ++i) count += std::popcount(data[i]);
for (int h = 1; h < height; ++h)
for (int i = 0; i < length[h - 1]; ++i)
if (data[offset[h - 1] + i]) data[offset[h] + (i >> 6)] |= std::uint64_t(1) << (i & 63);
rebuild_small();
}
template <int H, bool Forward> int descend(int p) const {
if constexpr (H == 0) return p;
else {
auto word = data[offset[H - 1] + p];
int bit = Forward ? std::countr_zero(word) : 63 - std::countl_zero(word);
return descend<H - 1, Forward>(p * 64 + bit);
}
}
template <int H, bool Forward> int ascend(int p) const {
if constexpr (H == 6) return Forward ? n : -1;
else {
if (H >= height) return Forward ? n : -1;
auto word = data[offset[H] + (p >> 6)];
auto mask = Forward ? (~std::uint64_t(1) << (p & 63)) : ~(~std::uint64_t(0) << (p & 63));
word &= mask;
if (word) {
int bit = Forward ? std::countr_zero(word) : 63 - std::countl_zero(word);
return descend<H, Forward>((p & ~63) + bit);
}
return ascend<H + 1, Forward>(p >> 6);
}
}
void rebuild_small() {
small_valid = count <= int(small.size());
if (!small_valid) return;
small.fill(n);
for (int i = 0, p = 0; i < count; ++i) {
auto word = data[p >> 6] >> (p & 63);
p = word ? p + std::countr_zero(word) : ascend<1, true>(p >> 6);
small[i] = p++;
}
}
int small_rank(int p) const {
#if defined(__AVX512F__) && defined(__x86_64__)
auto keys = _mm512_loadu_si512(small.data());
return std::popcount(unsigned(_mm512_cmp_epi32_mask(keys, _mm512_set1_epi32(p), _MM_CMPINT_LT)));
#elif defined(__AVX2__) && defined(__x86_64__)
auto key = _mm256_set1_epi32(p);
auto a = _mm256_cmpgt_epi32(key, _mm256_loadu_si256(reinterpret_cast<const __m256i *>(small.data())));
auto b = _mm256_cmpgt_epi32(key, _mm256_loadu_si256(reinterpret_cast<const __m256i *>(small.data() + 8)));
return std::popcount(unsigned(_mm256_movemask_ps(_mm256_castsi256_ps(a)))) + std::popcount(unsigned(_mm256_movemask_ps(_mm256_castsi256_ps(b))));
#else
int result = 0;
for (int x : small) result += x < p;
return result;
#endif
}
public:
int argmin_xor(std::uint32_t x) const {
if (!count) return -1;
std::uint64_t p = std::uint64_t(x) & ((std::uint64_t(1) << (height * 6)) - 1);
for (int h = 0; h < height; ++h, p >>= 6) {
auto index = p >> 6;
if (index >= unsigned(length[h])) continue;
auto word = data[offset[h] + index];
if (!word) continue;
p = index * 64 + xor_select_detail::argmin(word, p & 63);
while (h--) p = p * 64 + xor_select_detail::argmin(data[offset[h] + p], (x >> (h * 6)) & 63);
return int(p);
}
return -1;
}
int argmax_xor(std::uint32_t x) const { return argmin_xor(~x); }
explicit PredecessorSet(int n = 0, bool filled = false) { assign(n, filled); }
explicit PredecessorSet(std::string_view bits) { assign(bits); }
PredecessorSet(int n, std::span<const std::uint64_t> words) { assign(n, words); }
PredecessorSet(const PredecessorSet &) = default;
PredecessorSet &operator=(const PredecessorSet &) = default;
PredecessorSet(PredecessorSet &&other) noexcept : PredecessorSet() { swap(other); }
PredecessorSet &operator=(PredecessorSet &&other) noexcept {
if (this != &other) { PredecessorSet moved(std::move(other)); swap(moved); }
return *this;
}
void assign(int length, bool filled = false) {
assert(length >= 0);
n = length; count = filled ? n : 0; height = 0;
offset.fill(0); this->length.fill(0);
int total = 0;
for (std::size_t bits = n; bits;) {
std::size_t words = (bits + 63) / 64;
offset[height] = total; this->length[height++] = words;
total += words;
if (words == 1) break;
bits = words;
}
data.assign(total, filled ? ~std::uint64_t(0) : 0);
