test/dijkstra.test.cpp

test/dijkstra.test.cpp · GitHub で見る

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#define PROBLEM "https://judge.yosupo.jp/problem/shortest_path"
#include "../graph/dijkstra.hpp"
#include <algorithm>
#include <cstdint>
#include <iostream>
#include <tuple>
#include <utility>
#include <vector>

using namespace std;

int main() {
	cin.tie(nullptr)->sync_with_stdio(false);
	int n, m, s, t;
	cin >> n >> m >> s >> t;
	vector<vector<pair<int, int64_t>>> g(n);
	for (int repeat_index = 0; repeat_index < m; ++repeat_index) {
		int u, v;
		int64_t c;
		cin >> u >> v >> c;
		g[u].emplace_back(v, c);
	}
	auto d = dijkstra(g, s);
	if (d[t] == -1) {
		cout << -1 << '\n';
		return 0;
	}
	vector<int> parent(n, -1), todo{s};
	parent[s] = s;
	for (int i = 0; i < (static_cast<int>(todo.size())); ++i) {
		int v = todo[i];
		for (auto [to, c] : g[v])
			if (parent[to] == -1 && d[to] == d[v] + c) {
				parent[to] = v;
				todo.push_back(to);
			}
	}
	vector<pair<int, int>> path;
	for (int v = t; v != s; v = parent[v]) path.emplace_back(parent[v], v);
	reverse(path.begin(), path.end());
	cout << d[t] << ' ' << static_cast<int>(path.size()) << '\n';
	for (auto [u, v] : path) cout << u << ' ' << v << '\n';
}

#line 1 "test/dijkstra.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/shortest_path"
#line 1 "graph/dijkstra.hpp"



#line 1 "components/dijkstra_queue.hpp"



#line 1 "components/RadixHeap.hpp"



#include <algorithm>
#include <bit>
#include <cassert>
#include <cstddef>
#include <cstdint>
#include <limits>
#include <type_traits>
#include <utility>
#include <vector>

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 10 "components/dijkstra_queue.hpp"
#include <functional>
#line 15 "components/dijkstra_queue.hpp"

namespace shortest_path_detail {
template<class Weight, class Distance>
bool reaches_limit(const Weight &weight, const Distance &limit) {
	if constexpr (std::numeric_limits<Weight>::is_integer && std::numeric_limits<Weight>::is_bounded &&
				  std::numeric_limits<Distance>::is_integer && std::numeric_limits<Distance>::is_bounded) {
		using Compare = std::common_type_t<Weight, Distance>;
		return Compare(weight) >= Compare(limit);
	} else return weight >= limit;
}

template<class T> class RadixQueue {
	static_assert(std::is_integral_v<T> && sizeof(T) <= 8);
	struct State { T key; int vertex; };
	State small_[32];
	std::vector<std::uint64_t> buckets_[33];
	std::uint32_t minimum_[33];
	std::uint32_t occupied_ = 0;
	std::uint64_t last_ = 0;
	std::size_t count_ = 0;
	int mode_ = 0;
	RadixHeap<std::uint64_t> wide_;
	void put(std::uint64_t state) {
		std::uint32_t key = state >> 32;
		int index = std::bit_width(key ^ std::uint32_t(last_));
		buckets_[index].push_back(state);
		if (index) {
			occupied_ |= std::uint32_t(1) << (index - 1);
			minimum_[index] = std::min(minimum_[index], key);
		}
	}
	void promote() {
		if (mode_ == 0) {
			for (std::size_t i = 0; i < count_; ++i) wide_.push({std::uint64_t(small_[i].key), small_[i].vertex});
		} else {
			for (auto &bucket : buckets_) {
				for (auto state : bucket) {
					std::uint64_t key = last_ + std::uint32_t(std::uint32_t(state >> 32) - std::uint32_t(last_));
					wide_.push({key, int(std::uint32_t(state))});
				}
				bucket.clear();
			}
		}
		mode_ = 2;
	}

