geo/manhattan_mst.hpp

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• Last update: 2023-11-07 22:29:27+09:00
• Include: #include "geo/manhattan_mst.hpp"

Depends on

• ds/unionfind/unionfind.hpp
• graph/base.hpp

Verified with

• test/library_checker/graph/manhattan_mst.test.cpp
• test_atcoder/abc283f.test.cpp

Code

#include "graph/base.hpp"
#include "ds/unionfind/unionfind.hpp"

// 最小全域木を作るので、特に各点からの最近点をとる目的で使うこともできる
template <typename T>
Graph<T, 0> manhattan_mst(vc<pair<T, T>>& XY) {
  int N = XY.size();
  vc<tuple<T, int, int>> dat;
  dat.reserve(4 * N);
  vc<int> idx(N);
  iota(all(idx), 0);

  FOR(a, 2) {
    for (auto&& [x, y]: XY) x = -x;
    FOR(b, 2) {
      for (auto&& [x, y]: XY) swap(x, y);
      sort(all(idx), [&](const int& i, const int& j) -> bool {
        return XY[i].fi + XY[i].se < XY[j].fi + XY[j].se;
      });

      map<T, int> MP;
      for (const int i: idx) {
        auto& [x, y] = XY[i];
        for (auto it = MP.lower_bound(-y); it != MP.end(); it = MP.erase(it)) {
          const int j = it->se;
          auto& [xj, yj] = XY[j];
          const int dx = x - xj;
          const int dy = y - yj;
          if (dy > dx) break;
          dat.eb(dx + dy, i, j);
        }
        MP[-y] = i;
      }
    }
  }

  sort(all(dat));
  Graph<T, 0> G(N);
  UnionFind uf(N);
  for (auto&& [cost, i, j]: dat) {
    if (uf.merge(i, j)) G.add(i, j, cost);
  }
  G.build();
  return G;
}

#line 2 "graph/base.hpp"

template <typename T>
struct Edge {
  int frm, to;
  T cost;
  int id;
};

template <typename T = int, bool directed = false>
struct Graph {
  static constexpr bool is_directed = directed;
  int N, M;
  using cost_type = T;
  using edge_type = Edge<T>;
  vector<edge_type> edges;
  vector<int> indptr;
  vector<edge_type> csr_edges;
  vc<int> vc_deg, vc_indeg, vc_outdeg;
  bool prepared;

  class OutgoingEdges {
  public:
    OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}

    const edge_type* begin() const {
      if (l == r) { return 0; }
      return &G->csr_edges[l];
    }

    const edge_type* end() const {
      if (l == r) { return 0; }
      return &G->csr_edges[r];
    }

  private:
    const Graph* G;
    int l, r;
  };

  bool is_prepared() { return prepared; }

  Graph() : N(0), M(0), prepared(0) {}
  Graph(int N) : N(N), M(0), prepared(0) {}

  void build(int n) {
    N = n, M = 0;
    prepared = 0;
    edges.clear();
    indptr.clear();
    csr_edges.clear();
    vc_deg.clear();
    vc_indeg.clear();
    vc_outdeg.clear();
  }

  void add(int frm, int to, T cost = 1, int i = -1) {
    assert(!prepared);
    assert(0 <= frm && 0 <= to && to < N);
    if (i == -1) i = M;
    auto e = edge_type({frm, to, cost, i});
    edges.eb(e);
    ++M;
  }

#ifdef FASTIO
  // wt, off
  void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }

  void read_graph(int M, bool wt = false, int off = 1) {
    for (int m = 0; m < M; ++m) {
      INT(a, b);
      a -= off, b -= off;
      if (!wt) {
        add(a, b);
      } else {
        T c;
        read(c);
        add(a, b, c);
      }
    }
    build();
  }
#endif

  void build() {
    assert(!prepared);
    prepared = true;
    indptr.assign(N + 1, 0);
    for (auto&& e: edges) {
      indptr[e.frm + 1]++;
      if (!directed) indptr[e.to + 1]++;
    }
    for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; }
    auto counter = indptr;
    csr_edges.resize(indptr.back() + 1);
    for (auto&& e: edges) {
      csr_edges[counter[e.frm]++] = e;
      if (!directed)
        csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
    }
  }