if (filled) mask_tail();
rebuild_small();
}
void assign(std::string_view bits) {
assert(bits.size() <= std::size_t(std::numeric_limits<int>::max()));
PredecessorSet next(static_cast<int>(bits.size()));
std::size_t words = bits.size() / 64;
predecessor_set_detail::pack(bits.data(), next.data.data(), words);
for (std::size_t i = words * 64; i < bits.size(); ++i) {
assert(bits[i] == '0' || bits[i] == '1');
next.data[i >> 6] |= std::uint64_t(bits[i] - '0') << (i & 63);
}
next.rebuild(); swap(next);
}
void assign(int n, std::span<const std::uint64_t> words) {
assert(n >= 0 && words.size() == (std::size_t(n) + 63) / 64);
PredecessorSet next(n);
std::copy(words.begin(), words.end(), next.data.begin());
if (n & 63) next.data[next.length[0] - 1] &= ~std::uint64_t(0) >> (64 - (n & 63));
next.rebuild(); swap(next);
}
int universe_size() const { return n; }
int size() const { return count; }
bool empty() const { return count == 0; }
bool contains(int p) const { assert(0 <= p && p < n); return data[p >> 6] >> (p & 63) & 1; }
bool insert(int p) {
assert(0 <= p && p < n);
int index = p >> 6;
auto &leaf = data[index];
auto mask = std::uint64_t(1) << (p & 63), before = leaf;
leaf = before | mask;
bool changed = !(before & mask);
count += changed;
if (!before) for (int h = 1; h < height; ++h) {
auto &word = data[offset[h] + (index >> 6)];
auto old = word;
word |= std::uint64_t(1) << (index & 63);
if (old) break;
index >>= 6;
}
small_valid = false;
return changed;
}
bool erase(int p) {
assert(0 <= p && p < n);
int index = p >> 6;
auto &leaf = data[index];
auto mask = std::uint64_t(1) << (p & 63), before = leaf;
leaf = before & ~mask;
bool changed = (before & mask) != 0;
count -= changed;
if (before && !leaf) for (int h = 1; h < height; ++h) {
auto &word = data[offset[h] + (index >> 6)];
word &= ~(std::uint64_t(1) << (index & 63));
if (word) break;
index >>= 6;
}
small_valid = false;
return changed;
}
int next(int p) const {
p = std::max(p, 0);
if (p >= n || !count) return n;
if (small_valid) {
int index = small_rank(p);
return index == count ? n : small[index];
}
auto local = data[p >> 6] >> (p & 63);
if (local) return p + std::countr_zero(local);
return ascend<1, true>(p >> 6);
}
int prev(int p) const {
p = std::min(p, n - 1);
if (p < 0 || !count) return -1;
if (small_valid) {
int index = small_rank(p + 1);
return index ? small[index - 1] : -1;
}
auto local = data[p >> 6] << (63 - (p & 63));
if (local) return p - std::countl_zero(local);
return ascend<1, false>(p >> 6);
}
bool set(int p, bool present) {
assert(0 <= p && p < n);
int index = p >> 6;
auto &leaf = data[index];
auto mask = std::uint64_t(1) << (p & 63), before = leaf;
auto fill = std::uint64_t(0) - present;
leaf = before ^ ((before ^ fill) & mask);
bool old = (before & mask) != 0;
count += int(present) - int(old);
if ((!before) != (!leaf)) for (int h = 1; h < height; ++h) {
auto &word = data[offset[h] + (index >> 6)];
auto previous = word;
word = previous ^ ((previous ^ fill) & (std::uint64_t(1) << (index & 63)));
if ((!previous) == (!word)) break;
index >>= 6;
}
small_valid = false;
return old != present;
}
int min() const { return next(0); }
int max() const { return prev(n - 1); }
void clear() { std::fill(data.begin(), data.end(), 0); count = 0; small_valid = false; }
void fill() {
std::fill(data.begin(), data.end(), ~std::uint64_t(0));
mask_tail();
count = n;
rebuild_small();
}
template <class F> void for_each(int l, int r, F &&f) const {
assert(0 <= l && l <= r && r <= n);
for (int p = next(l); p < r;) {
