cp-library
競技プログラミング用 C++ ライブラリ
test/warshall_floyd.test.cpp
test/warshall_floyd.test.cpp · GitHub で見る
依存ライブラリ
コード
#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_1_C"
#include "graph/warshall_floyd.hpp"
#include "components/fast_io.hpp"
int main() {
FastInput input;
FastOutput output;
int n = 0, m = 0;
input.read(n); input.read(m);
WarshallFloyd<> graph(n);
for (int i = 0; i < m; ++i) {
int from = 0, to = 0;
std::int64_t weight = 0;
input.read(from); input.read(to); input.read(weight);
graph.add_edge(from, to, weight);
}
if (!graph.solve()) { output.println("NEGATIVE CYCLE"); return 0; }
for (int i = 0; i < n; ++i) for (int j = 0; j < n; ++j) {
if (j) output.write(' ');
if (graph(i, j) == graph.infinity()) output.write("INF");
else output.write(graph(i, j));
if (j + 1 == n) output.write('\n');
}
}
#line 1 "test/warshall_floyd.test.cpp"
#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_1_C"
#line 1 "graph/warshall_floyd.hpp"
#line 1 "components/warshall_floyd_kernel.hpp"
#line 1 "components/aligned_allocator.hpp"
#include <cstddef>
#include <limits>
#include <new>
template<class T, std::size_t Alignment = 64> struct AlignedAllocator {
static_assert(Alignment >= alignof(T) && !(Alignment & (Alignment - 1)));
using value_type = T;
template<class U> struct rebind { using other = AlignedAllocator<U, Alignment>; };
AlignedAllocator() = default;
template<class U> AlignedAllocator(const AlignedAllocator<U, Alignment> &) {}
T *allocate(std::size_t n) {
if (n > std::numeric_limits<std::size_t>::max() / sizeof(T)) throw std::bad_array_new_length();
return static_cast<T *>(::operator new(n * sizeof(T), std::align_val_t(Alignment)));
}
void deallocate(T *p, std::size_t) { ::operator delete(p, std::align_val_t(Alignment)); }
template<class U> bool operator==(const AlignedAllocator<U, Alignment> &) const { return true; }
};
#line 5 "components/warshall_floyd_kernel.hpp"
#include <algorithm>
#include <cassert>
#line 8 "components/warshall_floyd_kernel.hpp"
#include <cstdint>
#line 10 "components/warshall_floyd_kernel.hpp"
#include <type_traits>
#include <vector>
#if (defined(__x86_64__) || defined(__i386__)) && (defined(__GNUC__) || defined(__clang__))
#include <immintrin.h>
#endif
#if defined(__GNUC__) && !defined(__clang__)
#pragma GCC push_options
#pragma GCC optimize("O3")
#endif
namespace warshall_floyd_detail {
template<class T> using Storage = std::vector<T, AlignedAllocator<T>>;
template<class T> struct Unsigned { using type = std::make_unsigned_t<T>; };
template<> struct Unsigned<__int128_t> { using type = __uint128_t; };
inline int backend() {
#if (defined(__x86_64__) || defined(__i386__)) && (defined(__GNUC__) || defined(__clang__)) && !defined(WARSHALL_FLOYD_DISABLE_SIMD)
#ifndef WARSHALL_FLOYD_DISABLE_AVX512
if (__builtin_cpu_supports("avx512f")) return 2;
#endif
if (__builtin_cpu_supports("avx2")) return 1;
#endif
return 0;
}
template<class T, int B, bool Negative, bool Diagonal>
bool scalar(T* out, const T* a, const T* b, T inf) {
for (int k = 0; k < B; ++k) {
if constexpr (Diagonal && Negative) if (out[k * B + k] < 0) return false;
for (int i = 0; i < B; ++i) {
T x = a[i * B + k];
if (x == inf) continue;
for (int j = 0; j < B; ++j) {
