test/floor_sum.test.cpp

test/floor_sum.test.cpp · GitHub で見る

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#define PROBLEM "https://judge.yosupo.jp/problem/sum_of_floor_of_linear"
#include "../math/floor_sum.hpp"
#include "../components/fast_io.hpp"

int main() {
	FastInput in;
	FastOutput out;
	int t;
	in.read(t);
	while (t--) {
		std::uint64_t n, m, a, b;
		in.read(n);
		in.read(m);
		in.read(a);
		in.read(b);
		out.write(floor_sum(n, m, a, b));
		out.write('\n');
	}
}

#line 1 "test/floor_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/sum_of_floor_of_linear"
#line 1 "math/floor_sum.hpp"



#include <cassert>
#include <cstdint>
#include <limits>
#include <type_traits>
#include <utility>

namespace floor_sum_detail {
using U = std::uint64_t;

template <class R>
constexpr R triangular(U n) {
	return R(n >> 1) * R(n - 1 + (n & 1));
}

template <class R, class A>
constexpr std::pair<U, R> normalize(A value, U m) {
	U x = static_cast<U>(value);
	if constexpr (std::is_signed_v<A>) {
		if (value < 0) {
			x = U(0) - x;
			U q = x / m, r = x % m;
			return {r ? m - r : 0, R(0) - R(q) - R(r != 0)};
		}
	}
	if (x < m) return {x, R(0)};
	return {x % m, R(x / m)};
}

template <class R, class V>
constexpr R sum(V n, V m, V a, V b) {
	R result = 0;
	bool negative = false;
	for (;;) {
		R value = 0;
		if (a >= m) {
			value += triangular<R>(n) * R(a / m);
			a %= m;
		}
		if (b >= m) {
			value += R(n) * R(b / m);
			b %= m;
		}
		using W = std::conditional_t<sizeof(V) <= 4, U, __uint128_t>;
		W z = W(a) * (n - 1) + b;
		if (z < m) return result + (negative ? R(0) - value : value);
		V next;
		if constexpr (sizeof(V) <= 4) next = z / m;
		else next = z >> 64 ? V(z / m) : V(U(z) / m);
		value += R(n - 1) * R(next);
		result += negative ? R(0) - value : value;
		n = next;
		b = m - b - 1;
		std::swap(a, m);
		negative = !negative;
	}
}
}

template <class T = std::int64_t, class A, class B>
constexpr T floor_sum(std::uint64_t n, std::uint64_t m, A a, B b) {
	static_assert((std::is_integral_v<T> && !std::is_same_v<T, bool>) ||
		std::is_same_v<T, __int128_t> || std::is_same_v<T, __uint128_t>);
	static_assert(std::is_integral_v<A> && sizeof(A) <= 8 && std::is_integral_v<B> && sizeof(B) <= 8);
	assert(m > 0);
	if (!n) return T(0);
	using R = std::conditional_t<sizeof(T) <= 8, std::uint64_t, __uint128_t>;
	auto [rb, qb] = floor_sum_detail::normalize<R>(b, m);
	if (n == 1) return static_cast<T>(qb);
	auto [ra, qa] = floor_sum_detail::normalize<R>(a, m);
	R result = floor_sum_detail::triangular<R>(n) * qa + R(n) * qb;
	if (ra) {
		if (n <= std::numeric_limits<std::uint32_t>::max() && m <= std::numeric_limits<std::uint32_t>::max())
			result += floor_sum_detail::sum<R>(std::uint32_t(n), std::uint32_t(m), std::uint32_t(ra), std::uint32_t(rb));
		else result += floor_sum_detail::sum<R>(n, m, ra, rb);
	}
	return static_cast<T>(result);
}


#line 1 "components/fast_io.hpp"



#include <algorithm>
#include <array>
#include <bit>
#line 8 "components/fast_io.hpp"
#include <charconv>
#include <cstddef>
#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/floor_sum.test.cpp"

int main() {
	FastInput in;
	FastOutput out;
	int t;
	in.read(t);
	while (t--) {
		std::uint64_t n, m, a, b;
		in.read(n);
		in.read(m);
		in.read(a);
		in.read(b);
		out.write(floor_sum(n, m, a, b));
		out.write('\n');
	}
}