test/verify/yosupo-manhattanmst.test.cpp

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Last update: 2026-08-10 14:32:04+00:00
Problem: https://judge.yosupo.jp/problem/manhattanmst

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Code

// clang-format off
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/manhattanmst
// clang-format on

#include <iostream>
#include <vector>

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

using namespace std;

int main() {
  int N;
  cin >> N;
  vector<long long> 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"
// clang-format off
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/manhattanmst
// clang-format on

#include <iostream>
#include <vector>

#line 2 "graph/mst/kruskal.hpp"

#include <algorithm>
#include <iterator>

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

#line 4 "structure/union-find/union-find.hpp"
#include <cstddef>
#include <utility>
#line 7 "structure/union-find/union-find.hpp"

struct UnionFind {
  std::vector<int> data;

  UnionFind() = default;

  explicit UnionFind(std::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]) std::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); }

  std::vector<std::vector<int>> groups() {
    int n = (int)data.size();
    std::vector<std::vector<int>> ret(n);
    for (int i = 0; i < n; i++) {
      ret[find(i)].emplace_back(i);
    }
    ret.erase(
        std::remove_if(ret.begin(), ret.end(),
                       [&](const std::vector<int>& v) { return v.empty(); }),
        ret.end());
    return ret;
  }
};
#line 2 "graph/graph-template.hpp"

#line 6 "graph/graph-template.hpp"

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 {
  std::vector<std::vector<Edge<T> > > g;
  int es;

  Graph() = default;

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

  std::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;
      std::cin >> a >> b;
      a += padding;
      b += padding;
      T c = T(1);
      if (weighted) std::cin >> c;
      if (directed)
        add_directed_edge(a, b, c);
      else
        add_edge(a, b, c);
    }
  }

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

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

template <typename T = int>
using Edges = std::vector<Edge<T> >;
#line 8 "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) {
  std::sort(std::begin(edges), std::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 2 "graph/mst/manhattan-mst.hpp"

#line 4 "graph/mst/manhattan-mst.hpp"
#include <cassert>
#include <cstdlib>
#line 7 "graph/mst/manhattan-mst.hpp"
#include <map>
#include <numeric>
#line 11 "graph/mst/manhattan-mst.hpp"

#line 13 "graph/mst/manhattan-mst.hpp"

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

  std::vector<int> ord(n);
  std::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];
      };
      std::sort(ord.begin(), ord.end(), cmp);

      std::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,
                           std::abs(xs[i] - xs[j]) + std::abs(ys[i] - ys[j]));
        }
        idx[-ys[i]] = i;
      }
      std::swap(xs, ys);
    }
    for (int i = 0; i < n; i++) xs[i] *= -1;
  }
  return ret;
}
#line 10 "test/verify/yosupo-manhattanmst.test.cpp"

using namespace std;

int main() {
  int N;
  cin >> N;
  vector<long long> 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	344 ms	39 MB
g++	enclosed_01	AC	327 ms	39 MB
g++	enclosed_02	AC	330 ms	40 MB
g++	example_00	AC	2 ms	4 MB
g++	many_cluster_00	AC	379 ms	39 MB
g++	many_cluster_01	AC	394 ms	39 MB
g++	many_cluster_02	AC	368 ms	38 MB
g++	max_random_00	AC	416 ms	38 MB
g++	max_random_01	AC	423 ms	39 MB
g++	max_random_02	AC	427 ms	40 MB
g++	random_00	AC	260 ms	24 MB
g++	random_01	AC	316 ms	35 MB
g++	random_02	AC	107 ms	12 MB
g++	small_00	AC	2 ms	4 MB
g++	small_01	AC	2 ms	4 MB
g++	small_02	AC	2 ms	4 MB
clang++	enclosed_00	AC	414 ms	40 MB
clang++	enclosed_01	AC	404 ms	39 MB
clang++	enclosed_02	AC	406 ms	40 MB
clang++	example_00	AC	2 ms	4 MB
clang++	many_cluster_00	AC	378 ms	38 MB
clang++	many_cluster_01	AC	373 ms	40 MB
clang++	many_cluster_02	AC	373 ms	37 MB
clang++	max_random_00	AC	423 ms	39 MB
clang++	max_random_01	AC	416 ms	39 MB
clang++	max_random_02	AC	416 ms	39 MB
clang++	random_00	AC	259 ms	24 MB
clang++	random_01	AC	311 ms	35 MB
clang++	random_02	AC	107 ms	13 MB
clang++	small_00	AC	2 ms	4 MB
clang++	small_01	AC	2 ms	4 MB
clang++	small_02	AC	2 ms	4 MB