cp-library
競技プログラミング用 C++ ライブラリ
test/mo_inversions.test.cpp
test/mo_inversions.test.cpp · GitHub で見る
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コード
#define PROBLEM "https://judge.yosupo.jp/problem/static_range_inversions_query"
#include "data_structure/static_range_inversions.hpp"
#include "components/fast_io_bulk.hpp"
#include <cstdint>
int main() {
FastInput input;
FastOutput output;
int n = 0, q = 0;
input.read(n), input.read(q);
std::vector<int> a(n);
std::size_t position = 0;
read_unsigned_records<1>(input, n, [&](std::uint32_t value) { a[position++] = value; });
std::vector<std::pair<int, int>> ranges(q);
position = 0;
read_unsigned_records<2>(input, q, [&](std::uint32_t l, std::uint32_t r) { ranges[position++] = {int(l), int(r)}; });
auto answer = static_range_inversion_counts(a, ranges);
for (auto x : answer) output.println(x);
}
#line 1 "test/mo_inversions.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/static_range_inversions_query"
#line 1 "data_structure/static_range_inversions.hpp"
#line 1 "sequence/inversion_count.hpp"
#include <algorithm>
#include <cassert>
#include <cstddef>
#include <cstdint>
#include <functional>
#include <limits>
#include <ranges>
#include <type_traits>
#include <vector>
template<class Range, class Compare = std::less<>>
requires std::ranges::random_access_range<const Range> && std::ranges::sized_range<const Range>
std::int64_t inversion_count(const Range &a, Compare compare = {}) {
assert(std::ranges::size(a) <= std::size_t(std::numeric_limits<int>::max()));
const std::size_t n = std::ranges::size(a);
auto first = std::ranges::begin(a);
std::size_t ordered = 1;
while (ordered < n && !compare(first[ordered], first[ordered - 1])) ++ordered;
if (ordered >= n) return 0;
std::int64_t equal_pairs = 0;
std::size_t run = 1, reversed = 1;
for (; reversed < n && !compare(first[reversed - 1], first[reversed]); ++reversed) {
if (compare(first[reversed], first[reversed - 1])) run = 1;
else equal_pairs += static_cast<std::int64_t>(run++);
}
if (reversed == n) return static_cast<std::int64_t>(n) * (n - 1) / 2 - equal_pairs;
using T = std::ranges::range_value_t<const Range>;
constexpr bool cached = std::is_trivially_copyable_v<T> && sizeof(T) <= 16 &&
std::is_default_constructible_v<T> && std::is_copy_constructible_v<T> &&
std::is_copy_assignable_v<T> && !std::is_same_v<T, bool>;
using Stored = std::conditional_t<cached, T, int>;
std::vector<Stored> current(n), buffer(n);
for (std::size_t i = 0; i < n; ++i) {
if constexpr (cached) current[i] = first[i];
else current[i] = static_cast<int>(i);
}
auto value = [&](const Stored &x) -> decltype(auto) {
if constexpr (cached) return (x);
else return first[x];
};
std::int64_t result = 0;
constexpr std::size_t block = 8;
for (std::size_t l = 0; l < n; l += block) {
const auto end = std::min(l + block, n);
for (std::size_t i = l + 1; i < end; ++i) {
Stored x = current[i];
std::size_t j = i;
while (j > l && compare(value(x), value(current[j - 1]))) current[j] = current[j - 1], --j;
current[j] = x;
result += static_cast<std::int64_t>(i - j);
}
}
for (std::size_t width = block; width < n; width *= 2) {
for (std::size_t l = 0; l < n; l += 2 * width) {
