test/graph/kruskal.test.cpp

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• Last update: 2024-11-09 00:49:07+00:00
• Problem: https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_2_A

Depends on

• ds/dsu.hpp
• graph.hpp
• graph/csr.hpp
• graph/kruskal.hpp
• graph/traits.hpp
• prelude.hpp
• range.hpp

Code

// competitive-verifier: PROBLEM https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_2_A

#include "graph/kruskal.hpp"

int main() {
  int n, m; scanf("%d%d", &n, &m);
  vector<tuple<int, int, int>> edges(m);
  rep(i, m) {
    int s, t, w; scanf("%d%d%d", &s, &t, &w);
    edges[i] = {s, t, w};
  }
  ll tot = 0;
  for (auto [u, v, w] : kruskal(n, edges)) tot += w;
  printf("%lld\n", tot);
}

#line 1 "test/graph/kruskal.test.cpp"
// competitive-verifier: PROBLEM https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_2_A

#line 2 "prelude.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<int>;
using vvi = vector<vector<int>>;
using vll = vector<ll>;
using vvll = vector<vector<ll>>;
using vc = vector<char>;
#define rep2(i, m, n) for (auto i = (m); i < (n); i++)
#define rep(i, n) rep2(i, 0, n)
#define repr2(i, m, n) for (auto i = (n); i-- > (m);)
#define repr(i, n) repr2(i, 0, n)
#define all(x) begin(x), end(x)
auto ndvec(int n, auto e) { return vector(n, e); }
auto ndvec(int n, auto ...e) { return vector(n, ndvec(e...)); }
auto comp_key(auto&& f) { return [&](auto&& a, auto&& b) { return f(a) < f(b); }; }
auto& max(const auto& a, const auto& b) { return a < b ? b : a; }
auto& min(const auto& a, const auto& b) { return b < a ? b : a; }
#if __cpp_lib_ranges
namespace R = std::ranges;
namespace V = std::views;
#endif
#line 3 "graph/traits.hpp"

struct unit_edge {
  int to;
  operator int() const { return to; }
  int w() const { return 1; }
};

template <class Weight>
struct weighted_edge {
  int to;
  Weight weight;
  operator int() const { return to; }
  Weight w() const { return weight; }
};

template <class Inner>
struct basic_graph {
  using weight_type = void;
  const Inner& inner;
  basic_graph(const Inner& g) : inner(g) { }
  template <class F>
  void adj(int v, F f) const {
    for (auto u : inner[v]) f(unit_edge{u});
  }
  int deg(int v) const { return inner[v].size(); }
};

template <class Inner, class Weight>
struct basic_weighted_graph {
  using weight_type = Weight;
  const Inner& inner;
  basic_weighted_graph(const Inner& g) : inner(g) { }
  template <class F>
  void adj(int v, F f) const {
    for (auto [u, w] : inner[v]) f(weighted_edge<weight_type>{u, w});
  }
  int deg(int v) const { return inner[v].size(); }
};

template <class Inner>
struct graph_trait {
  using weight_type = typename Inner::weight_type;
  const Inner& g;
  graph_trait(const Inner& g) : g(g) { }
  int size() const { return g.size(); }
  template <class F>
  void adj(int v, F f) const {
    g.adj(v, f);
  }
  decltype(auto) operator[](int v) const { return g[v]; }
};

template <class T>
constexpr bool is_weighted_v =
    !is_same_v<typename graph_trait<T>::weight_type, void>;

template <class T>
using weight_t =
    conditional_t<is_weighted_v<T>, typename graph_trait<T>::weight_type, int>;

template <class T>
using edge_t =
    conditional_t<is_weighted_v<T>, weighted_edge<weight_t<T>>, unit_edge>;

template <size_t N>
struct graph_trait<vector<int>[N]> : basic_graph<vector<int>[N]> {
  using basic_graph<vector<int>[N]>::basic_graph;
  int size() const { return N; }
};

template <>
struct graph_trait<vector<vector<int>>> : basic_graph<vector<vector<int>>> {
  using basic_graph<vector<vector<int>>>::basic_graph;
  int size() const { return this->inner.size(); }
};

template <size_t N, class Weight>
struct graph_trait<vector<pair<int, Weight>>[N]>
    : basic_weighted_graph<vector<pair<int, Weight>>[N], Weight> {
      using basic_weighted_graph<
          vector<pair<int, Weight>>[N], Weight>::basic_weighted_graph;
      int size() const { return N; }
    };

template <class Weight>
struct graph_trait<vector<vector<pair<int, Weight>>>>
    : basic_weighted_graph<vector<vector<pair<int, Weight>>>, Weight> {
  using basic_weighted_graph<
      vector<vector<pair<int, Weight>>>, Weight>::basic_weighted_graph;
  int size() const { return this->inner.size(); }
};
#line 3 "range.hpp"

