Prim algorithm
(Mylib/Graph/MinimumSpanningTree/prim.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

• Basic graph (Mylib/Graph/Template/graph.cpp)

Verified with

• test/aoj/2559/main.binomial_heap.test.cpp
• test/aoj/2559/main.leftist_heap.test.cpp
• test/aoj/2559/main.pairing_heap.test.cpp
• test/aoj/2559/main.skew_heap.test.cpp
• test/aoj/GRL_2_A/main.prim.test.cpp

Code

#pragma once
#include <queue>
#include <vector>
#include "Mylib/Graph/Template/graph.cpp"

namespace haar_lib {
  template <typename T>
  std::vector<edge<T>> prim(const graph<T> &graph) {
    const int n = graph.size();
    std::vector<bool> visit(n, false);
    std::vector<edge<T>> ret;

    auto cmp = [](const auto &a, const auto &b) { return a.cost > b.cost; };
    std::priority_queue<edge<T>, std::vector<edge<T>>, decltype(cmp)> pq(cmp);

    visit[0] = true;
    for (auto &e : graph[0]) pq.push(e);

    while (not pq.empty()) {
      auto t = pq.top();
      pq.pop();

      if (visit[t.from] == visit[t.to]) continue;

      int i = visit[t.from] ? t.to : t.from;
      for (auto &e : graph[i]) {
        pq.push(e);
      }

      visit[i] = true;
      ret.push_back(t);
    }

    return ret;
  }
}  // namespace haar_lib

#line 2 "Mylib/Graph/MinimumSpanningTree/prim.cpp"
#include <queue>
#include <vector>
#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 5 "Mylib/Graph/MinimumSpanningTree/prim.cpp"

namespace haar_lib {
  template <typename T>
  std::vector<edge<T>> prim(const graph<T> &graph) {
    const int n = graph.size();
    std::vector<bool> visit(n, false);
    std::vector<edge<T>> ret;

    auto cmp = [](const auto &a, const auto &b) { return a.cost > b.cost; };
    std::priority_queue<edge<T>, std::vector<edge<T>>, decltype(cmp)> pq(cmp);

    visit[0] = true;
    for (auto &e : graph[0]) pq.push(e);

    while (not pq.empty()) {
      auto t = pq.top();
      pq.pop();

      if (visit[t.from] == visit[t.to]) continue;

      int i = visit[t.from] ? t.to : t.from;
      for (auto &e : graph[i]) {
        pq.push(e);
      }

      visit[i] = true;
      ret.push_back(t);
    }

    return ret;
  }
}  // namespace haar_lib

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