const auto mid = std::min(l + width, n), r = std::min(l + 2 * width, n);
if (mid == r || !compare(value(current[mid]), value(current[mid - 1]))) {
std::copy(current.begin() + l, current.begin() + r, buffer.begin() + l);
continue;
}
if (compare(value(current[r - 1]), value(current[l]))) {
result += static_cast<std::int64_t>(mid - l) * (r - mid);
std::copy(current.begin() + mid, current.begin() + r, buffer.begin() + l);
std::copy(current.begin() + l, current.begin() + mid, buffer.begin() + (l + r - mid));
continue;
}
std::size_t i = l, j = mid, k = l;
while (i < mid && j < r) {
if (compare(value(current[j]), value(current[i]))) {
buffer[k++] = current[j++];
result += static_cast<std::int64_t>(mid - i);
} else buffer[k++] = current[i++];
}
std::copy(current.begin() + i, current.begin() + mid, buffer.begin() + k);
std::copy(current.begin() + j, current.begin() + r, buffer.begin() + (k + mid - i));
}
current.swap(buffer);
}
return result;
}
#line 1 "components/radix_sort.hpp"
#line 5 "components/radix_sort.hpp"
#include <array>
#line 9 "components/radix_sort.hpp"
#include <utility>
#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 "data_structure/mo_order.hpp"
#line 7 "data_structure/mo_order.hpp"
#include <cmath>
#line 12 "data_structure/mo_order.hpp"
inline std::vector<int> mo_order(const std::vector<std::pair<int, int>>& ranges, int block_size = 0) {
assert(ranges.size() <= std::size_t(std::numeric_limits<int>::max()) && block_size >= 0);
if (ranges.empty()) return {};
int min_l = ranges[0].first, max_l = min_l, min_r = ranges[0].second, max_r = min_r;
for (auto [l, r] : ranges) {
assert(0 <= l && l <= r);
min_l = std::min(min_l, l), max_l = std::max(max_l, l);
min_r = std::min(min_r, r), max_r = std::max(max_r, r);
}
if (!block_size) block_size = std::max(1, int(std::sqrt((double(max_l) - min_l + 1) * (double(max_r) - min_r + 1) / ranges.size())));
std::vector<std::pair<std::uint64_t, int>> keys;
keys.reserve(ranges.size());
for (int i = 0; i < int(ranges.size()); ++i) {
auto [l, r] = ranges[i];
std::uint32_t block = (l - min_l) / block_size;
std::uint32_t right = block & 1 ? ~std::uint32_t(r) : std::uint32_t(r);
keys.emplace_back((std::uint64_t(block) << 32) | right, i);
}
if (keys.size() < 2048) std::sort(keys.begin(), keys.end());
else stable_radix_sort(keys, [](const auto &x) { return x.first; });
std::vector<int> order;
order.reserve(keys.size());
for (auto [key, i] : keys) { (void)key; order.push_back(i); }
return order;
}
#line 13 "data_structure/static_range_inversions.hpp"
#include <numeric>
#line 18 "data_structure/static_range_inversions.hpp"
template<class Range, class Compare = std::less<>>
requires std::ranges::random_access_range<const Range> && std::ranges::sized_range<const Range>
std::vector<std::int64_t> static_range_inversion_counts(const Range &values,
const std::vector<std::pair<int, int>> &ranges, Compare compare = {}) {
assert(std::ranges::size(values) <= std::size_t(std::numeric_limits<int>::max()));
assert(ranges.size() <= std::size_t(std::numeric_limits<int>::max()));
const int n = int(std::ranges::size(values)), q = int(ranges.size());
for ([[maybe_unused]] auto [l, r] : ranges) assert(0 <= l && l <= r && r <= n);