if constexpr (Negative) {
if (b[k * B + j] != inf) out[i * B + j] = std::min(out[i * B + j], T(x + b[k * B + j]));
} else {
using U = typename Unsigned<T>::type;
out[i * B + j] = T(std::min(U(out[i * B + j]), U(x) + U(b[k * B + j])));
}
}
}
}
return true;
}
#if (defined(__x86_64__) || defined(__i386__)) && (defined(__GNUC__) || defined(__clang__))
template<class T, int B, bool Negative, bool Diagonal>
__attribute__((target("avx512f")))
bool simple512(T* out, const T* a, const T* b, T inf) {
constexpr int lanes = 64 / sizeof(T);
[[maybe_unused]] __m512i infinity;
if constexpr (sizeof(T) == 4) infinity = _mm512_set1_epi32(inf);
else infinity = _mm512_set1_epi64(inf);
for (int k = 0; k < B; ++k) {
if constexpr (Diagonal && Negative) if (out[k * B + k] < 0) return false;
for (int i = 0; i < B; ++i) {
T x = a[i * B + k];
if constexpr (Negative) if (x == inf) continue;
__m512i alpha;
if constexpr (sizeof(T) == 4) alpha = _mm512_set1_epi32(x);
else alpha = _mm512_set1_epi64(x);
for (int j = 0; j < B; j += lanes) {
auto value = _mm512_loadu_si512(out + i * B + j);
auto beta = _mm512_loadu_si512(b + k * B + j);
[[maybe_unused]] __mmask16 valid = 0;
if constexpr (Negative && sizeof(T) == 4) valid = _mm512_cmpneq_epi32_mask(beta, infinity);
if constexpr (Negative && sizeof(T) == 8) valid = _mm512_cmpneq_epi64_mask(beta, infinity);
if constexpr (sizeof(T) == 4) {
auto sum = _mm512_add_epi32(alpha, beta);
if constexpr (Negative) value = _mm512_mask_min_epi32(value, valid, value, sum);
else value = _mm512_min_epu32(value, sum);
} else {
auto sum = _mm512_add_epi64(alpha, beta);
if constexpr (Negative) value = _mm512_mask_min_epi64(value, __mmask8(valid), value, sum);
else value = _mm512_min_epu64(value, sum);
}
_mm512_storeu_si512(out + i * B + j, value);
}
}
}
return true;
}
template<class T, int B, bool Negative>
__attribute__((target("avx512f")))
void product512(T* out, const T* a, const T* b, T inf) {
constexpr int lanes = 64 / sizeof(T), rows = 4, columns = 2;
[[maybe_unused]] __m512i infinity;
if constexpr (sizeof(T) == 4) infinity = _mm512_set1_epi32(inf);
else infinity = _mm512_set1_epi64(inf);
for (int i = 0; i < B; i += rows) for (int j = 0; j < B; j += lanes * columns) {
__m512i value[rows][columns];
for (int r = 0; r < rows; ++r) for (int q = 0; q < columns; ++q)
value[r][q] = _mm512_loadu_si512(out + (i + r) * B + j + q * lanes);
for (int k = 0; k < B; ++k) {
__m512i beta[columns];
[[maybe_unused]] __mmask16 valid[columns]{};
for (int q = 0; q < columns; ++q) {
beta[q] = _mm512_loadu_si512(b + k * B + j + q * lanes);
__mmask16 mask = 0;
if constexpr (Negative && sizeof(T) == 4) mask = _mm512_cmpneq_epi32_mask(beta[q], infinity);
if constexpr (Negative && sizeof(T) == 8) mask = _mm512_cmpneq_epi64_mask(beta[q], infinity);
valid[q] = mask;
}
for (int r = 0; r < rows; ++r) {
T x = a[(i + r) * B + k];
if constexpr (Negative) if (x == inf) continue;
__m512i alpha;
if constexpr (sizeof(T) == 4) alpha = _mm512_set1_epi32(x);
else alpha = _mm512_set1_epi64(x);
for (int q = 0; q < columns; ++q) {
if constexpr (sizeof(T) == 4) {
auto sum = _mm512_add_epi32(alpha, beta[q]);
if constexpr (Negative) value[r][q] = _mm512_mask_min_epi32(value[r][q], valid[q], value[r][q], sum);