  public:
	bool empty() const { return count_ == 0; }
	void push(T key, int vertex) {
		assert(key >= 0 && std::uint64_t(key) >= last_);
		if (mode_ == 0 && count_ < 32) {
			small_[count_++] = {key, vertex};
			return;
		}
		if (mode_ == 0) {
			bool narrow = std::uint64_t(key) - last_ <= std::uint64_t(std::numeric_limits<std::int32_t>::max());
			for (std::size_t i = 0; i < count_; ++i)
				narrow &= std::uint64_t(small_[i].key) - last_ <= std::uint64_t(std::numeric_limits<std::int32_t>::max());
			if (narrow) {
				std::fill_n(minimum_, 33, std::numeric_limits<std::uint32_t>::max());
				for (std::size_t i = 0; i < count_; ++i)
					put((std::uint64_t(std::uint32_t(small_[i].key)) << 32) | std::uint32_t(small_[i].vertex));
				mode_ = 1;
			} else promote();
		}
		if (mode_ == 1 && std::uint64_t(key) - last_ > std::uint64_t(std::numeric_limits<std::int32_t>::max())) promote();
		if (mode_ == 2) wide_.push({std::uint64_t(key), vertex});
		else put((std::uint64_t(std::uint32_t(key)) << 32) | std::uint32_t(vertex));
		++count_;
	}
	std::pair<T, int> pop() {
		assert(count_);
		if (mode_ == 0) {
			std::size_t best = 0;
			for (std::size_t i = 1; i < count_; ++i)
				if (small_[i].key < small_[best].key) best = i;
			State state = small_[best];
			small_[best] = small_[--count_];
			last_ = std::uint64_t(state.key);
			return {state.key, state.vertex};
		}
		if (mode_ == 2) {
			auto state = wide_.pop_value();
			last_ = state.first;
			--count_;
			return {T(state.first), state.second};
		}
		if (buckets_[0].empty()) {
			int index = std::countr_zero(occupied_) + 1;
			last_ += std::uint32_t(minimum_[index] - std::uint32_t(last_));
			minimum_[index] = std::numeric_limits<std::uint32_t>::max();
			occupied_ &= occupied_ - 1;
			if (buckets_[index].size() == 1) {
				auto state = buckets_[index].back();
				buckets_[index].clear();
				--count_;
				return {T(last_), int(std::uint32_t(state))};
			}
			for (auto state : buckets_[index]) put(state);
			buckets_[index].clear();
		}
		auto state = buckets_[0].back();
		buckets_[0].pop_back();
		--count_;
		return {T(last_), int(std::uint32_t(state))};
	}
};

template<class T> class BinaryQueue {
	using State = std::pair<T, int>;
	std::vector<State> heap_;

  public:
	bool empty() const { return heap_.empty(); }
	void push(T cost, int vertex) {
		heap_.emplace_back(std::move(cost), vertex);
		std::push_heap(heap_.begin(), heap_.end(), std::greater<State>());
	}
	State pop() {
		std::pop_heap(heap_.begin(), heap_.end(), std::greater<State>());
		State state = std::move(heap_.back());
		heap_.pop_back();
		return state;
	}
};

template<class T>
using DistanceQueue = std::conditional_t<std::is_integral_v<T> && sizeof(T) <= 8, RadixQueue<T>, BinaryQueue<T>>;
}


#line 1 "components/dijkstra_topological.hpp"



#line 11 "components/dijkstra_topological.hpp"