std::vector<std::int64_t> answer(q);
if (!q || n < 2) return answer;
auto first = std::ranges::begin(values);
if (q == 1) {
auto [l, r] = ranges[0];
answer[0] = inversion_count(std::ranges::subrange(first + l, first + r), compare);
return answer;
}
using T = std::ranges::range_value_t<const Range>;
std::vector<int> ordered(n), rank(n);
std::iota(ordered.begin(), ordered.end(), 0);
if constexpr (std::is_integral_v<T> && !std::is_same_v<T, bool> && sizeof(T) <= 8 &&
(std::is_same_v<Compare, std::less<>> || std::is_same_v<Compare, std::greater<>>)) {
using U = std::make_unsigned_t<T>;
stable_radix_sort(ordered, [&](int i) {
U key = U(first[i]);
if constexpr (std::is_signed_v<T>) key ^= U(1) << (std::numeric_limits<U>::digits - 1);
if constexpr (std::is_same_v<Compare, std::greater<>>) key = U(~key);
return key;
});
} else {
std::sort(ordered.begin(), ordered.end(), [&](int a, int b) {
if (compare(first[a], first[b])) return true;
return !compare(first[b], first[a]) && a < b;
});
}
for (int i = 0; i < n; ++i) rank[ordered[i]] = i;
auto queries = mo_order(ranges);
struct Event {
std::size_t next;
int left, right, query, kind;
};
constexpr std::size_t none = std::numeric_limits<std::size_t>::max();
std::vector<std::size_t> heads(n, none);
std::vector<Event> events;
events.reserve(std::size_t(q) * 2);
auto add = [&](int sweep, int l, int r, int sign, bool length, int query) {
if (sweep >= 0) {
events.push_back({heads[sweep], l, r, query, sign * (1 + int(length))});
heads[sweep] = events.size() - 1;
}
};
int left = 0, right = 0;
for (int i : queries) {
auto [l, r] = ranges[i];
if (right < r) add(left - 1, right, r, 1, false, i), right = r;
if (l < left) add(right - 1, l, left, 1, true, i), left = l;
if (r < right) add(left - 1, r, right, -1, false, i), right = r;
if (left < l) add(right - 1, left, l, -1, true, i), left = l;
}
int shift = 0;
while ((std::uint64_t(1) << (2 * shift + 2)) <= std::uint64_t(n)) ++shift;
const int block = 1 << shift;
std::vector<int> direct(n), lazy((std::size_t(n) + block - 1) >> shift);
std::vector<std::int64_t> prefix(std::size_t(n) + 1), delta(q);
for (int sweep = 0; sweep < n; ++sweep) {
const int key = rank[sweep], group = key >> shift;
prefix[sweep + 1] = prefix[sweep] + direct[key] + lazy[group];
for (int i = 0; i < group; ++i) ++lazy[i];
for (int i = group << shift; i <= key; ++i) ++direct[i];
for (std::size_t i = heads[sweep]; i != none; i = events[i].next) {
const auto &event = events[i];
std::int64_t sum = 0;
for (int p = event.left; p < event.right; ++p) {
int key = rank[p];
sum += int(event.kind == 2 || event.kind == -2) * (sweep - p + 1) - direct[key] - lazy[key >> shift];
}
delta[event.query] += event.kind > 0 ? sum : -sum;
}
}
std::int64_t sum = 0;
for (int i : queries) {
sum += delta[i];
auto [l, r] = ranges[i];
answer[i] = sum + prefix[r] - prefix[l];
}
return answer;
}
#line 1 "components/fast_io_bulk.hpp"
#line 1 "components/fast_io_output.hpp"
#line 1 "components/fast_io.hpp"
#line 6 "components/fast_io.hpp"
#include <bit>
#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 7 "components/fast_io_output.hpp"
namespace fast_io_detail {
struct BulkOutput {
