cp-library
競技プログラミング用 C++ ライブラリ
test/bellman_ford_path.test.cpp
test/bellman_ford_path.test.cpp · GitHub で見る
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コード
#define PROBLEM "https://judge.yosupo.jp/problem/shortest_path"
#include "../graph/bellman_ford.hpp"
#include "../components/fast_io.hpp"
int main() {
FastInput in;
FastOutput out;
int n = 0, m = 0, source = 0, target = 0;
in.read(n); in.read(m); in.read(source); in.read(target);
DirectedCSR<int> g(n, m, [&](auto emit) {
for (int i = 0; i < m; ++i) {
int v = 0, to = 0, w = 0;
in.read(v); in.read(to); in.read(w);
emit(DirectedCSR<int>::Edge{v, to, w});
}
});
auto result = bellman_ford(g, source);
if (!result.reachable(target)) { out.println(-1); return 0; }
auto path = result.path(target);
out.write(result.distance[target]); out.write(' '); out.println(path.size() - 1);
for (std::size_t i = 1; i < path.size(); ++i) { out.write(path[i - 1]); out.write(' '); out.println(path[i]); }
}
#line 1 "test/bellman_ford_path.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/shortest_path"
#line 1 "graph/bellman_ford.hpp"
#line 1 "components/shortest_path_scc.hpp"
#include <algorithm>
#include <cassert>
#include <cstddef>
#include <limits>
#include <vector>
namespace negative_path_detail {
struct Components {
std::vector<int> id, vertices;
std::vector<std::size_t> offset{0};
};
template<class Graph>
Components reachable_components(const Graph &g, int source) {
assert(std::size_t(g.size()) <= std::size_t(std::numeric_limits<int>::max()));
int n = static_cast<int>(g.size());
assert(0 <= source && source < n);
Components result;
result.id.assign(n, -1);
std::vector<int> index(n, -1), low(n), pending;
struct Frame { int vertex; std::size_t next; };
std::vector<Frame> stack;
int clock = 0, count = 0;
auto enter = [&](int v) {
index[v] = low[v] = clock++;
pending.push_back(v);
stack.push_back({v, 0});
};
enter(source);
while (!stack.empty()) {
int v = stack.back().vertex;
if (stack.back().next < g[v].size()) {
int to = g[v][stack.back().next++].first;
assert(0 <= to && to < n);
if (index[to] == -1) enter(to);
else if (result.id[to] == -1) low[v] = std::min(low[v], index[to]);
} else {
stack.pop_back();
if (low[v] == index[v]) {
int u;
do {
u = pending.back();
pending.pop_back();
result.id[u] = count;
result.vertices.push_back(u);
} while (u != v);
++count;
result.offset.push_back(result.vertices.size());
}
if (!stack.empty()) {
int parent = stack.back().vertex;
low[parent] = std::min(low[parent], low[v]);
}
}
}
return result;
}
}
#line 1 "components/directed_csr.hpp"
#line 7 "components/directed_csr.hpp"
#include <cstdint>
#include <memory>
#include <span>
#include <stdexcept>
#include <type_traits>
#include <utility>
#line 14 "components/directed_csr.hpp"
namespace directed_csr_detail { struct Access; }
template<class T>
class DirectedCSR {
public:
struct Edge { int from, to; T weight; };
using Arc = std::pair<int, T>;
using weight_type = T;
using distance_type = std::conditional_t<std::is_integral_v<T> && sizeof(T) < 8, std::int64_t, T>;
private:
friend struct directed_csr_detail::Access;
std::vector<std::size_t> offset_;
std::vector<Arc> arcs_;
int single_gap_ = -2;
bool unique_incoming_ = true;
void reset(int n, std::size_t m) {
assert(n >= 0);
offset_.assign(std::size_t(n) + 1, 0);
single_gap_ = -2;
unique_incoming_ = m <= std::size_t(n);
}
void count_edge(const Edge &edge, std::vector<std::uint64_t> &seen) {
