hadlock.hpp

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#pragma once
 
#include <algorithm>
#include <cassert>
#include <functional>
#include <limits>
#include <map>
#include <py2cpp/dict.hpp>
#include <py2cpp/set.hpp>
#include <queue>
#include <set>
#include <utility>
#include <vector>
#include <xnetwork/thread_pool.hpp>
 
// Hash for std::pair - needed by py::set<std::pair<...>> (backed by unordered_set)
namespace std {
    template <typename T1, typename T2> struct hash<pair<T1, T2>> {
        size_t operator()(const pair<T1, T2>& p) const {
            return hash<T1>{}(p.first) ^ (hash<T2>{}(p.second) << 1);
        }
    };
}  // namespace std
 
namespace detail {
 
    constexpr int INF = std::numeric_limits<int>::max() / 2;
 
    template <typename Node> struct DualEdge {
        int neighbor;
        int weight;
        std::pair<Node, Node> primal;
    };
 
    // -------------------------------------------------------------------
    // Dual graph construction
    //
    // Each face -> dual vertex. Two dual vertices connect if faces share a
    // primal edge. Parallel edges -> only the minimum-weight edge is kept.
    // -------------------------------------------------------------------
    template <typename Node, typename WeightFunc>
    auto build_dual(const std::vector<std::vector<Node>>& faces, WeightFunc weight)
        -> std::vector<std::vector<DualEdge<Node>>> {
        const auto n_face = static_cast<int>(faces.size());
 
        std::map<std::pair<Node, Node>, std::vector<int>> edge_face_map;
        for (int fi = 0; fi < n_face; ++fi) {
            const auto& f = faces[fi];
            const auto sz = static_cast<int>(f.size());
            for (int i = 0; i < sz; ++i) {
                auto u = f[i];
                auto v = f[(i + 1) % sz];
                if (u > v) std::swap(u, v);
                edge_face_map[{u, v}].push_back(fi);
            }
        }
 
        std::map<std::pair<int, int>, std::pair<int, std::pair<Node, Node>>> best;
        for (const auto& [primal_key, face_ids] : edge_face_map) {
            if (face_ids.size() < 2) continue;
            const auto& [u, v] = primal_key;
            const int w = weight(u, v);
            for (size_t a = 0; a < face_ids.size(); ++a) {
                for (size_t b = a + 1; b < face_ids.size(); ++b) {
                    int fi = face_ids[a];
                    int fj = face_ids[b];
                    if (fi > fj) std::swap(fi, fj);
                    auto it = best.find({fi, fj});
                    if (it == best.end() || w < it->second.first) {
                        best[{fi, fj}] = {w, {u, v}};
                    }
                }
            }
        }
 
        std::vector<std::vector<DualEdge<Node>>> dual(n_face);
        for (const auto& [key, info] : best) {
            const auto& [fi, fj] = key;
            const auto& [w, primal] = info;
            dual[fi].push_back({fj, w, primal});
            dual[fj].push_back({fi, w, primal});
        }
        return dual;
    }
 
    // -------------------------------------------------------------------
    // Dijkstra shortest path
    // -------------------------------------------------------------------
    template <typename Node>
    auto dijkstra(const std::vector<std::vector<DualEdge<Node>>>& dual, int src)
        -> std::pair<std::vector<int>, std::vector<int>>;
 
    inline auto reconstruct_path(const std::vector<int>& prev, int src, int dst)
        -> std::vector<int> {
        std::vector<int> path;
        for (int v = dst; v != -1 && v != src; v = prev[v]) {
            path.push_back(v);
        }
        if (path.empty() && src != dst) return {};
        path.push_back(src);
        std::reverse(path.begin(), path.end());
        return path;
    }
 
    // -------------------------------------------------------------------
    // Minimum Weight Perfect Matching
    // -------------------------------------------------------------------
 
    template <typename Node>
    auto greedy_mwpm(const std::vector<int>& odd_faces, const std::vector<std::vector<int>>& dist)
        -> std::vector<std::pair<int, int>>;
 
    template <typename Node>
    auto exact_mwpm(const std::vector<int>& odd_faces, const std::vector<std::vector<int>>& dist)
        -> std::vector<std::pair<int, int>>;
 
    template <typename Node>
    auto min_weight_perfect_matching(const std::vector<int>& odd_faces,
                                     const std::vector<std::vector<int>>& dist)
        -> std::vector<std::pair<int, int>> {
        const int n = static_cast<int>(odd_faces.size());
        if (n <= 18) {
            return exact_mwpm<Node>(odd_faces, dist);
        }
        return greedy_mwpm<Node>(odd_faces, dist);
    }
 