static char *small(char *out, std::uint32_t value) {
unsigned n = 1 + (value >= 10) + (value >= 100) + (value >= 1000);
if constexpr (std::endian::native == std::endian::little) {
std::uint32_t word;
std::memcpy(&word, FastOutput::quads[value].data(), 4);
word >>= (4 - n) * 8;
std::memcpy(out, &word, 4);
} else std::memcpy(out, FastOutput::quads[value].data() + 4 - n, n);
return out + n;
}
static char *number(char *out, std::uint32_t value) {
if (value >= 100000000) {
out = small(out, value / 100000000);
value %= 100000000;
std::memcpy(out, FastOutput::quads[value / 10000].data(), 4);
std::memcpy(out + 4, FastOutput::quads[value % 10000].data(), 4);
return out + 8;
}
if (value >= 10000) {
out = small(out, value / 10000);
std::memcpy(out, FastOutput::quads[value % 10000].data(), 4);
return out + 4;
}
return small(out, value);
}
template<std::size_t Fields, class Read>
#if defined(__GNUC__) || defined(__clang__)
[[gnu::noinline]]
#endif
static void records(FastOutput &out, std::size_t count, Read read) {
constexpr auto bytes = 11 * Fields;
constexpr auto block = std::max<std::size_t>(1, (1 << 16) / bytes);
for (std::size_t base = 0; base < count;) {
const auto n = std::min(count - base, block);
char *begin = out.reserve(n * bytes), *p = begin;
for (std::size_t i = 0; i < n; ++i) {
auto values = read(base + i);
for (std::size_t j = 0; j < Fields; ++j) {
p = number(p, std::uint32_t(values[j]));
*p++ = j + 1 == Fields ? '\n' : ' ';
}
}
out.length += p - begin;
base += n;
}
}
static void write(FastOutput &out, std::string_view text) {
if (text.size() <= (1 << 16)) return out.write(text);
if (out.length && !out.flush()) throw std::runtime_error("output failed");
std::size_t done = 0;
while (done < text.size()) {
const auto written = std::fwrite(text.data() + done, 1, text.size() - done, out.file);
if (!written) throw std::runtime_error("output failed");
done += written;
}
}
};
}
template<std::size_t Fields, class Read>
void write_unsigned_records(FastOutput &output, std::size_t count, Read read) {
static_assert(Fields > 0 && Fields <= std::numeric_limits<std::size_t>::max() / 11);
fast_io_detail::BulkOutput::records<Fields>(output, count, std::move(read));
}
#line 6 "components/fast_io_bulk.hpp"
#include <span>
#line 8 "components/fast_io_bulk.hpp"
#if defined(__linux__) && defined(__x86_64__) && defined(__GNUC__) && !defined(__clang__)
#include <immintrin.h>
#pragma GCC push_options
_Pragma("GCC target(\"avx2\")")
#pragma GCC optimize("O3")
namespace fast_io_detail {
struct BulkInput {
alignas(32) static inline constexpr auto rows = [] {
std::array<std::array<unsigned char, 16>, 11> r{};
for (int n = 0; n <= 10; ++n)
for (int i = 0; i < 16; ++i) r[n][i] = i < 16 - n ? 128 : i - (16 - n);
return r;
}();
static constexpr std::size_t kChunk = 1 << 17, kCapacity = kChunk / 4 + 66;
static unsigned separators(__m256i bytes) {
return unsigned(_mm256_movemask_epi8(_mm256_cmpeq_epi8(_mm256_max_epu8(bytes, _mm256_set1_epi8(' ')), _mm256_set1_epi8(' '))));
}
[[gnu::always_inline]] static __m256i two(const char *&p, __m256i &invalid) {
const auto bytes = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(p));