int base = p & ~63;
auto word = data[p >> 6] & (~std::uint64_t(0) << (p & 63));
if (r - base < 64) word &= ~std::uint64_t(0) >> (64 - (r - base));
while (word) { f(base + std::countr_zero(word)); word &= word - 1; }
if (r - base <= 64) break;
p = next(base + 64);
}
}
template <class F> void for_each(F &&f) const { for_each(0, n, f); }
std::vector<int> to_vector() const {
std::vector<int> out; out.reserve(count);
for_each([&](int x) { out.push_back(x); }); return out;
}
std::span<const std::uint64_t> words() const & { return {data.data(), std::size_t(length[0])}; }
void words() const && = delete;
void swap(PredecessorSet &other) noexcept {
using std::swap;
swap(n, other.n); swap(count, other.count); swap(height, other.height);
offset.swap(other.offset); length.swap(other.length); data.swap(other.data); small.swap(other.small); swap(small_valid, other.small_valid);
}
std::size_t memory_usage() const { return data.capacity() * sizeof(std::uint64_t); }
};
#line 14 "data_structure/sortable_segtree.hpp"
template <class Key, class S, auto op, auto e, bool commutative = false>
class SortableSegtree {
static_assert(std::is_integral_v<Key> && !std::is_same_v<Key, bool> && sizeof(Key) <= 8);
using U = std::make_unsigned_t<Key>;
static constexpr U sign = std::is_signed_v<Key> ? U(1) << (std::numeric_limits<U>::digits - 1) : 0;
struct Empty {};
using Back = std::conditional_t<commutative, Empty, S>;
struct Node {
int left = 0, right = 0, count = 1, bit = -1, leaf;
S forward;
[[no_unique_address]] Back backward;
static Back back(const S &value) { if constexpr (commutative) return {}; else return value; }
Node(S value, int leaf) : leaf(leaf), forward(std::move(value)), backward(back(forward)) {}
};
int n = 0, base = 1, free = 0;
std::vector<U> keys;
std::vector<Node> pool;
std::vector<int> roots;
std::vector<unsigned char> reversed;
std::vector<S> aggregate;
PredecessorSet boundaries;
int difference(int a, int b) const {
U x = keys[pool[a].leaf] ^ keys[pool[b].leaf];
return x ? 30 + int(std::bit_width(x)) : int(std::bit_width(unsigned(pool[a].leaf ^ pool[b].leaf))) - 1;
}
bool side(int x, int bit) const {
return bit >= 31 ? keys[pool[x].leaf] >> (bit - 31) & 1 : unsigned(pool[x].leaf) >> bit & 1;
}
S product(int x, [[maybe_unused]] bool reverse) const {
if constexpr (commutative) return pool[x].forward;
else return reverse ? pool[x].backward : pool[x].forward;
}
void pull(int x) {
auto &node = pool[x];
const auto &a = pool[node.left], &b = pool[node.right];
node.leaf = a.leaf;
node.count = a.count + b.count;
node.forward = op(a.forward, b.forward);
if constexpr (!commutative) node.backward = op(b.backward, a.backward);
}
void release(int x) { pool[x].left = free; free = x; }
int branch(int bit, int a, int b) {
if (side(a, bit)) std::swap(a, b);
int x;
if (free) { x = free; free = pool[x].left; }
else { x = pool.size(); pool.emplace_back(e(), 0); }
pool[x].left = a; pool[x].right = b; pool[x].bit = bit;
pull(x); return x;
}
int meld(int a, int b) {
if (!a || !b) return a | b;
int bit = difference(a, b), ab = pool[a].bit, bb = pool[b].bit;
if (bit > std::max(ab, bb)) return branch(bit, a, b);
assert(ab >= 0 || bb >= 0);
if (ab == bb) {
pool[a].left = meld(pool[a].left, pool[b].left);
pool[a].right = meld(pool[a].right, pool[b].right);
release(b);
} else {
if (ab < bb) std::swap(a, b), std::swap(ab, bb);
if (side(b, ab)) pool[a].right = meld(pool[a].right, b);
else pool[a].left = meld(pool[a].left, b);
}
pull(a); return a;
}
std::pair<int, int> split(int x, int k) {
