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:heavy_check_mark: Src/Graph/ShortestPath/BFS.hpp

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#pragma once

#include "../../Template/TypeAlias.hpp"
#include "./ShortestPathTree.hpp"

#include <utility>
#include <vector>

namespace zawa {

class BFS {
public:
    using ShortestPathTree = internal::ShortestPathTree;
private:
    usize n_;
    std::vector<std::vector<std::pair<u32, u32>>> adj_;

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

public:
    BFS() = default;
    BFS(usize n) : n_{n}, adj_(n) {
        adj_.shrink_to_fit();
    }

    usize size() const noexcept {
        return n_;
    }
    void addDirectedEdge(u32 from, u32 to, u32 id = invalid()) {
        assert(from < size());
        assert(to < size());
        adj_[from].emplace_back(to, id);
    }
    void addUndirectedEdge(u32 u, u32 v, u32 id = invalid()) {
        assert(u < size());
        assert(v < size());
        adj_[u].emplace_back(v, id);
        adj_[v].emplace_back(u, id);
    }

    BFS(const std::vector<std::vector<u32>>& g) : n_{g.size()}, adj_(g.size()) {
        adj_.shrink_to_fit();
        for (u32 v{} ; v < size() ; v++) {
            for (u32 x : g[v]) {
                adj_[v].emplace_back(x, invalid());
            }
        }
    }

    ShortestPathTree build(u32 start) {
        std::vector<u32> queue;
        queue.reserve(n_);
        ShortestPathTree res(n_, start);
        queue.emplace_back(start);
        for (u32 head{} ; head < queue.size() ; head++) {
            u32 v{queue[head]};
            for (auto [x, id] : adj_[v]) {
                if (res.relax(v, x, id)) {
                    queue.emplace_back(x);
                }
            }
        }
        return res;
    }
};

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

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

namespace zawa {

namespace internal {

class ShortestPathTree {
public:
    using E = Edge;
    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<u32> dist_;
public:
    ShortestPathTree() = default;
    ShortestPathTree(usize n, u32 root) : n_{n}, root_{root}, tree_(n), dist_(n, INVALID) {
        assert(root < n);
        tree_.shrink_to_fit();
        dist_.shrink_to_fit();
        dist_[root] = 0;
    }

    inline usize size() const noexcept {
        return n_;
    }
    inline usize 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 root() == v or tree_[v].exist();
    }
    inline u32 dist(u32 v) const noexcept {
        assert(v < size());
        return dist_[v];
    }

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

    bool relax(u32 from, u32 to, u32 id) {
        if (dist_[to] > dist_[from] + 1) {
            dist_[to] = dist_[from] + 1;
            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(dist(v) + 1);
        res[dist(v)] = v;
        for (u32 i{dist(v)} ; i-- ; ) {
            v = parent(v);
            res[i] = v;
        }
        return res;
    }
    
    std::vector<E> pathE(u32 v) {
        assert(v < size());
        assert(connect(v));
        std::vector<E> res(dist(v));
        for (u32 i{dist(v)} ; i-- ; ) {
            res[i] = tree_[v];
            v = parent(v);
        }
        return res;
    }
};

} // namespace internal

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

#include <utility>
#line 8 "Src/Graph/ShortestPath/BFS.hpp"

namespace zawa {

class BFS {
public:
    using ShortestPathTree = internal::ShortestPathTree;
private:
    usize n_;
    std::vector<std::vector<std::pair<u32, u32>>> adj_;

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

public:
    BFS() = default;
    BFS(usize n) : n_{n}, adj_(n) {
        adj_.shrink_to_fit();
    }

    usize size() const noexcept {
        return n_;
    }
    void addDirectedEdge(u32 from, u32 to, u32 id = invalid()) {
        assert(from < size());
        assert(to < size());
        adj_[from].emplace_back(to, id);
    }
    void addUndirectedEdge(u32 u, u32 v, u32 id = invalid()) {
        assert(u < size());
        assert(v < size());
        adj_[u].emplace_back(v, id);
        adj_[v].emplace_back(u, id);
    }

    BFS(const std::vector<std::vector<u32>>& g) : n_{g.size()}, adj_(g.size()) {
        adj_.shrink_to_fit();
        for (u32 v{} ; v < size() ; v++) {
            for (u32 x : g[v]) {
                adj_[v].emplace_back(x, invalid());
            }
        }
    }

    ShortestPathTree build(u32 start) {
        std::vector<u32> queue;
        queue.reserve(n_);
        ShortestPathTree res(n_, start);
        queue.emplace_back(start);
        for (u32 head{} ; head < queue.size() ; head++) {
            u32 v{queue[head]};
            for (auto [x, id] : adj_[v]) {
                if (res.relax(v, x, id)) {
                    queue.emplace_back(x);
                }
            }
        }
        return res;
    }
};

} // namespace zawa
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