Kruskal algorithm
(Mylib/Graph/MinimumSpanningTree/kruskal.cpp)

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• Last update: 2021-04-23 23:44:44+09:00
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Operations

Requirements

Notes

Problems

References

Depends on

• Union-find (Mylib/DataStructure/UnionFind/unionfind.cpp)
• Basic graph (Mylib/Graph/Template/graph.cpp)

Verified with

• test/aoj/GRL_2_A/main.kruskal.test.cpp
• test/yosupo-judge/manhattanmst/main.test.cpp

Code

#pragma once
#include <algorithm>
#include <vector>
#include "Mylib/DataStructure/UnionFind/unionfind.cpp"
#include "Mylib/Graph/Template/graph.cpp"

namespace haar_lib {
  template <typename T>
  std::vector<edge<T>> kruskal(const graph<T> &graph) {
    const int n = graph.size();
    std::vector<edge<T>> edges;
    for (auto &v : graph) {
      for (auto &e : v) {
        edges.push_back(e);
      }
    }

    std::sort(
        edges.begin(), edges.end(),
        [](const auto &a, const auto &b) { return a.cost < b.cost; });

    unionfind uf(n);

    std::vector<edge<T>> ret;

    for (auto &e : edges) {
      if (not uf.is_same(e.from, e.to)) {
        uf.merge(e.from, e.to);
        ret.push_back(e);
      }
    }

    return ret;
  }
}  // namespace haar_lib

#line 2 "Mylib/Graph/MinimumSpanningTree/kruskal.cpp"
#include <algorithm>
#include <vector>
#line 3 "Mylib/DataStructure/UnionFind/unionfind.cpp"
#include <numeric>
#line 5 "Mylib/DataStructure/UnionFind/unionfind.cpp"

namespace haar_lib {
  class unionfind {
    int n_, count_;
    mutable std::vector<int> parent_;
    std::vector<int> depth_, size_;

  public:
    unionfind() {}
    unionfind(int n) : n_(n), count_(n), parent_(n), depth_(n, 1), size_(n, 1) {
      std::iota(parent_.begin(), parent_.end(), 0);
    }

    int root_of(int i) const {
      if (parent_[i] == i)
        return i;
      else
        return parent_[i] = root_of(parent_[i]);
    }

    bool is_same(int i, int j) const { return root_of(i) == root_of(j); }

    int merge(int i, int j) {
      const int ri = root_of(i), rj = root_of(j);
      if (ri == rj)
        return ri;
      else {
        --count_;
        if (depth_[ri] < depth_[rj]) {
          parent_[ri] = rj;
          size_[rj] += size_[ri];
          return rj;
        } else {
          parent_[rj] = ri;
          size_[ri] += size_[rj];
          if (depth_[ri] == depth_[rj]) ++depth_[ri];
          return ri;
        }
      }
    }

    int size_of(int i) const { return size_[root_of(i)]; }

    int count_groups() const { return count_; }

    auto get_groups() const {
      std::vector<std::vector<int>> ret(n_);

      for (int i = 0; i < n_; ++i) {
        ret[root_of(i)].push_back(i);
      }

      ret.erase(
          std::remove_if(
              ret.begin(), ret.end(),
              [](const auto &a) { return a.empty(); }),
          ret.end());

      return ret;
    }
  };
}  // namespace haar_lib
#line 2 "Mylib/Graph/Template/graph.cpp"
#include <iostream>
#line 4 "Mylib/Graph/Template/graph.cpp"

namespace haar_lib {
  template <typename T>
  struct edge {
    int from, to;
    T cost;
    int index = -1;
    edge() {}
    edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
    edge(int from, int to, T cost, int index) : from(from), to(to), cost(cost), index(index) {}
  };

  template <typename T>
  struct graph {
    using weight_type = T;
    using edge_type   = edge<T>;

    std::vector<std::vector<edge<T>>> data;

    auto& operator[](size_t i) { return data[i]; }
    const auto& operator[](size_t i) const { return data[i]; }

    auto begin() const { return data.begin(); }
    auto end() const { return data.end(); }

    graph() {}
    graph(int N) : data(N) {}

    bool empty() const { return data.empty(); }
    int size() const { return data.size(); }

    void add_edge(int i, int j, T w, int index = -1) {
      data[i].emplace_back(i, j, w, index);
    }

    void add_undirected(int i, int j, T w, int index = -1) {
      add_edge(i, j, w, index);
      add_edge(j, i, w, index);
    }

    template <size_t I, bool DIRECTED = true, bool WEIGHTED = true>
    void read(int M) {
      for (int i = 0; i < M; ++i) {
        int u, v;
        std::cin >> u >> v;
        u -= I;
        v -= I;
        T w = 1;
        if (WEIGHTED) std::cin >> w;
        if (DIRECTED)
          add_edge(u, v, w, i);
        else
          add_undirected(u, v, w, i);
      }
    }
  };

  template <typename T>
  using tree = graph<T>;
}  // namespace haar_lib
#line 6 "Mylib/Graph/MinimumSpanningTree/kruskal.cpp"

namespace haar_lib {
  template <typename T>
  std::vector<edge<T>> kruskal(const graph<T> &graph) {
    const int n = graph.size();
    std::vector<edge<T>> edges;
    for (auto &v : graph) {
      for (auto &e : v) {
        edges.push_back(e);
      }
    }

    std::sort(
        edges.begin(), edges.end(),
        [](const auto &a, const auto &b) { return a.cost < b.cost; });

    unionfind uf(n);

    std::vector<edge<T>> ret;

    for (auto &e : edges) {
      if (not uf.is_same(e.from, e.to)) {
        uf.merge(e.from, e.to);
        ret.push_back(e);
      }
    }

    return ret;
  }
}  // namespace haar_lib

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