  OutgoingEdges operator[](int v) const {
    assert(prepared);
    return {this, indptr[v], indptr[v + 1]};
  }

  vc<int> deg_array() {
    if (vc_deg.empty()) calc_deg();
    return vc_deg;
  }

  pair<vc<int>, vc<int>> deg_array_inout() {
    if (vc_indeg.empty()) calc_deg_inout();
    return {vc_indeg, vc_outdeg};
  }

  int deg(int v) {
    if (vc_deg.empty()) calc_deg();
    return vc_deg[v];
  }

  int in_deg(int v) {
    if (vc_indeg.empty()) calc_deg_inout();
    return vc_indeg[v];
  }

  int out_deg(int v) {
    if (vc_outdeg.empty()) calc_deg_inout();
    return vc_outdeg[v];
  }

#ifdef FASTIO
  void debug() {
    print("Graph");
    if (!prepared) {
      print("frm to cost id");
      for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id);
    } else {
      print("indptr", indptr);
      print("frm to cost id");
      FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id);
    }
  }
#endif

  vc<int> new_idx;
  vc<bool> used_e;

  // G における頂点 V[i] が、新しいグラフで i になるようにする
  // {G, es}
  Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {
    if (len(new_idx) != N) new_idx.assign(N, -1);
    if (len(used_e) != M) used_e.assign(M, 0);
    int n = len(V);
    FOR(i, n) new_idx[V[i]] = i;
    Graph<T, directed> G(n);
    vc<int> history;
    FOR(i, n) {
      for (auto&& e: (*this)[V[i]]) {
        if (used_e[e.id]) continue;
        int a = e.frm, b = e.to;
        if (new_idx[a] != -1 && new_idx[b] != -1) {
          history.eb(e.id);
          used_e[e.id] = 1;
          int eid = (keep_eid ? e.id : -1);
          G.add(new_idx[a], new_idx[b], e.cost, eid);
        }
      }
    }
    FOR(i, n) new_idx[V[i]] = -1;
    for (auto&& eid: history) used_e[eid] = 0;
    G.build();
    return G;
  }

private:
  void calc_deg() {
    assert(vc_deg.empty());
    vc_deg.resize(N);
    for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++;
  }

  void calc_deg_inout() {
    assert(vc_indeg.empty());
    vc_indeg.resize(N);
    vc_outdeg.resize(N);
    for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; }
  }
};
#line 2 "ds/unionfind/unionfind.hpp"

struct UnionFind {
  int n, n_comp;
  vc<int> dat; // par or (-size)
  UnionFind(int n = 0) { build(n); }

  void build(int m) {
    n = m, n_comp = m;
    dat.assign(n, -1);
  }

  void reset() { build(n); }

  int operator[](int x) {
    while (dat[x] >= 0) {
      int pp = dat[dat[x]];
      if (pp < 0) { return dat[x]; }
      x = dat[x] = pp;
    }
    return x;
  }

  ll size(int x) {
    x = (*this)[x];
    return -dat[x];
  }

  bool merge(int x, int y) {
    x = (*this)[x], y = (*this)[y];
    if (x == y) return false;
    if (-dat[x] < -dat[y]) swap(x, y);
    dat[x] += dat[y], dat[y] = x, n_comp--;
    return true;
  }
};
#line 3 "geo/manhattan_mst.hpp"

// 最小全域木を作るので、特に各点からの最近点をとる目的で使うこともできる
template <typename T>
Graph<T, 0> manhattan_mst(vc<pair<T, T>>& XY) {
  int N = XY.size();
  vc<tuple<T, int, int>> dat;
  dat.reserve(4 * N);
  vc<int> idx(N);
  iota(all(idx), 0);

  FOR(a, 2) {
    for (auto&& [x, y]: XY) x = -x;
    FOR(b, 2) {
      for (auto&& [x, y]: XY) swap(x, y);
      sort(all(idx), [&](const int& i, const int& j) -> bool {
        return XY[i].fi + XY[i].se < XY[j].fi + XY[j].se;
      });

      map<T, int> MP;
      for (const int i: idx) {
        auto& [x, y] = XY[i];
        for (auto it = MP.lower_bound(-y); it != MP.end(); it = MP.erase(it)) {
          const int j = it->se;
          auto& [xj, yj] = XY[j];
          const int dx = x - xj;
          const int dy = y - yj;
          if (dy > dx) break;
          dat.eb(dx + dy, i, j);
        }
        MP[-y] = i;
      }
    }
  }

  sort(all(dat));
  Graph<T, 0> G(N);
  UnionFind uf(N);
  for (auto&& [cost, i, j]: dat) {
    if (uf.merge(i, j)) G.add(i, j, cost);
  }
  G.build();
  return G;
}

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