assert(0 <= edge.from && edge.from < size() && 0 <= edge.to && edge.to < size());
++offset_[edge.from];
if (unique_incoming_) {
auto mask = std::uint64_t(1) << (edge.to % 64);
auto &word = seen[edge.to / 64];
unique_incoming_ = !(word & mask);
word |= mask;
}
}
void finish(std::span<const Edge> edges) {
const auto n = offset_.size() - 1;
single_gap_ = -2;
if (edges.size() >= n - (n != 0) && edges.size() <= n &&
std::all_of(offset_.begin(), offset_.end() - 1, [](std::size_t x) { return x <= 1; })) {
single_gap_ = -1;
if (edges.size() != n) single_gap_ = int(std::find(offset_.begin(), offset_.end() - 1, 0) - offset_.begin());
for (std::size_t v = 0; v <= n; ++v) offset_[v] = v - (single_gap_ >= 0 && v > std::size_t(single_gap_));
arcs_.resize(edges.size());
for (const auto &edge : edges) arcs_[edge.from - (single_gap_ >= 0 && edge.from > single_gap_)] = {edge.to, edge.weight};
return;
}
std::size_t active = offset_[0] != 0;
for (std::size_t v = 1; v < offset_.size(); ++v) {
active += offset_[v] != 0;
offset_[v] += offset_[v - 1];
}
arcs_.resize(edges.size());
std::size_t i = edges.size();
#if defined(__GNUC__) || defined(__clang__)
if (active >= 8192) {
for (; i > 32; --i) {
const auto from = edges[i - 33].from;
__builtin_prefetch(&offset_[from], 1, 3);
__builtin_prefetch(&arcs_[offset_[from] - 1], 1, 3);
const auto &edge = edges[i - 1];
arcs_[--offset_[edge.from]] = {edge.to, edge.weight};
}
}
#endif
for (; i; --i) {
const auto &edge = edges[i - 1];
arcs_[--offset_[edge.from]] = {edge.to, edge.weight};
}
}
void clear_edges() {
single_gap_ = -2;
unique_incoming_ = true;
std::fill(offset_.begin(), offset_.end(), 0);
arcs_.clear();
}
public:
explicit DirectedCSR(int n = 0) {
assert(n >= 0);
offset_.assign(std::size_t(n) + 1, 0);
}
DirectedCSR(int n, std::span<const Edge> edges) { build(n, edges); }
template<class Producer>
DirectedCSR(int n, std::size_t m, Producer &&produce) { build(n, m, std::forward<Producer>(produce)); }
void build(int n, std::span<const Edge> edges) {
reset(n, edges.size());
try {
std::vector<std::uint64_t> seen(unique_incoming_ ? (std::size_t(n) + 63) / 64 : 0);
for (const auto &edge : edges) count_edge(edge, seen);
finish(edges);
}
catch (...) { clear_edges(); throw; }
}
template<class Producer>
void build(int n, std::size_t m, Producer &&produce) {
reset(n, m);
try {
std::vector<std::uint64_t> seen(unique_incoming_ ? (std::size_t(n) + 63) / 64 : 0);
auto edges = std::make_unique_for_overwrite<Edge[]>(m);
std::size_t count = 0;
auto emit = [&](Edge edge) {
if (count == m) throw std::length_error("DirectedCSR edge count");
count_edge(edge, seen);
edges[count++] = std::move(edge);
};
std::forward<Producer>(produce)(emit);
if (count != m) throw std::length_error("DirectedCSR edge count");
finish(std::span<const Edge>(edges.get(), m));
} catch (...) { clear_edges(); throw; }
}
int size() const { return offset_.empty() ? 0 : int(offset_.size() - 1); }
bool empty() const { return size() == 0; }
std::size_t edge_count() const { return arcs_.size(); }
std::span<const Arc> operator[](int v) const {
assert(0 <= v && v < size());
return std::span<const Arc>(arcs_).subspan(offset_[v], offset_[v + 1] - offset_[v]);
}
};
namespace directed_csr_detail {
template<class T>
struct SingleEdgeView {
std::span<const typename DirectedCSR<T>::Arc> arcs;
int n, gap;
int size() const { return n; }
std::span<const typename DirectedCSR<T>::Arc> operator[](int v) const {