const unsigned sep = separators(bytes), a = std::countr_zero(sep), b = std::countr_zero(sep & (sep - 1));
if (a < 1 || a > 10 || b <= a + 1 || b - a - 1 > 10) [[unlikely]] {
invalid = _mm256_set1_epi32(-1);
p += std::min(b + 1, 32u);
return _mm256_setzero_si256();
}
const auto window = _mm256_inserti128_si256(bytes, _mm_loadu_si128(reinterpret_cast<const __m128i *>(p + a + 1)), 1);
const auto control = _mm256_set_m128i(_mm_loadu_si128(reinterpret_cast<const __m128i *>(rows[b - a - 1].data())),
_mm_loadu_si128(reinterpret_cast<const __m128i *>(rows[a].data())));
const auto digits = _mm256_shuffle_epi8(_mm256_sub_epi8(window, _mm256_set1_epi8('0')), control);
invalid = _mm256_or_si256(invalid, _mm256_subs_epu8(digits, _mm256_set1_epi8(9)));
p += b + 1;
return _mm256_madd_epi16(_mm256_maddubs_epi16(digits, _mm256_set1_epi16(0x010a)), _mm256_set1_epi32(0x00010064));
}
static std::uint32_t one(const char *&p, bool &bad) {
const auto bytes = _mm_loadu_si128(reinterpret_cast<const __m128i *>(p));
const auto spaces = _mm_cmpeq_epi8(_mm_max_epu8(bytes, _mm_set1_epi8(' ')), _mm_set1_epi8(' '));
const unsigned n = std::countr_zero(unsigned(_mm_movemask_epi8(spaces)) | 0x10000u);
if (n < 1 || n > 10) [[unlikely]] {
bad = true;
p += std::min(n + 1, 16u);
return 0;
}
const auto digits = _mm_shuffle_epi8(_mm_sub_epi8(bytes, _mm_set1_epi8('0')),
_mm_loadu_si128(reinterpret_cast<const __m128i *>(rows[n].data())));
const auto invalid = _mm_subs_epu8(digits, _mm_set1_epi8(9));
bad |= !_mm_testz_si128(invalid, invalid);
const auto groups = _mm_madd_epi16(_mm_maddubs_epi16(digits, _mm_set1_epi16(0x010a)), _mm_set1_epi32(0x00010064));
const auto halves = _mm_madd_epi16(_mm_packus_epi32(groups, groups), _mm_set1_epi32(0x00012710));
const std::uint64_t value = std::uint64_t(unsigned(_mm_cvtsi128_si32(halves))) * 100000000 + unsigned(_mm_extract_epi32(halves, 1));
bad |= value > 0xffffffffULL;
p += n + 1;
return std::uint32_t(value);
}
static const char *after_separator(const char *p) {
const unsigned mask = separators(_mm256_loadu_si256(reinterpret_cast<const __m256i *>(p)));
return mask ? p + std::countr_zero(mask) + 1 : nullptr;
}
static std::size_t lockstep(const char *(&streams)[4], const char *const (&end)[4], unsigned *const (&out)[4], __m256i &invalid) {
const char *p[4] = {streams[0], streams[1], streams[2], streams[3]};
std::size_t done = 0;
for (;;) {
std::ptrdiff_t left = end[0] - p[0];
for (int k = 1; k < 4; ++k) left = std::min(left, end[k] - p[k]);
const auto steps = std::min(left / 33, std::ptrdiff_t((kCapacity - done) / 2));
if (steps <= 0) break;
for (auto j = steps; j; --j, done += 2) {
const auto g0 = two(p[0], invalid), g1 = two(p[1], invalid), g2 = two(p[2], invalid), g3 = two(p[3], invalid);
const auto k = _mm256_set1_epi32(0x00012710);
const auto h01 = _mm256_castsi256_ps(_mm256_madd_epi16(_mm256_packus_epi32(g0, g1), k));
const auto h23 = _mm256_castsi256_ps(_mm256_madd_epi16(_mm256_packus_epi32(g2, g3), k));
const auto high = _mm256_castps_si256(_mm256_shuffle_ps(h01, h23, 0x88));
const auto low = _mm256_castps_si256(_mm256_shuffle_ps(h01, h23, 0xdd));
const auto overflow = _mm256_or_si256(_mm256_cmpgt_epi32(high, _mm256_set1_epi32(42)),