namespace shortest_path_detail {
template<bool Path, class G, class T>
std::vector<T> topological_run(const G &g, int start, int target, T inf, std::vector<int> &parent) {
	std::size_t n = std::size_t(g.size());
	assert(n <= static_cast<std::size_t>(std::numeric_limits<int>::max()));
	assert(start >= 0 && static_cast<std::size_t>(start) < n);
	assert(inf > 0);
	std::vector<T> distance(n, inf);
	std::vector<std::size_t> indegree(n);
	std::vector<int> ready;
	ready.reserve(n);
	for (std::size_t v = 0; v < n; ++v)
		for (const auto &[to, weight] : g[int(v)]) {
			assert(to >= 0 && static_cast<std::size_t>(to) < n);
			assert(weight >= 0);
			++indegree[to];
		}
	for (std::size_t v = 0; v < n; ++v)
		if (!indegree[v]) ready.push_back(int(v));
	distance[start] = 0;
	auto improve = [&](int from, const T &cost, const T &allowance, int to, const auto &weight) {
		if (reaches_limit(weight, allowance)) return false;
		T next = cost + weight;
		if (next >= distance[to]) return false;
		if constexpr (Path) {
			if (next >= distance[target]) return false;
			parent[to] = from;
		}
		distance[to] = std::move(next);
		return true;
	};
	for (std::size_t head = 0; head < ready.size(); ++head) {
		int v = ready[head];
		if constexpr (Path) if (v == target) return distance;
		T cost = distance[v];
		bool active = cost < inf;
		if constexpr (Path) active &= cost < distance[target];
		T allowance = active ? inf - cost : T(0);
		for (const auto &[to, weight] : g[v]) {
			if (active) improve(v, cost, allowance, to, weight);
			if (--indegree[to] == 0) ready.push_back(to);
		}
	}
	DistanceQueue<T> queue;
	for (std::size_t v = 0; v < n; ++v) {
		if (!indegree[v] || distance[v] == inf || g[v].empty()) continue;
		if constexpr (Path) if (int(v) == target || distance[v] >= distance[target]) continue;
		queue.push(distance[v], int(v));
	}
	while (!queue.empty()) {
		const auto [cost, v] = queue.pop();
		if (cost != distance[v]) continue;
		if constexpr (Path) if (cost >= distance[target]) break;
		T allowance = inf - cost;
		for (const auto &[to, weight] : g[v]) {
			if (!improve(v, cost, allowance, to, weight)) continue;
			if constexpr (Path) if (to == target) continue;
			if (!g[to].empty()) queue.push(distance[to], to);
		}
	}
	return distance;
}
}


#line 1 "components/dijkstra_unique.hpp"



#line 9 "components/dijkstra_unique.hpp"

namespace shortest_path_detail {
template<class G, class T>
std::pair<T, std::vector<int>> unique_path(const G &g, int st, int target, T inf, std::vector<int> &parent) {
	using State = std::pair<T, int>;
	std::vector<State> pending;
	pending.emplace_back(T(0), st);
	while (!pending.empty()) {
		auto [cost, v] = std::move(pending.back());
		pending.pop_back();
		for (const auto &first : g[v]) {
			const auto *edge = &first;
			int from = v;
			T prefix = cost;
			for (;;) {
				const auto &[to, weight] = *edge;
				assert(weight >= 0);
				if (to == st) break;
				if (reaches_limit(weight, T(inf - prefix))) break;
				T next = prefix + weight;
				if (to == target) {
					std::vector<int> path{to};
					for (int u = from; u != st; u = parent[u]) path.push_back(u);
					path.push_back(st);
					std::reverse(path.begin(), path.end());
					return {std::move(next), std::move(path)};
				}
				const auto &outgoing = g[to];
				if (outgoing.empty()) break;
				parent[to] = from;
				if (outgoing.size() != 1) {
					pending.emplace_back(std::move(next), to);
					break;
				}
				from = to;
				edge = &outgoing[0];
				prefix = std::move(next);
			}
		}
	}
	return {T(-1), {}};
}
}


#line 1 "components/directed_csr.hpp"