if (v == gap) return {};
return arcs.subspan(v - (gap >= 0 && v > gap), 1);
}
};
struct Access {
template<class T>
static bool unique_incoming(const DirectedCSR<T> &g) { return g.offset_.empty() || g.unique_incoming_; }
template<class T>
static bool has_single_edge_layout(const DirectedCSR<T> &g) { return !g.offset_.empty() && g.single_gap_ >= -1; }
template<class T>
static SingleEdgeView<T> single_edge_view(const DirectedCSR<T> &g) { return {g.arcs_, g.size(), g.single_gap_}; }
};
}
#line 1 "components/RadixHeap.hpp"
#line 5 "components/RadixHeap.hpp"
#include <bit>
#line 13 "components/RadixHeap.hpp"
template <class Key = std::uint64_t, class T = int>
class RadixHeap {
static_assert(std::is_integral_v<Key> && !std::is_same_v<Key, bool> && sizeof(Key) <= 8);
using U = std::make_unsigned_t<Key>;
using State = std::pair<Key, T>;
std::vector<State> bucket[std::numeric_limits<U>::digits + 1];
Key lower;
std::size_t count = 0;
int index(Key key) const { return std::bit_width(U(U(key) ^ U(lower))); }
void refill() {
assert(count);
if (!bucket[0].empty()) return;
int i = 1;
while (bucket[i].empty()) ++i;
lower = bucket[i][0].first;
for (const auto &s : bucket[i]) lower = std::min(lower, s.first);
for (auto &s : bucket[i]) bucket[index(s.first)].push_back(std::move(s));
bucket[i].clear();
}
public:
explicit RadixHeap(Key minimum = 0) : lower(minimum) {}
RadixHeap(const RadixHeap &) = default;
RadixHeap &operator=(const RadixHeap &) = default;
RadixHeap(RadixHeap &&other) noexcept : lower(other.lower), count(std::exchange(other.count, 0)) {
for (int i = 0; i <= std::numeric_limits<U>::digits; ++i) bucket[i] = std::move(other.bucket[i]);
}
RadixHeap &operator=(RadixHeap &&other) noexcept {
if (this != &other) {
lower = other.lower;
count = std::exchange(other.count, 0);
for (int i = 0; i <= std::numeric_limits<U>::digits; ++i) bucket[i] = std::move(other.bucket[i]);
}
return *this;
}
bool empty() const { return count == 0; }
std::size_t size() const { return count; }
Key last() const { return lower; }
void clear(Key minimum = 0) {
for (auto &b : bucket) b.clear();
lower = minimum;
count = 0;
}
void push(State s) {
assert(s.first >= lower);
bucket[index(s.first)].push_back(std::move(s));
++count;
}
const State &top() {
refill();
return bucket[0].back();
}
void pop() {
refill();
bucket[0].pop_back();
--count;
}
State pop_value() {
refill();
State s = std::move(bucket[0].back());
bucket[0].pop_back();
--count;
return s;
}
};
#line 8 "graph/bellman_ford.hpp"
#include <functional>
#line 12 "graph/bellman_ford.hpp"
template<class Distance>
struct BellmanFordResult {
std::vector<Distance> distance;
std::vector<int> parent, negative_cycle;
std::vector<std::size_t> parent_edge, negative_cycle_edges;
Distance infinity;
int source;
bool has_negative_cycle() const { return !negative_cycle.empty(); }
bool reachable(int v) const {
assert(!has_negative_cycle() && 0 <= v && std::size_t(v) < distance.size());
return distance[v] != infinity;
}
std::vector<int> path(int v) const {
if (!reachable(v)) return {};
std::vector<int> result;
for (; v != source; v = parent[v]) result.push_back(v);
result.push_back(source);
std::reverse(result.begin(), result.end());
return result;
}
std::vector<std::size_t> path_edges(int v) const {
if (!reachable(v)) return {};
std::vector<std::size_t> result;
for (; v != source; v = parent[v]) result.push_back(parent_edge[v]);
std::reverse(result.begin(), result.end());