else value[r][q] = _mm512_min_epu32(value[r][q], sum);
} else {
auto sum = _mm512_add_epi64(alpha, beta[q]);
if constexpr (Negative) value[r][q] = _mm512_mask_min_epi64(value[r][q], __mmask8(valid[q]), value[r][q], sum);
else value[r][q] = _mm512_min_epu64(value[r][q], sum);
}
}
}
}
for (int r = 0; r < rows; ++r) for (int q = 0; q < columns; ++q)
_mm512_storeu_si512(out + (i + r) * B + j + q * lanes, value[r][q]);
}
}
template<class T, int B, bool Negative, bool Diagonal>
__attribute__((target("avx2")))
bool simple256(T* out, const T* a, const T* b, T inf) {
constexpr int lanes = 32 / sizeof(T);
[[maybe_unused]] __m256i infinity;
if constexpr (sizeof(T) == 4) infinity = _mm256_set1_epi32(inf);
else infinity = _mm256_set1_epi64x(inf);
for (int k = 0; k < B; ++k) {
if constexpr (Diagonal && Negative) if (out[k * B + k] < 0) return false;
for (int i = 0; i < B; ++i) {
T x = a[i * B + k];
if constexpr (Negative) if (x == inf) continue;
__m256i alpha;
if constexpr (sizeof(T) == 4) alpha = _mm256_set1_epi32(x);
else alpha = _mm256_set1_epi64x(x);
for (int j = 0; j < B; j += lanes) {
auto value = _mm256_loadu_si256(reinterpret_cast<const __m256i*>(out + i * B + j));
auto beta = _mm256_loadu_si256(reinterpret_cast<const __m256i*>(b + k * B + j));
[[maybe_unused]] __m256i valid = _mm256_setzero_si256();
if constexpr (Negative && sizeof(T) == 4) valid = _mm256_cmpeq_epi32(beta, infinity);
if constexpr (Negative && sizeof(T) == 8) valid = _mm256_cmpeq_epi64(beta, infinity);
if constexpr (sizeof(T) == 4) {
auto sum = _mm256_add_epi32(alpha, beta);
if constexpr (Negative) value = _mm256_min_epi32(value, _mm256_blendv_epi8(sum, infinity, valid));
else value = _mm256_min_epu32(value, sum);
} else {
auto sum = _mm256_add_epi64(alpha, beta);
if constexpr (Negative) {
sum = _mm256_blendv_epi8(sum, infinity, valid);
value = _mm256_blendv_epi8(value, sum, _mm256_cmpgt_epi64(value, sum));
} else {
auto choose = _mm256_andnot_si256(_mm256_cmpgt_epi64(_mm256_setzero_si256(), sum), _mm256_cmpgt_epi64(value, sum));
value = _mm256_blendv_epi8(value, sum, choose);
}
}
_mm256_storeu_si256(reinterpret_cast<__m256i*>(out + i * B + j), value);
}
}
}
return true;
}
template<class T, int B, bool Negative>
__attribute__((target("avx2")))
void product256(T* out, const T* a, const T* b, T inf) {
constexpr int lanes = 32 / sizeof(T), rows = 4, columns = 2;
[[maybe_unused]] __m256i infinity;
if constexpr (sizeof(T) == 4) infinity = _mm256_set1_epi32(inf);
else infinity = _mm256_set1_epi64x(inf);
for (int i = 0; i < B; i += rows) for (int j = 0; j < B; j += lanes * columns) {
__m256i value[rows][columns];
for (int r = 0; r < rows; ++r) for (int q = 0; q < columns; ++q)
value[r][q] = _mm256_loadu_si256(reinterpret_cast<const __m256i*>(out + (i + r) * B + j + q * lanes));
for (int k = 0; k < B; ++k) {
__m256i beta[columns];
[[maybe_unused]] __m256i valid[columns]{};
for (int q = 0; q < columns; ++q) {
beta[q] = _mm256_loadu_si256(reinterpret_cast<const __m256i*>(b + k * B + j + q * lanes));
__m256i mask = _mm256_setzero_si256();
if constexpr (Negative && sizeof(T) == 4) mask = _mm256_cmpeq_epi32(beta[q], infinity);