#line 8 "components/directed_csr.hpp"
#include <memory>
#include <span>
#include <stdexcept>
#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 16 "graph/dijkstra.hpp"

inline constexpr std::int64_t DIJKSTRA_INF = 4'000'000'000'000'000'000;

namespace shortest_path_detail {
template<class T> T infinity() {
	if constexpr (std::numeric_limits<T>::is_bounded && std::numeric_limits<T>::is_integer && std::numeric_limits<T>::digits < 62)
		return std::numeric_limits<T>::max();
	else return T(DIJKSTRA_INF);
}

template<bool Path, class G, class T>
std::vector<T> run(const G &g, int st, int target, T inf, std::vector<int> &parent) {
	const auto n = static_cast<std::size_t>(g.size());
	assert(n <= static_cast<std::size_t>(std::numeric_limits<int>::max()));
	assert(st >= 0 && static_cast<std::size_t>(st) < n);
	assert(inf > 0);
	std::vector<T> d(n, inf);
	d[st] = 0;
	DistanceQueue<T> pq;
	pq.push(0, st);
	while (!pq.empty()) {
		const auto [cost, v] = pq.pop();
		if (d[v] != cost) continue;
		if constexpr (Path) if (cost >= d[target]) break;
		T allowance = inf - cost;
		for (const auto &[to, c] : g[v]) {
			assert(to >= 0 && static_cast<std::size_t>(to) < n);
			assert(c >= 0);
			if (reaches_limit(c, allowance)) continue;
			T next = cost + c;
			if (next >= d[to]) continue;
			if constexpr (Path) {
				if (next >= d[target]) continue;
				parent[to] = v;
			}
			d[to] = next;
			if constexpr (Path) if (to == target) continue;
			if (!g[to].empty()) pq.push(std::move(next), to);
		}
	}
	return d;
}

template<bool Topological, class G, class T>
std::vector<T> distances(const G &g, int st, T inf) {
	std::vector<int> parent;
	auto d = [&] {
		if constexpr (Topological) return topological_run<false>(g, st, -1, inf, parent);
		else return run<false>(g, st, -1, inf, parent);
	}();
	for (T &val : d)
		if (val == inf) val = -1;
	return d;
}

template<bool Topological, class G, class T>
std::pair<T, std::vector<int>> path(const G &g, int st, int target, T inf) {
	[[maybe_unused]] const auto n = static_cast<std::size_t>(g.size());
	assert(n <= static_cast<std::size_t>(std::numeric_limits<int>::max()));
	assert(st >= 0 && static_cast<std::size_t>(st) < n);
	assert(target >= 0 && static_cast<std::size_t>(target) < n);
	assert(inf > 0);
	if (st == target) return {T(0), {st}};
	if (g[st].empty()) return {T(-1), {}};
	if (g[st].size() == 1) {
		using Weight = std::remove_cvref_t<decltype(g[st][0].second)>;
		std::vector<int> direct{st};
		T cost = 0;
		int v = st, checkpoint = st;
		std::size_t power = 1, length = 0;
		while (g[v].size() == 1) {
			const auto &[to, weight] = g[v][0];
			assert(to >= 0 && static_cast<std::size_t>(to) < n);
			assert(weight >= 0);
			if (reaches_limit(weight, T(inf - cost))) return {T(-1), {}};
			cost += weight;
			v = to;
			direct.push_back(v);
			if (v == target) return {std::move(cost), std::move(direct)};
			if (v == checkpoint) return {T(-1), {}};
			if (++length == power) {
				checkpoint = v;
				power *= 2;
				length = 0;
			}
		}
		if (g[v].empty()) return {T(-1), {}};
		if constexpr (std::numeric_limits<Weight>::is_integer && std::numeric_limits<T>::is_integer && std::numeric_limits<T>::is_bounded) {
			auto suffix = shortest_path_detail::path<Topological>(g, v, target, T(inf - cost));
			if (suffix.first == T(-1)) return {T(-1), {}};
			direct.pop_back();
			direct.insert(direct.end(), suffix.second.begin(), suffix.second.end());
			return {cost + suffix.first, std::move(direct)};
		}
	}
	std::vector<int> parent(g.size(), -1);
	if constexpr (requires { directed_csr_detail::Access::unique_incoming(g); })
		if (directed_csr_detail::Access::unique_incoming(g)) return unique_path(g, st, target, inf, parent);
	auto d = [&] {
		if constexpr (Topological) return topological_run<true>(g, st, target, inf, parent);
		else return run<true>(g, st, target, inf, parent);
	}();
	if (d[target] == inf) return {T(-1), {}};
	std::vector<int> path;
	for (int v = target; v != st; v = parent[v]) path.push_back(v);
	path.push_back(st);
	std::reverse(path.begin(), path.end());
	return {std::move(d[target]), std::move(path)};
}
}

