Test/LC/shortest_path.test.cpp

View this file on GitHub
Last update: 2023-12-14 22:32:29+09:00
Problem: https://judge.yosupo.jp/problem/shortest_path

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/shortest_path"

#include "../../Src/Template/IOSetting.hpp"
#include "../../Src/Graph/ShortestPath/Dijkstra.hpp"

int main() {
    using namespace zawa;
    SetFastIO();
    int n, m, s, t; std::cin >> n >> m >> s >> t;
    Dijkstra<u64> solver(n);
    for (int _{} ; _ < m ; _++) {
        int a, b, c; std::cin >> a >> b >> c;
        solver.addDirectedEdge(a, b, (u64)c);
    }
    auto tree{solver.build(s)};
    if (tree.connect(t)) {
        auto recover{tree.pathV(t)};
        std::cout << tree.dist(t) << ' ' << recover.size() - 1 << '\n';
        for (u32 i{} ; i + 1 < recover.size() ; i++) {
            std::cout << recover[i] << ' ' << recover[i + 1] << '\n';
        }
    }
    else {
        std::cout << -1 << '\n';
    }
}

#line 1 "Test/LC/shortest_path.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/shortest_path"

#line 2 "Src/Template/IOSetting.hpp"

#line 2 "Src/Template/TypeAlias.hpp"

#include <cstdint>
#include <cstddef>

namespace zawa {

using i16 = std::int16_t;
using i32 = std::int32_t;
using i64 = std::int64_t;
using i128 = __int128_t;

using u8 = std::uint8_t;
using u16 = std::uint16_t;
using u32 = std::uint32_t;
using u64 = std::uint64_t;

using usize = std::size_t;

} // namespace zawa
#line 4 "Src/Template/IOSetting.hpp"

#include <iostream>
#include <iomanip>

namespace zawa {

void SetFastIO() {
    std::cin.tie(nullptr)->sync_with_stdio(false);
}

void SetPrecision(u32 dig) {
    std::cout << std::fixed << std::setprecision(dig);
}

} // namespace zawa
#line 2 "Src/Graph/ShortestPath/Dijkstra.hpp"

#line 2 "Src/Graph/ShortestPath/WeightedShortestPathTree.hpp"

#line 2 "Src/Graph/ShortestPath/Edge.hpp"

#line 4 "Src/Graph/ShortestPath/Edge.hpp"

namespace zawa {

namespace internal {

class Edge {
protected:
    static constexpr u32 INVALID{static_cast<u32>(-1)};
public:
    u32 parent{INVALID}; 
    u32 id{INVALID};
    Edge() = default;
    Edge(u32 parent, u32 id) : parent{parent}, id{id} {}
    Edge& operator=(const Edge& edge) {
        parent = edge.parent;
        id = edge.id;
        return *this;
    }
    inline bool exist() const noexcept {
        return parent != INVALID;
    }
    static constexpr u32 invalid() noexcept {
        return INVALID; 
    }
};

template <class Weight>
class WeightedEdge : public Edge {
public:
    Weight weight{INVALID};
    WeightedEdge() = default;
    WeightedEdge(u32 parent, const Weight& weight, u32 id)
        : Edge{parent, id}, weight{weight} {}

    WeightedEdge& operator=(const WeightedEdge& edge) {
        parent = edge.parent;
        id = edge.id;
        weight = edge.weight;
        return *this;
    }

};

} // namespace internal

} // namespace zawa
#line 5 "Src/Graph/ShortestPath/WeightedShortestPathTree.hpp"

#include <algorithm>
#include <cassert>
#include <type_traits>
#include <vector>

namespace zawa {

namespace internal {

template <class Weight>
class WeightedShortestPathTree {
public:
    static_assert(std::is_unsigned_v<Weight>, "Dijkstra's Algorithm only be work well by unsigned weight");
    using E = WeightedEdge<Weight>;
    static constexpr u32 invalid() noexcept {
        return E::invalid();
    }
private:
    static constexpr u32 INVALID{E::invalid()};
    usize n_;
    u32 root_;
    std::vector<E> tree_;
    std::vector<Weight> dist_;
public:
    WeightedShortestPathTree() = default;
    WeightedShortestPathTree(u32 n, u32 root) 
        : n_{n}, root_{root}, tree_(n), dist_(n, static_cast<Weight>(-1)) {
        assert(root < n);
        tree_.shrink_to_fit();
        dist_.shrink_to_fit();
        dist_[root] = Weight{};
    }