if constexpr (Negative && sizeof(T) == 8) mask = _mm256_cmpeq_epi64(beta[q], infinity);
valid[q] = mask;
}
for (int r = 0; r < rows; ++r) {
T x = a[(i + r) * B + k];
if constexpr (Negative) if (x == inf) continue;
__m256i alpha;
if constexpr (sizeof(T) == 4) alpha = _mm256_set1_epi32(x);
else alpha = _mm256_set1_epi64x(x);
for (int q = 0; q < columns; ++q) {
if constexpr (sizeof(T) == 4) {
auto sum = _mm256_add_epi32(alpha, beta[q]);
if constexpr (Negative) value[r][q] = _mm256_min_epi32(value[r][q], _mm256_blendv_epi8(sum, infinity, valid[q]));
else value[r][q] = _mm256_min_epu32(value[r][q], sum);
} else {
auto sum = _mm256_add_epi64(alpha, beta[q]);
if constexpr (Negative) {
sum = _mm256_blendv_epi8(sum, infinity, valid[q]);
value[r][q] = _mm256_blendv_epi8(value[r][q], sum, _mm256_cmpgt_epi64(value[r][q], sum));
} else {
auto choose = _mm256_andnot_si256(_mm256_cmpgt_epi64(_mm256_setzero_si256(), sum), _mm256_cmpgt_epi64(value[r][q], sum));
value[r][q] = _mm256_blendv_epi8(value[r][q], sum, choose);
}
}
}
}
}
for (int r = 0; r < rows; ++r) for (int q = 0; q < columns; ++q)
_mm256_storeu_si256(reinterpret_cast<__m256i*>(out + (i + r) * B + j + q * lanes), value[r][q]);
}
}
#endif
template<class T, int B, bool Negative, int Backend>
struct Kernel {
static bool close(T* out, T inf) {
#if (defined(__x86_64__) || defined(__i386__)) && (defined(__GNUC__) || defined(__clang__))
if constexpr (Backend == 2) return simple512<T, B, Negative, true>(out, out, out, inf);
if constexpr (Backend == 1) return simple256<T, B, Negative, true>(out, out, out, inf);
#endif
return scalar<T, B, Negative, true>(out, out, out, inf);
}
static void edge(T* out, const T* a, const T* b, T inf) {
#if (defined(__x86_64__) || defined(__i386__)) && (defined(__GNUC__) || defined(__clang__))
if constexpr (Backend == 2) { simple512<T, B, Negative, false>(out, a, b, inf); return; }
if constexpr (Backend == 1) { simple256<T, B, Negative, false>(out, a, b, inf); return; }
#endif
scalar<T, B, Negative, false>(out, a, b, inf);
}
static void product(T* out, const T* a, const T* b, T inf) {
#if (defined(__x86_64__) || defined(__i386__)) && (defined(__GNUC__) || defined(__clang__))
if constexpr (Backend == 2) { product512<T, B, Negative>(out, a, b, inf); return; }
if constexpr (Backend == 1) { product256<T, B, Negative>(out, a, b, inf); return; }
#endif
scalar<T, B, Negative, false>(out, a, b, inf);
}
};
template<class T, int B, bool Negative, int Backend>
bool solve(T* data, int blocks, T inf) {
using K = Kernel<T, B, Negative, Backend>;
auto tile = [&](int i, int j) { return data + (std::size_t(i) * blocks + j) * B * B; };
auto product = [&](int row, int col, int pivot, int rows, int cols, int inner) {
for (int k = pivot; k < pivot + inner; ++k)
for (int i = row; i < row + rows; ++i)
for (int j = col; j < col + cols; ++j) K::product(tile(i, j), tile(i, k), tile(k, j), inf);
};
constexpr int macro = 16;
for (int base = 0; base < blocks; base += macro) {
int size = std::min(macro, blocks - base);
for (int k = base; k < base + size; ++k) {
if (!K::close(tile(k, k), inf)) return false;
for (int j = base; j < base + size; ++j) if (j != k) K::edge(tile(k, j), tile(k, k), tile(k, j), inf);