    // -------------------------------------------------------------------
    // Biconnected Component Decomposition (for MAX-CUT speedup)
    // -------------------------------------------------------------------
 
    template <typename Graph> auto biconnected_components(const Graph& G)
        -> std::vector<py::set<typename Graph::node_t>>;
 
    // -------------------------------------------------------------------
    // Core Hadlock solver (single component)
    // -------------------------------------------------------------------
 
    template <typename Graph, typename WeightFunc>
    auto solve_hadlock_component(const Graph& G, WeightFunc weight,
                                 const std::vector<std::vector<typename Graph::node_t>>& faces)
        -> py::set<std::pair<typename Graph::node_t, typename Graph::node_t>> {
        using node_t = typename Graph::node_t;
 
        // (1) Build the dual graph
        const auto dual = build_dual<node_t>(faces, weight);
 
        // (2) Identify odd-degree faces
        std::vector<int> odd_faces;
        for (int i = 0; i < static_cast<int>(faces.size()); ++i) {
            if (faces[i].size() % 2 == 1) {
                odd_faces.push_back(i);
            }
        }
 
        // No odd faces -> graph is bipartite -> all edges are in the cut
        if (odd_faces.size() < 2) {
            py::set<std::pair<node_t, node_t>> all_edges;
            for (const auto& e : G.edges()) {
                all_edges.insert(e);
            }
            return all_edges;
        }
 
        // Odd number of odd faces -> drop one (planar graphs have even #odd faces)
        if (odd_faces.size() % 2 != 0) {
            odd_faces.pop_back();
            if (odd_faces.size() < 2) {
                py::set<std::pair<node_t, node_t>> all_edges;
                for (const auto& e : G.edges()) {
                    all_edges.insert(e);
                }
                return all_edges;
            }
        }
 
        const int n_odd = static_cast<int>(odd_faces.size());
 
        // odd_faces[k] -> k lookup
        std::map<int, int> odd_idx;
        for (int k = 0; k < n_odd; ++k) {
            odd_idx[odd_faces[k]] = k;
        }
 
        // (3) All-pairs shortest paths between odd faces
        std::vector<std::vector<int>> dist_mat(n_odd);
        std::vector<std::vector<std::vector<int>>> path_mat(n_odd,
                                                            std::vector<std::vector<int>>(n_odd));
 
        for (int i = 0; i < n_odd; ++i) {
            auto [dist, prev] = dijkstra<node_t>(dual, odd_faces[i]);
            dist_mat[i] = std::move(dist);
            for (int j = 0; j < n_odd; ++j) {
                if (i != j) {
                    path_mat[i][j] = reconstruct_path(prev, odd_faces[i], odd_faces[j]);
                }
            }
        }
 
        // (4) Minimum weight perfect matching on odd-face distances
        auto matching = min_weight_perfect_matching<node_t>(odd_faces, dist_mat);
 
        // (5) Collect primal edges excluded from the cut
        // Build dual-edge -> primal-edge lookup
        std::map<std::pair<int, int>, std::pair<node_t, node_t>> dedge_primal;
        for (int fi = 0; fi < static_cast<int>(dual.size()); ++fi) {
            for (const auto& e : dual[fi]) {
                int a = fi;
                int b = e.neighbor;
                if (a > b) std::swap(a, b);
                dedge_primal[{a, b}] = e.primal;
            }
        }
 
        // Walk each matched-pair path in the dual to find primal edges to exclude
        std::set<std::pair<node_t, node_t>> excluded;
        for (const auto& [u_face, v_face] : matching) {
            auto ui = odd_idx.find(u_face);
            auto vi = odd_idx.find(v_face);
            if (ui == odd_idx.end() || vi == odd_idx.end()) continue;
 
            const auto& path = path_mat[ui->second][vi->second];
            for (size_t k = 0; k + 1 < path.size(); ++k) {
                int a = path[k];
                int b = path[k + 1];
                if (a > b) std::swap(a, b);
                auto it = dedge_primal.find({a, b});
                if (it != dedge_primal.end()) {
                    auto [pu, pv] = it->second;
                    if (pu > pv) std::swap(pu, pv);
                    excluded.insert({pu, pv});
                }
            }
        }
 
        // (6) Max-cut = all edges not excluded
        py::set<std::pair<node_t, node_t>> cut_edges;
        for (const auto& e : G.edges()) {
            auto [u, v] = e;
            if (u > v) std::swap(u, v);
            if (!excluded.count({u, v})) {
                cut_edges.insert(e);
            }
        }
        return cut_edges;
    }
 