template<bool Topological, class T>
std::vector<T> dijkstra(const std::vector<std::vector<std::pair<int, T>>> &g, int st, T inf = shortest_path_detail::infinity<T>()) {
	return shortest_path_detail::distances<Topological>(g, st, inf);
}

template<class T>
std::vector<T> dijkstra(const std::vector<std::vector<std::pair<int, T>>> &g, int st, T inf = shortest_path_detail::infinity<T>()) {
	return dijkstra<false>(g, st, inf);
}

template<bool Topological, class T>
std::pair<T, std::vector<int>> dijkstra_path(const std::vector<std::vector<std::pair<int, T>>> &g, int st, int target, T inf = shortest_path_detail::infinity<T>()) {
	return shortest_path_detail::path<Topological>(g, st, target, inf);
}

template<class T>
std::pair<T, std::vector<int>> dijkstra_path(const std::vector<std::vector<std::pair<int, T>>> &g, int st, int target, T inf = shortest_path_detail::infinity<T>()) {
	return dijkstra_path<false>(g, st, target, inf);
}

template<bool Topological, class W, class T = typename DirectedCSR<W>::distance_type>
std::vector<T> dijkstra(const DirectedCSR<W> &g, int st, T inf = shortest_path_detail::infinity<T>()) {
	return shortest_path_detail::distances<Topological>(g, st, inf);
}

template<class W, class T = typename DirectedCSR<W>::distance_type>
std::vector<T> dijkstra(const DirectedCSR<W> &g, int st, T inf = shortest_path_detail::infinity<T>()) {
	return dijkstra<false>(g, st, inf);
}

template<bool Topological, class W, class T = typename DirectedCSR<W>::distance_type>
std::pair<T, std::vector<int>> dijkstra_path(const DirectedCSR<W> &g, int st, int target, T inf = shortest_path_detail::infinity<T>()) {
	if (directed_csr_detail::Access::has_single_edge_layout(g))
		return shortest_path_detail::path<Topological>(directed_csr_detail::Access::single_edge_view(g), st, target, inf);
	return shortest_path_detail::path<Topological>(g, st, target, inf);
}

template<class W, class T = typename DirectedCSR<W>::distance_type>
std::pair<T, std::vector<int>> dijkstra_path(const DirectedCSR<W> &g, int st, int target, T inf = shortest_path_detail::infinity<T>()) {
	return dijkstra_path<false>(g, st, target, inf);
}


#line 5 "test/dijkstra.test.cpp"
#include <iostream>
#include <tuple>
#line 9 "test/dijkstra.test.cpp"

using namespace std;

int main() {
	cin.tie(nullptr)->sync_with_stdio(false);
	int n, m, s, t;
	cin >> n >> m >> s >> t;
	vector<vector<pair<int, int64_t>>> g(n);
	for (int repeat_index = 0; repeat_index < m; ++repeat_index) {
		int u, v;
		int64_t c;
		cin >> u >> v >> c;
		g[u].emplace_back(v, c);
	}
	auto d = dijkstra(g, s);
	if (d[t] == -1) {
		cout << -1 << '\n';
		return 0;
	}
	vector<int> parent(n, -1), todo{s};
	parent[s] = s;
	for (int i = 0; i < (static_cast<int>(todo.size())); ++i) {
		int v = todo[i];
		for (auto [to, c] : g[v])
			if (parent[to] == -1 && d[to] == d[v] + c) {
				parent[to] = v;
				todo.push_back(to);
			}
	}
	vector<pair<int, int>> path;
	for (int v = t; v != s; v = parent[v]) path.emplace_back(parent[v], v);
	reverse(path.begin(), path.end());
	cout << d[t] << ' ' << static_cast<int>(path.size()) << '\n';
	for (auto [u, v] : path) cout << u << ' ' << v << '\n';
}