for (int i = base; i < base + size; ++i) if (i != k) K::edge(tile(i, k), tile(i, k), tile(k, k), inf);
for (int i = base; i < base + size; ++i) if (i != k)
for (int j = base; j < base + size; ++j) if (j != k) K::product(tile(i, j), tile(i, k), tile(k, j), inf);
}
for (int j = 0; j < blocks; j += macro) if (j != base)
product(base, j, base, size, std::min(macro, blocks - j), size);
for (int i = 0; i < blocks; i += macro) if (i != base)
product(i, base, base, std::min(macro, blocks - i), size, size);
for (int i = 0; i < blocks; i += macro) if (i != base)
for (int j = 0; j < blocks; j += macro) if (j != base)
product(i, j, base, std::min(macro, blocks - i), std::min(macro, blocks - j), size);
}
return true;
}
template<class T, int B, bool Negative>
bool run(T* data, int blocks, T inf, int selected = backend()) {
if constexpr (sizeof(T) <= 8) {
if (selected == 2) return solve<T, B, Negative, 2>(data, blocks, inf);
if (selected == 1) return solve<T, B, Negative, 1>(data, blocks, inf);
}
return solve<T, B, Negative, 0>(data, blocks, inf);
}
}
#if defined(__GNUC__) && !defined(__clang__)
#pragma GCC pop_options
#endif
#line 5 "graph/warshall_floyd.hpp"
#include <stdexcept>
template<class T = std::int64_t>
class WarshallFloyd {
static_assert(std::is_integral_v<T> && std::is_signed_v<T> && (sizeof(T) == 4 || sizeof(T) == 8));
static constexpr int block = 32;
int n_ = 0, blocks_ = 0;
T infinity_ = std::numeric_limits<T>::max();
warshall_floyd_detail::Storage<T> data_;
static int checked_size(std::size_t n) {
if (n > std::size_t(std::numeric_limits<int>::max())) throw std::length_error("Warshall-Floyd size");
return int(n);
}
std::size_t index(int i, int j) const {
return (std::size_t(i / block) * blocks_ + j / block) * block * block + i % block * block + j % block;
}
template<class U> bool run_as(bool negative) {
const U inf = std::numeric_limits<U>::max();
warshall_floyd_detail::Storage<U> work(data_.size());
for (std::size_t i = 0; i < data_.size(); ++i) work[i] = data_[i] == infinity_ ? inf : U(data_[i]);
bool success = negative ? warshall_floyd_detail::run<U, block, true>(work.data(), blocks_, inf)
: warshall_floyd_detail::run<U, block, false>(work.data(), blocks_, inf);
if (success)
for (U value : work) if (value != inf && (__int128_t(value) < std::numeric_limits<T>::lowest() || __int128_t(value) >= infinity_))
throw std::overflow_error("Warshall-Floyd distance");
for (std::size_t i = 0; i < data_.size(); ++i) {
if (work[i] == inf) data_[i] = infinity_;
else data_[i] = T(std::clamp(__int128_t(work[i]), __int128_t(std::numeric_limits<T>::lowest()), __int128_t(infinity_) - 1));
}
return success;
}
public:
using value_type = T;
explicit WarshallFloyd(int n = 0, T inf = std::numeric_limits<T>::max()) : n_(n), infinity_(inf) {
if (n < 0 || inf <= 0) throw std::invalid_argument("Warshall-Floyd shape or infinity");
blocks_ = n / block + (n % block != 0);
std::size_t padded = std::size_t(blocks_) * block;
data_.assign(padded * padded, infinity_);
for (std::size_t i = 0; i < padded; ++i) data_[index(int(i), int(i))] = 0;
}
explicit WarshallFloyd(const std::vector<std::vector<T>>& distance, T inf = std::numeric_limits<T>::max())
: WarshallFloyd(checked_size(distance.size()), inf) {