return result;
}
};
namespace negative_path_detail {
template<class Distance, class Weight>
Distance add(Distance a, Weight b) {
static_assert(std::numeric_limits<Distance>::is_integer && std::numeric_limits<Distance>::is_signed);
static_assert(std::numeric_limits<Weight>::is_integer && std::numeric_limits<Weight>::is_signed);
static_assert(std::numeric_limits<Distance>::digits >= std::numeric_limits<Weight>::digits);
Distance value;
#if defined(__GNUC__) || defined(__clang__)
if (__builtin_add_overflow(a, Distance(b), &value)) throw std::overflow_error("Bellman-Ford distance");
#else
Distance w = b;
if ((w > 0 && a > std::numeric_limits<Distance>::max() - w) ||
(w < 0 && a < std::numeric_limits<Distance>::lowest() - w)) throw std::overflow_error("Bellman-Ford distance");
value = a + w;
#endif
if (value == std::numeric_limits<Distance>::max()) throw std::overflow_error("Bellman-Ford infinity");
return value;
}
template<bool Decompose, int Passes, class Distance, class Graph>
BellmanFordResult<Distance> solve(const Graph &g, int source) {
assert(std::size_t(g.size()) <= std::size_t(std::numeric_limits<int>::max()));
int n = static_cast<int>(g.size());
assert(0 <= source && source < n);
Distance inf = std::numeric_limits<Distance>::max();
BellmanFordResult<Distance> result{std::vector<Distance>(n, inf), std::vector<int>(n, -1), {},
std::vector<std::size_t>(n, std::size_t(-1)), {}, inf, source};
result.distance[source] = 0;
result.parent[source] = source;
auto &d = result.distance;
std::vector<int> active, order;
auto relax = [&](int v, std::size_t i) {
const auto &[to, w] = g[v][i];
Distance next = add(d[v], w);
if (next >= d[to]) return false;
d[to] = next;
result.parent[to] = v;
result.parent_edge[to] = i;
return true;
};
for (int pass = 0; pass < Passes; ++pass) {
bool changed = false;
for (int v = 0; v < n; ++v) if (d[v] != inf)
for (std::size_t i = 0; i < g[v].size(); ++i) changed |= relax(v, i);
if (!changed) return result;
}
std::vector<int> position(n, -1);
std::vector<unsigned char> labeled(n);
Components components;
if constexpr (Decompose) components = reachable_components(g, source);
else {
components.id.assign(n, 0);
components.vertices.resize(n);
for (int v = 0; v < n; ++v) components.vertices[v] = v;
components.offset.push_back(n);
}
struct Frame { int vertex; std::size_t next, incoming; };
std::vector<Frame> stack;
using State = std::pair<Distance, int>;
constexpr bool radix = std::is_integral_v<Distance> && sizeof(Distance) <= 8;
std::conditional_t<radix, RadixHeap<Distance>, std::vector<State>> heap;
for (int c = static_cast<int>(components.offset.size()) - 2; c >= 0; --c) {
auto begin = components.offset[c], end = components.offset[c + 1];
auto internal = [&](int to) { return components.id[to] == c; };
bool negative = !Decompose;
Distance minimum = inf;
for (auto j = begin; j < end; ++j) {
int v = components.vertices[j];
minimum = std::min(minimum, d[v]);
if constexpr (Decompose)
for (const auto &[to, w] : g[v]) if (internal(to) && w < 0) negative = true;
}
if (minimum == inf) continue;
if (negative) {
active.clear();
for (auto j = begin; j < end; ++j) {
int v = components.vertices[j];
if (d[v] != inf) active.push_back(v);
}
while (!active.empty()) {
order.clear();
for (int v : active) labeled[v] = 0;
for (int root : active) {
if (position[root] != -1) continue;
bool useful = false;
for (const auto &[to, w] : g[root])