if (!k) return {0, x};
if (k == pool[x].count) return {x, 0};
int a = pool[x].left, b = pool[x].right, count = pool[a].count;
if (k == count) { release(x); return {a, b}; }
if (k < count) {
auto [first, second] = split(a, k);
pool[x].left = second; pull(x); return {first, x};
}
auto [first, second] = split(b, k - count);
pool[x].right = first; pull(x); return {x, second};
}
int at(int x, int k) const {
while (pool[x].bit >= 0) {
int count = pool[pool[x].left].count;
if (k < count) x = pool[x].left;
else k -= count, x = pool[x].right;
}
return x;
}
[[gnu::always_inline]] int locate(int p) const {
assert(0 <= p && p < n);
int l = boundaries.prev(p), x = roots[l], k = p - l;
return at(x, reversed[l] ? pool[x].count - 1 - k : k);
}
S fold(int x, int l, int r, bool reverse) const {
if (!l && r == pool[x].count) return product(x, reverse);
int a = reverse ? pool[x].right : pool[x].left, b = reverse ? pool[x].left : pool[x].right;
int count = pool[a].count;
if (r <= count) return fold(a, l, r, reverse);
if (l >= count) return fold(b, l - count, r - count, reverse);
return op(fold(a, l, count, reverse), fold(b, 0, r - count, reverse));
}
void update(int p, S value) {
aggregate[p += base] = std::move(value);
while (p >>= 1) aggregate[p] = op(aggregate[p * 2], aggregate[p * 2 + 1]);
}
S middle_prod(int l, int r) const {
S a = e(), b = e();
for (l += base, r += base; l < r; l >>= 1, r >>= 1) {
if (l & 1) a = op(std::move(a), aggregate[l++]);
if (r & 1) b = op(aggregate[--r], std::move(b));
}
return op(std::move(a), std::move(b));
}
void cut(int p) {
if (boundaries.contains(p)) return;
int l = boundaries.prev(p), x = roots[l], k = p - l;
if (reversed[l]) k = pool[x].count - k;
auto [a, b] = split(x, k);
if (reversed[l]) std::swap(a, b);
roots[l] = a; roots[p] = b; reversed[p] = reversed[l];
boundaries.insert(p);
update(l, product(a, reversed[l])); update(p, product(b, reversed[p]));
}
void set_value(int x, int k, S value) {
if (pool[x].bit < 0) {
pool[x].forward = std::move(value);
if constexpr (!commutative) pool[x].backward = pool[x].forward;
return;
}
int count = pool[pool[x].left].count;
if (k < count) set_value(pool[x].left, k, std::move(value));
else set_value(pool[x].right, k - count, std::move(value));
pull(x);
}
void collect(int x, bool reverse, std::vector<std::pair<Key, S>> &out) const {
if (pool[x].bit < 0) { out.emplace_back(Key(keys[pool[x].leaf] ^ sign), pool[x].forward); return; }
collect(reverse ? pool[x].right : pool[x].left, reverse, out);
collect(reverse ? pool[x].left : pool[x].right, reverse, out);
}
public:
SortableSegtree() : aggregate(2, e()) {}
explicit SortableSegtree(const std::vector<std::pair<Key, S>> &a) { assign(a); }
SortableSegtree(const SortableSegtree &) = default;
SortableSegtree &operator=(const SortableSegtree &) = default;
SortableSegtree(SortableSegtree &&other) : SortableSegtree() { swap(other); }
SortableSegtree &operator=(SortableSegtree &&other) {
if (this != &other) { SortableSegtree moved(std::move(other)); swap(moved); }
return *this;
}
void swap(SortableSegtree &other) {
using std::swap;
swap(n, other.n); swap(base, other.base); swap(free, other.free);
keys.swap(other.keys); pool.swap(other.pool); roots.swap(other.roots); reversed.swap(other.reversed);
aggregate.swap(other.aggregate); swap(boundaries, other.boundaries);
}
void assign(const std::vector<std::pair<Key, S>> &a) {
assert(a.size() < (std::size_t(1) << 29));
n = a.size(); base = std::bit_ceil(unsigned(std::max(n, 1))); free = 0;
