test/verify/yosupo-manhattanmst.test.cpp

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Last update: 2024-05-01 23:44:47+09:00
Problem: https://judge.yosupo.jp/problem/manhattanmst

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Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/manhattanmst

#include "../../template/template.hpp"

#include "../../graph/mst/manhattan-mst.hpp"
#include "../../graph/mst/kruskal.hpp"

int main() {
  int N;
  cin >> N;
  vector< int64_t > X(N), Y(N);
  for(int i = 0; i < N; i++) {
    cin >> X[i] >> Y[i];
  }
  auto es = manhattan_mst(X, Y);
  auto ret = kruskal(es, N);
  cout << ret.cost << "\n";
  for(auto &e : ret.edges) cout << e.from << " " << e.to << "\n";
}

#line 1 "test/verify/yosupo-manhattanmst.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/manhattanmst

#line 1 "template/template.hpp"
#include <bits/stdc++.h>

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/yosupo-manhattanmst.test.cpp"

#line 2 "graph/mst/manhattan-mst.hpp"

#line 2 "graph/graph-template.hpp"

/**
 * @brief Graph Template(グラフテンプレート)
 */
template <typename T = int>
struct Edge {
  int from, to;
  T cost;
  int idx;

  Edge() = default;

  Edge(int from, int to, T cost = 1, int idx = -1)
      : from(from), to(to), cost(cost), idx(idx) {}

  operator int() const { return to; }
};

template <typename T = int>
struct Graph {
  vector<vector<Edge<T> > > g;
  int es;

  Graph() = default;

  explicit Graph(int n) : g(n), es(0) {}

  size_t size() const { return g.size(); }

  void add_directed_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es++);
  }

  void add_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es);
    g[to].emplace_back(to, from, cost, es++);
  }

  void read(int M, int padding = -1, bool weighted = false,
            bool directed = false) {
    for (int i = 0; i < M; i++) {
      int a, b;
      cin >> a >> b;
      a += padding;
      b += padding;
      T c = T(1);
      if (weighted) cin >> c;
      if (directed)
        add_directed_edge(a, b, c);
      else
        add_edge(a, b, c);
    }
  }

  inline vector<Edge<T> > &operator[](const int &k) { return g[k]; }

  inline const vector<Edge<T> > &operator[](const int &k) const { return g[k]; }
};

template <typename T = int>
using Edges = vector<Edge<T> >;
#line 4 "graph/mst/manhattan-mst.hpp"

/**
 * @brief Manhattan MST
 */
template <typename T>
Edges<T> manhattan_mst(vector<T> xs, vector<T> ys) {
  assert(xs.size() == ys.size());
  Edges<T> ret;
  int n = (int)xs.size();

  vector<int> ord(n);
  iota(ord.begin(), ord.end(), 0);

  for (int s = 0; s < 2; s++) {
    for (int t = 0; t < 2; t++) {
      auto cmp = [&](int i, int j) -> bool {
        return xs[i] + ys[i] < xs[j] + ys[j];
      };
      sort(ord.begin(), ord.end(), cmp);

      map<T, int> idx;
      for (int i : ord) {
        for (auto it = idx.lower_bound(-ys[i]); it != idx.end();
             it = idx.erase(it)) {
          int j = it->second;
          if (xs[i] - xs[j] < ys[i] - ys[j]) break;
          ret.emplace_back(i, j, abs(xs[i] - xs[j]) + abs(ys[i] - ys[j]));
        }
        idx[-ys[i]] = i;
      }
      swap(xs, ys);
    }
    for (int i = 0; i < n; i++) xs[i] *= -1;
  }
  return ret;
}
#line 2 "graph/mst/kruskal.hpp"

#line 2 "structure/union-find/union-find.hpp"

struct UnionFind {
  vector<int> data;

  UnionFind() = default;

  explicit UnionFind(size_t sz) : data(sz, -1) {}

  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y) return false;
    if (data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return true;
  }

  int find(int k) {
    if (data[k] < 0) return (k);
    return data[k] = find(data[k]);
  }

  int size(int k) { return -data[find(k)]; }

  bool same(int x, int y) { return find(x) == find(y); }

  vector<vector<int> > groups() {
    int n = (int)data.size();
    vector<vector<int> > ret(n);
    for (int i = 0; i < n; i++) {
      ret[find(i)].emplace_back(i);
    }
    ret.erase(remove_if(begin(ret), end(ret),
                        [&](const vector<int> &v) { return v.empty(); }),
              end(ret));
    return ret;
  }
};
#line 5 "graph/mst/kruskal.hpp"

/**
 * @brief Kruskal(最小全域木)
 *
 */
template <typename T>
struct MinimumSpanningTree {
  T cost;
  Edges<T> edges;
};

template <typename T>
MinimumSpanningTree<T> kruskal(Edges<T> &edges, int V) {
  sort(begin(edges), end(edges),
       [](const Edge<T> &a, const Edge<T> &b) { return a.cost < b.cost; });
  UnionFind tree(V);
  T total = T();
  Edges<T> es;
  for (auto &e : edges) {
    if (tree.unite(e.from, e.to)) {
      es.emplace_back(e);
      total += e.cost;
    }
  }
  return {total, es};
}
#line 7 "test/verify/yosupo-manhattanmst.test.cpp"

int main() {
  int N;
  cin >> N;
  vector< int64_t > X(N), Y(N);
  for(int i = 0; i < N; i++) {
    cin >> X[i] >> Y[i];
  }
  auto es = manhattan_mst(X, Y);
  auto ret = kruskal(es, N);
  cout << ret.cost << "\n";
  for(auto &e : ret.edges) cout << e.from << " " << e.to << "\n";
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	enclosed_00	AC	278 ms	40 MB
g++	enclosed_01	AC	268 ms	39 MB
g++	enclosed_02	AC	264 ms	40 MB
g++	example_00	AC	7 ms	4 MB
g++	many_cluster_00	AC	294 ms	39 MB
g++	many_cluster_01	AC	294 ms	39 MB
g++	many_cluster_02	AC	291 ms	39 MB
g++	max_random_00	AC	335 ms	39 MB
g++	max_random_01	AC	339 ms	38 MB
g++	max_random_02	AC	338 ms	38 MB
g++	random_00	AC	211 ms	24 MB
g++	random_01	AC	257 ms	34 MB
g++	random_02	AC	88 ms	13 MB
g++	small_00	AC	7 ms	4 MB
g++	small_01	AC	6 ms	4 MB
g++	small_02	AC	6 ms	4 MB
clang++	enclosed_00	AC	321 ms	40 MB
clang++	enclosed_01	AC	319 ms	39 MB
clang++	enclosed_02	AC	320 ms	39 MB
clang++	example_00	AC	6 ms	4 MB
clang++	many_cluster_00	AC	292 ms	40 MB
clang++	many_cluster_01	AC	292 ms	40 MB
clang++	many_cluster_02	AC	287 ms	40 MB
clang++	max_random_00	AC	337 ms	39 MB
clang++	max_random_01	AC	338 ms	38 MB
clang++	max_random_02	AC	339 ms	39 MB
clang++	random_00	AC	212 ms	24 MB
clang++	random_01	AC	253 ms	34 MB
clang++	random_02	AC	87 ms	13 MB
clang++	small_00	AC	6 ms	4 MB
clang++	small_01	AC	6 ms	4 MB
clang++	small_02	AC	6 ms	4 MB