cp-library
競技プログラミング用 C++ ライブラリ
test/binomial_mod.test.cpp
test/binomial_mod.test.cpp · GitHub で見る
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コード
#define PROBLEM "https://judge.yosupo.jp/problem/binomial_coefficient"
#include "math/binomial_mod.hpp"
#include "components/fast_io.hpp"
int main() {
FastInput input;
FastOutput output;
int queries = 0;
std::uint32_t modulus = 0;
input.read(queries), input.read(modulus);
BinomialMod binomial(modulus);
while (queries--) {
std::int64_t n = 0, k = 0;
input.read(n), input.read(k);
output.println(binomial(n, k));
}
}
#line 1 "test/binomial_mod.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/binomial_coefficient"
#line 1 "math/binomial_mod.hpp"
#line 1 "components/barrett32.hpp"
#include <cassert>
#include <cstdint>
struct Barrett32 {
std::uint32_t mod;
std::uint64_t reciprocal;
explicit Barrett32(std::uint32_t m) : mod(m), reciprocal(m > 1 ? std::uint64_t((__uint128_t(1) << 64) / m) : 0) {
assert(m > 0);
}
std::uint32_t reduce(std::uint64_t x) const {
if (mod == 1) return 0;
std::uint64_t q = (__uint128_t(x) * reciprocal) >> 64, r = x - q * mod;
return r < mod ? r : r - mod;
}
std::uint32_t mul(std::uint32_t a, std::uint32_t b) const { return reduce(std::uint64_t(a) * b); }
std::uint32_t pow(std::uint32_t a, std::uint64_t e) const {
std::uint32_t r = mod == 1 ? 0 : 1;
for (; e; e >>= 1, a = mul(a, a)) if (e & 1) r = mul(r, a);
return r;
}
};
#line 1 "math/linear_congruence.hpp"
#line 5 "math/linear_congruence.hpp"
#include <optional>
#include <stdexcept>
#include <utility>
struct LinearCongruenceSolution {
std::int64_t residue, period, count;
bool operator==(const LinearCongruenceSolution &) const = default;
};
constexpr std::optional<LinearCongruenceSolution> linear_congruence(std::int64_t a, std::int64_t b, std::int64_t m) {
if (m <= 0) throw std::invalid_argument("linear_congruence modulus");
a %= m;
b %= m;
if (a < 0) a += m;
if (b < 0) b += m;
std::int64_t r = m, s = a, u = 0, v = 1;
while (s) {
std::int64_t q = r / s;
r -= q * s;
u -= q * v;
std::swap(r, s);
std::swap(u, v);
}
if (b % r) return std::nullopt;
std::int64_t period = m / r;
if (u < 0) u += period;
std::int64_t residue = __int128_t(u) * (b / r) % period;
return LinearCongruenceSolution{residue, period, r};
}
#line 6 "math/binomial_mod.hpp"
#include <algorithm>
#include <array>
#include <bit>
#include <limits>
#include <vector>
class BinomialMod {
using U = std::uint32_t;
using W = std::uint64_t;
struct PrimePower {
U prime, exponent, coefficient;
Barrett32 modulus;
std::vector<U> factorial, inverse, powers;
PrimePower(U p, U e, U q, U limit, U weight)
: prime(p), exponent(e), coefficient(weight), modulus(q),
factorial(std::size_t(std::min(limit, q - 1)) + 1), inverse(factorial.size()), powers(e, 1) {
factorial[0] = 1;
for (std::size_t i = 1; i < factorial.size(); ++i)
factorial[i] = i % p ? modulus.mul(factorial[i - 1], U(i)) : factorial[i - 1];
inverse.back() = U(linear_congruence(factorial.back(), 1, q)->residue);
for (std::size_t i = factorial.size() - 1; i; --i)
inverse[i - 1] = i % p ? modulus.mul(inverse[i], U(i)) : inverse[i];
for (U i = 1; i < e; ++i) powers[i] = U(W(powers[i - 1]) * p);
}
template<bool Binary> U choose_power(W n, W k) const {
struct Level { W n, k, r; };
std::array<Level, 64> levels;
W r = n - k;
U valuation = 0;
bool negative = false;
if constexpr (Binary) {
valuation = U(std::popcount(k) + std::popcount(r) - std::popcount(n));