}  // namespace detail
 
// ===================================================================
// Public API
// ===================================================================
 
template <typename Graph, typename WeightFunc>
auto solve_hadlock_max_cut(const Graph& G, WeightFunc weight,
                           const std::vector<std::vector<typename Graph::node_t>>& faces)
    -> py::set<std::pair<typename Graph::node_t, typename Graph::node_t>> {
    return detail::solve_hadlock_component(G, weight, faces);
}
 
template <typename Graph, typename WeightFunc> auto solve_hadlock_max_cut(
    const Graph& G, WeightFunc weight,
    const std::vector<std::vector<std::vector<typename Graph::node_t>>>& component_faces)
    -> py::set<std::pair<typename Graph::node_t, typename Graph::node_t>> {
    using node_t = typename Graph::node_t;
    using edge_t = std::pair<node_t, node_t>;
 
    // Decompose into biconnected components
    auto comp_nodes = detail::biconnected_components(G);
 
    const auto n_comps = std::min(comp_nodes.size(), component_faces.size());
 
    // Components are independent (edges are disjoint), so no
    // synchronization is needed beyond collecting results.
    xnetwork::thread_pool pool;
    std::vector<std::future<py::set<edge_t>>> futures;
    futures.reserve(n_comps);
 
    for (size_t i = 0; i < n_comps; ++i) {
        futures.push_back(pool.enqueue([&, i]() -> py::set<edge_t> {
            const auto& comp_faces = component_faces[i];
 
            auto comp_weight = [&weight](node_t u, node_t v) -> int { return weight(u, v); };
 
            // Extract edges belonging to this component by scanning faces
            std::vector<std::pair<node_t, node_t>> comp_edges;
            for (const auto& face : comp_faces) {
                for (size_t j = 0; j < face.size(); ++j) {
                    auto u = face[j];
                    auto v = face[(j + 1) % face.size()];
                    if (u > v) std::swap(u, v);
                    edge_t e{u, v};
                    if (std::find(comp_edges.begin(), comp_edges.end(), e) == comp_edges.end()) {
                        comp_edges.push_back(e);
                    }
                }
            }
 
            struct CompGraph {
                using node_t = typename std::remove_reference<
                    decltype(comp_edges)>::type::value_type::first_type;
                const std::vector<std::pair<node_t, node_t>>& edge_list;
                auto edges() const { return edge_list; }
            };
 
            CompGraph comp_g{comp_edges};
            return detail::solve_hadlock_component(comp_g, comp_weight, comp_faces);
        }));
    }
 
    py::set<edge_t> cut_edges;
    for (auto& f : futures) {
        auto comp_cut = f.get();
        for (const auto& e : comp_cut) {
            cut_edges.insert(e);
        }
    }
 
    return cut_edges;
}
 
template <typename Graph, typename WeightFunc> auto validate_max_cut(
    [[maybe_unused]] const Graph& G,
    const py::set<std::pair<typename Graph::node_t, typename Graph::node_t>>& cut_edges,
    WeightFunc weight) -> std::pair<bool, int> {
    using node_t = typename Graph::node_t;
 
    std::map<node_t, std::vector<node_t>> cut_adj;
    int total_weight = 0;
    for (const auto& e : cut_edges) {
        cut_adj[e.first].push_back(e.second);
        cut_adj[e.second].push_back(e.first);
        total_weight += weight(e.first, e.second);
    }
 
    std::map<node_t, int> colour;
    bool is_bipartite = true;
    for (const auto& [start, _] : cut_adj) {
        if (colour.count(start)) continue;
        colour[start] = 1;
        std::queue<node_t> q;
        q.push(start);
        while (!q.empty() && is_bipartite) {
            auto u = q.front();
            q.pop();
            for (const auto& v : cut_adj[u]) {
                if (!colour.count(v)) {
                    colour[v] = (colour[u] == 1) ? 2 : 1;
                    q.push(v);
                } else if (colour[v] == colour[u]) {
                    is_bipartite = false;
                    break;
                }
            }
        }
    }
    return {is_bipartite, total_weight};
}
 
template <typename Graph> auto validate_max_cut(
    [[maybe_unused]] const Graph& G,
    const py::set<std::pair<typename Graph::node_t, typename Graph::node_t>>& cut_edges)
    -> std::pair<bool, int> {
    return validate_max_cut(G, cut_edges, [](auto, auto) { return 1; });
}