_mm256_and_si256(_mm256_cmpeq_epi32(high, _mm256_set1_epi32(42)), _mm256_cmpgt_epi32(low, _mm256_set1_epi32(94967295))));
invalid = _mm256_or_si256(invalid, overflow);
const auto value = _mm256_add_epi32(_mm256_mullo_epi32(high, _mm256_set1_epi32(100000000)), low);
const auto q = _mm256_permutevar8x32_epi32(value, _mm256_setr_epi32(0, 4, 1, 5, 2, 6, 3, 7));
const auto q01 = _mm256_castsi256_si128(q), q23 = _mm256_extracti128_si256(q, 1);
_mm_storel_epi64(reinterpret_cast<__m128i *>(out[0] + done), q01);
_mm_storeh_pd(reinterpret_cast<double *>(out[1] + done), _mm_castsi128_pd(q01));
_mm_storel_epi64(reinterpret_cast<__m128i *>(out[2] + done), q23);
_mm_storeh_pd(reinterpret_cast<double *>(out[3] + done), _mm_castsi128_pd(q23));
}
}
for (int k = 0; k < 4; ++k) streams[k] = p[k];
return done;
}
template <class Emit>
static std::size_t chunk_blocks(const char *&p, const char *limit, std::size_t count, unsigned *const (&out)[4], Emit &&emit) {
const auto bytes = std::min({kChunk, 2 * (count - 32), std::size_t(limit - p) - 64}) & ~std::size_t(3);
const std::size_t stream = bytes / 4;
const char *p1 = after_separator(p + stream), *p2 = after_separator(p + 2 * stream);
const char *p3 = after_separator(p + 3 * stream), *last = after_separator(p + bytes);
if (!p1 || !p2 || !p3 || !last) return 0;
const char *s[4] = {p, p1, p2, p3}, *const end[4] = {p1, p2, p3, last};
auto invalid = _mm256_setzero_si256();
const auto done = lockstep(s, end, out, invalid);
bool bad = !_mm256_testz_si256(invalid, invalid);
std::size_t n[4];
for (int k = 0; k < 4; ++k) {
n[k] = done;
while (s[k] < end[k] && n[k] < kCapacity) out[k][n[k]++] = one(s[k], bad);
bad |= s[k] != end[k];
}
const auto parsed = n[0] + n[1] + n[2] + n[3];
if (bad || parsed > count) return 0;
for (int k = 0; k < 4; ++k) emit(out[k], n[k]);
p = last;
return parsed;
}
static std::size_t chunk(const char *&p, const char *limit, unsigned *dst, std::size_t count, unsigned *scratch) {
unsigned *const out[4] = {dst, scratch, scratch + kCapacity, scratch + 2 * kCapacity};
bool first = true;
unsigned *next = dst;
return chunk_blocks(p, limit, count, out, [&](const unsigned *values, std::size_t n) {
if (!first) std::memcpy(next, values, n * sizeof(unsigned));
first = false;
next += n;
});
}
template <class Emit>
static void read_blocks(FastInput &in, std::size_t count, Emit emit) {
std::unique_ptr<unsigned[]> scratch;
std::size_t done = 0;
bool chunks = true;
while (done < count) {
const char *p = in.current;
while (p != in.end && static_cast<unsigned char>(*p) <= ' ') ++p;
while (chunks && count - done >= 1024 && in.end - p >= 1088) {
if (!scratch) scratch = std::make_unique_for_overwrite<unsigned[]>(4 * kCapacity);
unsigned *const out[4] = {scratch.get(), scratch.get() + kCapacity, scratch.get() + 2 * kCapacity, scratch.get() + 3 * kCapacity};
const auto parsed = chunk_blocks(p, in.end, count - done, out, emit);
if (!parsed) {
chunks = false;
break;
}
done += parsed;
}
unsigned tail[64];
std::size_t used = 0;
while (done + 2 <= count && in.end - p >= 32) {
const char *next = p;
auto invalid = _mm256_setzero_si256();
const auto groups = two(next, invalid);
if (!_mm256_testz_si256(invalid, invalid)) break;