    inline usize size() const noexcept {
        return n_;
    }
    inline u32 root() const noexcept {
        return root_;
    }
    inline u32 parent(u32 v) const noexcept {
        assert(v < size());
        return tree_[v].parent;
    }
    inline u32 id(u32 v) const noexcept {
        assert(v < size());
        return tree_[v].id;
    }
    inline bool connect(u32 v) const noexcept {
        assert(v < size());
        return v == root_ or tree_[v].exist();
    }
    inline const Weight& dist(u32 v) const noexcept {
        assert(v < size());
        return dist_[v];
    }

    const Weight& operator[](u32 v) const noexcept {
        assert(v < size());
        return dist_[v];
    }

    bool relax(u32 from, u32 to, const Weight& weight, u32 id) {
        if (dist_[to] > dist_[from] + weight) {
            dist_[to] = dist_[from] + weight;
            tree_[to].parent = from;
            tree_[to].id = id;
            return true;
        }
        return false;
    }

    std::vector<u32> pathV(u32 v) {
        assert(v < size());
        assert(connect(v));
        std::vector<u32> res(1);
        res[0] = v;
        while (parent(v) != invalid()) {
            v = parent(v);
            res.emplace_back(v);
        }
        std::reverse(res.begin(), res.end());
        return res;
    }

    std::vector<E> pathE(u32 v) {
        assert(v < size());
        assert(connect(v));
        std::vector<E> res;
        while (v != root()) {
            res.emplace_back(tree_[v]);
            v = parent(v);
        }
        std::reverse(res.begin(), res.end());
        return res;
    }
};

} // namespace internal

} // namespace zawa
#line 5 "Src/Graph/ShortestPath/Dijkstra.hpp"

#line 7 "Src/Graph/ShortestPath/Dijkstra.hpp"
#include <queue>
#include <tuple>
#include <utility>
#line 11 "Src/Graph/ShortestPath/Dijkstra.hpp"

namespace zawa {

template <class Weight>
class Dijkstra {
public:
    using ShortestPathTree = internal::WeightedShortestPathTree<Weight>;
private:
    usize n_;
    std::vector<std::vector<std::tuple<u32, Weight, u32>>> adj_;

    static constexpr u32 invalid() noexcept {
        return ShortestPathTree::invalid();
    }

public:
    Dijkstra() = default;
    Dijkstra(usize n) : n_{n}, adj_(n) {
        adj_.shrink_to_fit();
    }
    usize size() const noexcept {
        return n_;
    }
    Dijkstra(const std::vector<std::pair<u32, Weight>>& g) : n_{g.size()}, adj_(g.size()) {
        adj_.shrink_to_fit();
        for (u32 v{} ; v < size() ; v++) {
            for (auto [x, w] : g[v]) {
                adj_[v].emplace_back(x, w, invalid);
            }
        }
    }
    void addDirectedEdge(u32 from, u32 to, const Weight& weight, u32 id = invalid()) {
        assert(from < size());
        assert(to < size());
        adj_[from].emplace_back(to, weight, id);
    }
    void addUndirectedEdge(u32 u, u32 v, const Weight& weight, u32 id = invalid()) {
        assert(u < size());
        assert(v < size());
        adj_[u].emplace_back(v, weight, id);
        adj_[v].emplace_back(u, weight, id);
    }

    ShortestPathTree build(u32 start) {
        using QueueData = std::pair<Weight, u32>;
        std::priority_queue<QueueData, std::vector<QueueData>, std::greater<QueueData>> queue;
        queue.emplace(Weight{}, start);
        ShortestPathTree res(n_, start);
        while (queue.size()) {
            auto [w, v]{queue.top()};
            queue.pop();
            if (res.dist(v) < w) {
                continue;
            }
            for (auto [x, w, id] : adj_[v]) {
                if (res.relax(v, x, w, id)) {
                    queue.emplace(res.dist(x), x);
                }
            } 
        }
        return res;
    }
};

} // namespace zawa
#line 5 "Test/LC/shortest_path.test.cpp"

int main() {
    using namespace zawa;
    SetFastIO();
    int n, m, s, t; std::cin >> n >> m >> s >> t;
    Dijkstra<u64> solver(n);
    for (int _{} ; _ < m ; _++) {
        int a, b, c; std::cin >> a >> b >> c;
        solver.addDirectedEdge(a, b, (u64)c);
    }
    auto tree{solver.build(s)};
    if (tree.connect(t)) {
        auto recover{tree.pathV(t)};
        std::cout << tree.dist(t) << ' ' << recover.size() - 1 << '\n';
        for (u32 i{} ; i + 1 < recover.size() ; i++) {
            std::cout << recover[i] << ' ' << recover[i + 1] << '\n';
        }
    }
    else {
        std::cout << -1 << '\n';
    }
}