keys.clear(); keys.reserve(n);
pool.clear(); pool.reserve(2 * std::size_t(n) + 1);
pool.emplace_back(e(), 0); pool[0].count = 0;
roots.resize(n); reversed.assign(n, 0); aggregate.assign(2 * base, e());
boundaries.assign(n + 1, true);
for (int i = 0; i < n; ++i) {
keys.push_back(U(a[i].first) ^ sign);
pool.emplace_back(a[i].second, i); roots[i] = i + 1;
aggregate[base + i] = a[i].second;
}
for (int i = base - 1; i; --i) aggregate[i] = op(aggregate[i * 2], aggregate[i * 2 + 1]);
}
int size() const { return n; }
bool empty() const { return n == 0; }
std::pair<Key, S> get(int p) const {
int x = locate(p);
return {Key(keys[pool[x].leaf] ^ sign), pool[x].forward};
}
Key key(int p) const { return Key(keys[pool[locate(p)].leaf] ^ sign); }
void set(int p, Key key, S value) {
assert(0 <= p && p < n);
cut(p); cut(p + 1);
int x = roots[p]; keys[pool[x].leaf] = U(key) ^ sign;
pool[x].forward = std::move(value);
if constexpr (!commutative) pool[x].backward = pool[x].forward;
update(p, pool[x].forward);
}
void set(int p, S value) {
assert(0 <= p && p < n);
int l = boundaries.prev(p), x = roots[l], k = p - l;
set_value(x, reversed[l] ? pool[x].count - 1 - k : k, std::move(value));
update(l, product(x, reversed[l]));
}
S prod(int l, int r) const {
assert(0 <= l && l <= r && r <= n);
if (l == r) return e();
int first = boundaries.prev(l), last = boundaries.prev(r - 1);
if (first == last) return fold(roots[first], l - first, r - first, reversed[first]);
int end = first + pool[roots[first]].count;
S value = fold(roots[first], l - first, end - first, reversed[first]);
if (end < last) value = op(std::move(value), middle_prod(end, last));
return op(std::move(value), fold(roots[last], 0, r - last, reversed[last]));
}
S all_prod() const { return aggregate[1]; }
void sort(int l, int r, bool descending = false) {
assert(0 <= l && l <= r && r <= n);
if (r - l <= 1) return;
cut(l); cut(r);
for (int p = boundaries.next(l + 1); p < r; p = boundaries.next(p + 1)) {
roots[l] = meld(roots[l], roots[p]); roots[p] = 0;
boundaries.erase(p); update(p, e());
}
reversed[l] = descending; update(l, product(roots[l], descending));
}
std::vector<std::pair<Key, S>> to_vector() const {
std::vector<std::pair<Key, S>> out;
out.reserve(n);
for (int i = 0; i < n; ++i) if (roots[i]) collect(roots[i], reversed[i], out);
return out;
}
void clear() { assign({}); }
std::size_t memory_usage() const {
return keys.capacity() * sizeof(U) + pool.capacity() * sizeof(Node) + roots.capacity() * sizeof(int)
+ reversed.capacity() + aggregate.capacity() * sizeof(S) + boundaries.memory_usage();
}
};
#line 4 "test/sortable_segtree.test.cpp"
struct Affine { std::uint32_t a, b; };
Affine compose(Affine f, Affine g) {
return {std::uint32_t(std::uint64_t(g.a) * f.a % 998244353), std::uint32_t((std::uint64_t(g.a) * f.b + g.b) % 998244353)};
}
Affine identity() { return {1, 0}; }
int main() {
FastInput in;
FastOutput out;
int n = 0, q = 0;
in.read(n), in.read(q);
std::vector<std::pair<std::uint32_t, Affine>> a(n);
for (auto &[key, f] : a) in.read(key), in.read(f.a), in.read(f.b);
SortableSegtree<std::uint32_t, Affine, compose, identity> tree(a);
while (q--) {
int type = 0, l = 0, r = 0;
in.read(type), in.read(l);
if (type == 0) {
std::uint32_t key = 0, x = 0, y = 0;
in.read(key), in.read(x), in.read(y);
tree.set(l, key, {x, y});
} else {
in.read(r);
if (type == 1) {
std::uint32_t x = 0;
in.read(x);
auto f = tree.prod(l, r);
out.println((std::uint64_t(f.a) * x + f.b) % 998244353);
} else tree.sort(l, r, type == 3);
}
}
}