const auto halves = _mm256_madd_epi16(_mm256_packus_epi32(groups, groups), _mm256_set1_epi32(0x00012710));
const unsigned h0 = _mm256_extract_epi32(halves, 0), l0 = _mm256_extract_epi32(halves, 1);
const unsigned h1 = _mm256_extract_epi32(halves, 4), l1 = _mm256_extract_epi32(halves, 5);
if (h0 > 42 || (h0 == 42 && l0 > 94967295) || h1 > 42 || (h1 == 42 && l1 > 94967295)) break;
tail[used++] = h0 * 100000000 + l0;
tail[used++] = h1 * 100000000 + l1;
if (used == 64) {
emit(tail, used);
used = 0;
}
done += 2;
p = next;
}
if (used) emit(tail, used);
in.current = p;
if (done < count) {
unsigned value = 0;
in.read(value);
emit(&value, 1);
++done;
}
}
}
static void read(FastInput &in, unsigned *out, std::size_t count) {
read_blocks(in, count, [&](const unsigned *values, std::size_t n) {
std::memcpy(out, values, n * sizeof(unsigned));
out += n;
});
}
};
}
#pragma GCC pop_options
#endif
namespace fast_io_detail {
template <class Emit, std::size_t... I>
void emit_record(Emit &emit, const std::uint32_t *values, std::index_sequence<I...>) {
emit(values[I]...);
}
}
template <class Emit>
void read_unsigned_blocks(FastInput &input, std::size_t count, Emit emit) {
#if defined(__linux__) && defined(__x86_64__) && defined(__GNUC__) && !defined(__clang__)
if (__builtin_cpu_supports("avx2")) {
fast_io_detail::BulkInput::read_blocks(input, count, emit);
return;
}
#endif
std::uint32_t values[64];
while (count) {
const auto n = std::min<std::size_t>(count, 64);
for (std::size_t i = 0; i < n; ++i) input.read(values[i]);
emit(values, n);
count -= n;
}
}
inline void read_unsigned(FastInput &input, std::span<std::uint32_t> out) {
read_unsigned_blocks(input, out.size(), [&](const std::uint32_t *values, std::size_t count) {
std::memcpy(out.data(), values, count * sizeof(std::uint32_t));
out = out.subspan(count);
});
}
template <std::size_t Fields, class Emit>
void read_unsigned_records(FastInput &input, std::size_t count, Emit emit) {
static_assert(Fields > 0);
if (count > std::numeric_limits<std::size_t>::max() / Fields) throw std::length_error("input size");
std::array<std::uint32_t, Fields> pending;
std::size_t used = 0;
constexpr auto indices = std::make_index_sequence<Fields>();
read_unsigned_blocks(input, count * Fields, [&](const std::uint32_t *values, std::size_t n) {
std::size_t i = 0;
if (used) {
while (used < Fields && i < n) pending[used++] = values[i++];
if (used == Fields) {
fast_io_detail::emit_record(emit, pending.data(), indices);
used = 0;
}
}
for (; i < n && n - i >= Fields; i += Fields) fast_io_detail::emit_record(emit, values + i, indices);
while (i < n) pending[used++] = values[i++];
});
}
#line 5 "test/mo_inversions.test.cpp"
int main() {
FastInput input;
FastOutput output;
int n = 0, q = 0;
input.read(n), input.read(q);
std::vector<int> a(n);
std::size_t position = 0;
read_unsigned_records<1>(input, n, [&](std::uint32_t value) { a[position++] = value; });
std::vector<std::pair<int, int>> ranges(q);
position = 0;
read_unsigned_records<2>(input, q, [&](std::uint32_t l, std::uint32_t r) { ranges[position++] = {int(l), int(r)}; });
auto answer = static_range_inversion_counts(a, ranges);
for (auto x : answer) output.println(x);
}