Manhattan MST
(graph/mst/manhattan-mst.hpp)

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• Last update: 2022-09-11 00:53:50+09:00
• Include: #include "graph/mst/manhattan-mst.hpp"

Depends on

• Graph Template(グラフテンプレート) (graph/graph-template.hpp)

Verified with

• test/verify/yosupo-manhattanmst.test.cpp

Code

#pragma once

#include "../graph-template.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/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;
}

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