if (internal(to) && add(d[root], w) < d[to]) { useful = true; break; }
if (!useful) continue;
position[root] = 0;
stack.push_back({root, 0, std::size_t(-1)});
while (!stack.empty()) {
int v = stack.back().vertex;
if (stack.back().next == g[v].size()) {
position[v] = -2;
order.push_back(v);
stack.pop_back();
continue;
}
std::size_t i = stack.back().next++;
int to = g[v][i].first;
if (!internal(to) || !relax(v, i)) continue;
if (position[to] >= 0) {
for (auto j = std::size_t(position[to]); j < stack.size(); ++j) {
result.negative_cycle.push_back(stack[j].vertex);
if (j + 1 < stack.size()) result.negative_cycle_edges.push_back(stack[j + 1].incoming);
}
result.negative_cycle.push_back(to);
result.negative_cycle_edges.push_back(i);
return result;
}
if (position[to] == -1) {
position[to] = static_cast<int>(stack.size());
stack.push_back({to, 0, i});
}
}
}
active.clear();
for (auto it = order.rbegin(); it != order.rend(); ++it) {
int v = *it;
for (std::size_t i = 0; i < g[v].size(); ++i) {
int to = g[v][i].first;
if (internal(to) && relax(v, i) && !labeled[to]) active.push_back(to), labeled[to] = 1;
}
}
for (int v : order) position[v] = -1;
}
} else if (end - begin > 1) {
auto push = [&](Distance cost, int v) {
if constexpr (radix) heap.push({cost, v});
else { heap.emplace_back(cost, v); std::push_heap(heap.begin(), heap.end(), std::greater<State>()); }
};
if constexpr (radix) heap.clear(minimum);
for (auto j = begin; j < end; ++j) {
int v = components.vertices[j];
if (d[v] != inf) push(d[v], v);
}
while (!heap.empty()) {
auto [cost, v] = [&] {
if constexpr (radix) return heap.pop_value();
else { std::pop_heap(heap.begin(), heap.end(), std::greater<State>()); auto state = heap.back(); heap.pop_back(); return state; }
}();
if (cost != d[v]) continue;
for (std::size_t i = 0; i < g[v].size(); ++i) {
int to = g[v][i].first;
if (internal(to) && relax(v, i)) push(d[to], to);
}
}
}
if constexpr (Decompose)
for (auto j = begin; j < end; ++j) {
int v = components.vertices[j];
for (std::size_t i = 0; i < g[v].size(); ++i) if (!internal(g[v][i].first)) relax(v, i);
}
}
return result;
}
}
template<class Distance = std::int64_t, class Graph>
BellmanFordResult<Distance> bellman_ford(const Graph &g, int source) {
return negative_path_detail::solve<true, 2, Distance>(g, source);
}
template<class Distance = std::int64_t, class Graph>
BellmanFordResult<Distance> goldberg_radzik(const Graph &g, int source) {
return negative_path_detail::solve<false, 0, Distance>(g, source);
}
#line 1 "components/fast_io.hpp"
#line 5 "components/fast_io.hpp"
#include <array>
#line 8 "components/fast_io.hpp"
#include <charconv>
#line 11 "components/fast_io.hpp"
#include <cstdio>
#include <cstring>
#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/bellman_ford_path.test.cpp"
int main() {
FastInput in;
FastOutput out;
int n = 0, m = 0, source = 0, target = 0;
in.read(n); in.read(m); in.read(source); in.read(target);
DirectedCSR<int> g(n, m, [&](auto emit) {
for (int i = 0; i < m; ++i) {
int v = 0, to = 0, w = 0;
in.read(v); in.read(to); in.read(w);
emit(DirectedCSR<int>::Edge{v, to, w});
}
});
auto result = bellman_ford(g, source);
if (!result.reachable(target)) { out.println(-1); return 0; }
auto path = result.path(target);
out.write(result.distance[target]); out.write(' '); out.println(path.size() - 1);
for (std::size_t i = 1; i < path.size(); ++i) { out.write(path[i - 1]); out.write(' '); out.println(path[i]); }
}