for (int i = 0; i < n_; ++i) {
if (distance[i].size() != std::size_t(n_)) throw std::invalid_argument("Warshall-Floyd matrix");
for (int j = 0; j < n_; ++j) {
if (distance[i][j] == infinity_) continue;
add_edge(i, j, distance[i][j]);
}
}
}
int size() const { return n_; }
T infinity() const { return infinity_; }
T operator()(int i, int j) const {
assert(0 <= i && i < n_ && 0 <= j && j < n_);
return data_[index(i, j)];
}
void add_edge(int from, int to, T weight) {
assert(0 <= from && from < n_ && 0 <= to && to < n_);
if (weight >= infinity_) throw std::invalid_argument("Warshall-Floyd edge");
auto& value = data_[index(from, to)];
value = std::min(value, weight);
}
bool solve() {
__int128_t maximum = 0;
std::size_t finite = 0;
bool negative = false;
for (T value : data_) if (value != infinity_) {
++finite;
__int128_t x = value;
negative |= x < 0;
maximum = std::max(maximum, x < 0 ? -x : x);
}
__int128_t bound = 2 * (__int128_t(n_) + 1) * maximum;
bool complete = finite == std::size_t(n_) * n_ + std::size_t(blocks_) * block - n_;
if constexpr (sizeof(T) == 8) {
#ifndef WARSHALL_FLOYD_DISABLE_NARROWING
__int128_t limit = std::min(__int128_t(infinity_), __int128_t(std::numeric_limits<std::int32_t>::max()));
if (negative ? bound < limit : maximum < limit && (complete || (__int128_t(n_) - 1) * maximum < limit))
return run_as<std::int32_t>(negative);
#endif
}
if (negative ? bound >= infinity_ : !complete && (__int128_t(n_) - 1) * maximum >= infinity_) {
if constexpr (sizeof(T) == 4) {
if (bound < std::numeric_limits<std::int64_t>::max()) return run_as<std::int64_t>(negative);
}
return run_as<__int128_t>(negative);
}
return negative ? warshall_floyd_detail::run<T, block, true>(data_.data(), blocks_, infinity_)
: warshall_floyd_detail::run<T, block, false>(data_.data(), blocks_, infinity_);
}
std::vector<std::vector<T>> distances() const {
std::vector<std::vector<T>> result(n_, std::vector<T>(n_));
for (int i = 0; i < n_; ++i) for (int j = 0; j < n_; ++j) result[i][j] = data_[index(i, j)];
return result;
}
};
template<class T>
bool warshall_floyd(std::vector<std::vector<T>>& distance, T inf = std::numeric_limits<T>::max()) {
WarshallFloyd<T> work(distance, inf);
bool success = work.solve();
distance = work.distances();
return success;
}
#line 1 "components/fast_io.hpp"
#line 5 "components/fast_io.hpp"
#include <array>
#include <bit>
#line 8 "components/fast_io.hpp"
#include <charconv>
#line 11 "components/fast_io.hpp"
#include <cstdio>
#include <cstring>
#include <memory>
#line 15 "components/fast_io.hpp"
#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/warshall_floyd.test.cpp"
int main() {
FastInput input;
FastOutput output;
int n = 0, m = 0;
input.read(n); input.read(m);
WarshallFloyd<> graph(n);
for (int i = 0; i < m; ++i) {
int from = 0, to = 0;
std::int64_t weight = 0;
input.read(from); input.read(to); input.read(weight);
graph.add_edge(from, to, weight);
}
if (!graph.solve()) { output.println("NEGATIVE CYCLE"); return 0; }
for (int i = 0; i < n; ++i) for (int j = 0; j < n; ++j) {
if (j) output.write(' ');
if (graph(i, j) == graph.infinity()) output.write("INF");
else output.write(graph(i, j));
if (j + 1 == n) output.write('\n');
}
}