if (valuation >= exponent) return 0;
negative = exponent == 2 && ((valuation - ((n >> 1) - (k >> 1) - (r >> 1))) & 1);
}
U length = 0;
while (n) {
levels[length++] = {n, k, r};
if constexpr (Binary) n >>= 1, k >>= 1, r >>= 1;
else {
n /= prime, k /= prime, r /= prime;
U carry = U(n - k - r);
valuation += carry;
if (valuation >= exponent) return 0;
if (length >= exponent) negative ^= carry != 0;
}
}
U a = 1, b = 1, c = 1;
for (U i = 0; i < length; ++i) {
auto value = levels[i];
if constexpr (Binary) value.n &= modulus.mod - 1, value.k &= modulus.mod - 1, value.r &= modulus.mod - 1;
else if (i + exponent < length) {
auto q = levels[i + exponent];
value.n -= q.n * modulus.mod;
value.k -= q.k * modulus.mod;
value.r -= q.r * modulus.mod;
}
a = modulus.mul(a, factorial[std::size_t(value.n)]);
b = modulus.mul(b, inverse[std::size_t(value.k)]);
c = modulus.mul(c, inverse[std::size_t(value.r)]);
}
U result = modulus.mul(modulus.mul(a, b), c);
if (negative) result = modulus.mod - result;
return modulus.mul(result, powers[valuation]);
}
U choose(W n, W k) const {
if (exponent == 1) {
if (prime == 2) return (n & k) == k;
U result = 1;
while (n) {
U a = U(n % prime), b = U(k % prime);
if (a < b) return 0;
result = modulus.mul(result, modulus.mul(factorial[a], modulus.mul(inverse[b], inverse[a - b])));
n /= prime, k /= prime;
}
return result;
}
return prime == 2 ? choose_power<true>(n, k) : choose_power<false>(n, k);
}
};
Barrett32 modulus_;
std::vector<PrimePower> factors_;
std::int64_t max_n_ = std::numeric_limits<std::int64_t>::max();
static U checked_(U m) {
if (!m) throw std::invalid_argument("BinomialMod modulus");
return m;
}
public:
explicit BinomialMod(U modulus, U table_limit = 1000000) : modulus_(checked_(modulus)) {
auto add = [&](U p, U e, U q) {
U weight = U(W(modulus / q) * W(linear_congruence(modulus / q, 1, q)->residue));
factors_.emplace_back(p, e, q, table_limit, weight);
if (q - 1 > table_limit) max_n_ = table_limit;
};
U remaining = modulus;
for (U p = 2; p <= remaining / p; p += p == 2 ? 1 : 2) {
if (remaining % p) continue;
U q = 1, e = 0;
do { remaining /= p; q *= p; ++e; } while (remaining % p == 0);
add(p, e, q);
}
if (remaining > 1) add(remaining, 1, remaining);
}
U mod() const { return modulus_.mod; }
std::int64_t max_n() const { return max_n_; }
U comb(std::int64_t n, std::int64_t k) const {
if (n < 0 || k < 0 || n < k || mod() == 1) return 0;
if (n > max_n_) throw std::out_of_range("BinomialMod n");
if (!k || n == k) return 1;
if (factors_.size() == 1) return factors_[0].choose(W(n), W(k));
U answer = 0;
for (const auto &f : factors_)
answer = modulus_.reduce(W(answer) + modulus_.mul(f.coefficient, f.choose(W(n), W(k))));
return answer;
}
U operator()(std::int64_t n, std::int64_t k) const { return comb(n, k); }
};
#line 1 "components/fast_io.hpp"
#line 8 "components/fast_io.hpp"
#include <charconv>
#include <cstddef>
#line 11 "components/fast_io.hpp"
#include <cstdio>
#include <cstring>
#include <memory>
#line 15 "components/fast_io.hpp"
#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 4 "test/binomial_mod.test.cpp"
int main() {
FastInput input;
FastOutput output;
int queries = 0;
std::uint32_t modulus = 0;
input.read(queries), input.read(modulus);
BinomialMod binomial(modulus);
while (queries--) {
std::int64_t n = 0, k = 0;
input.read(n), input.read(k);
output.println(binomial(n, k));
}
}