template <class It>
struct range : pair<It, It> {
  using pair<It, It>::pair;
  It begin() const { return this->first; }
  It end() const { return this->second; }
  It cbegin() const { return begin(); }
  It cend() const { return end(); }
  int size() const { return this->second - this->first; }
};
#line 4 "graph/csr.hpp"

template <size_t>
struct stdin_reader;

template <class Weight = void>
class csr_graph {
 private:
  struct directed_t {};

 public:
  using weight_type = Weight;

  csr_graph() = default;
  template <class It>
  csr_graph(int n, It e, It e_last) : n(n), m(distance(e, e_last)) {
    init<false>(e, e_last);
  }
  template <size_t Size = 1 << 26>
  csr_graph(int n, int m, stdin_reader<Size>& read) : n(n), m(m) {
    auto e = read_e(read);
    init<false>(all(e));
  }

  template <class It>
  static csr_graph directed(int n, It e, It e_last) {
    return csr_graph(directed_t{}, n, e, e_last);
  }
  template <size_t Size = 1 << 26>
  static csr_graph directed(int n, int m, stdin_reader<Size>& read) {
    return csr_graph(directed_t{}, n, m, read);
  }

  template <size_t Size = 1 << 26>
  static csr_graph tree(int n, stdin_reader<Size>& read) {
    return csr_graph(n, n - 1, read);
  }
  template <size_t Size = 1 << 26>
  static csr_graph tree(stdin_reader<Size>& read) {
    int n = read;
    return csr_graph(n, n - 1, read);
  }

  int size() const { return n; }
  range<typename vector<edge_t<csr_graph>>::iterator> operator[](int v) const {
    return {ls[v], rs[v]};
  }
  int deg(int v) { return rs[v] - ls[v]; }
  template <class F>
  void adj(int v, F f) const {
    for_each(ls[v], rs[v], f);
  }

 private:
  template <class It>
  csr_graph(directed_t, int n, It e, It e_last) : n(n), m(distance(e, e_last)) {
    init<true>(e, e_last);
  }
  template <size_t Size = 1 << 26>
  csr_graph(directed_t, int n, int m, stdin_reader<Size>& read) : n(n), m(m) {
    auto e = read_e(read);
    init<true>(all(e));
  }

  vector<typename vector<edge_t<csr_graph>>::iterator> ls, rs;
  int n, m;
  vector<edge_t<csr_graph>> es;
  template <bool OneBased = true, size_t Size = 1 << 26>
  auto read_e(stdin_reader<Size>& read) {
    using E = conditional_t<is_weighted_v<csr_graph>, tuple<int, int, Weight>,
                            pair<int, int>>;
    vector<E> res(m);
    for (auto& e : res) {
      read(e);
      if (OneBased) get<0>(e)--, get<1>(e)--;
    }
    return res;
  }
  template <bool Directed, class It>
  void init(It e, It e_last) {
    if (!Directed) m *= 2;
    es.resize(m);
    ls.resize(n), rs.resize(n);
    vector<int> sz(n);
    for (auto it = e; it != e_last; it++) {
      int from = get<0>(*it), to = get<1>(*it);
      sz[from]++;
      if (!Directed) sz[to]++;
    }
    partial_sum(all(sz), sz.begin());
    rep(v, n) ls[v] = rs[v] = es.begin() + sz[v];
    for (auto it = e; it != e_last; it++) {
      int from = get<0>(*it), to = get<1>(*it);
      if constexpr (is_weighted_v<csr_graph>)
        *--ls[from] = edge_t<csr_graph>{to, get<2>(*it)};
      else
        *--ls[from] = edge_t<csr_graph>{to};
      if (!Directed) {
        if constexpr (is_weighted_v<csr_graph>)
          *--ls[to] = edge_t<csr_graph>{from, get<2>(*it)};
        else
          *--ls[to] = edge_t<csr_graph>{from};
      }
    }
  }
};
#line 3 "ds/dsu.hpp"

class dsu {
 public:
  dsu(int n) : par(n, -1), cnt(n) {}
  int count() const { return cnt; }
  void clear() {
    fill(par.begin(), par.end(), -1);
    cnt = par.size();
  }
  int find(int x) { return par[x] < 0 ? x : par[x] = (int)find(par[x]); }
  bool same(int x, int y) { return find(x) == find(y); }
  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y) return false;
    if (par[x] > par[y]) swap(x, y);
    par[x] += par[y], par[y] = x;
    cnt--;
    return true;
  }
  int size(int x) { return -par[find(x)]; }
  vector<vector<int>> groups() {
    vector<vector<int>> res(par.size());
    for (int x = 0; x < par.size(); x++) res[find(x)].push_back(x);
    res.erase(remove_if(all(res), [](const auto& v) { return v.empty(); }),
              res.end());
    return res;
  }

 private:
  vector<int> par;
  int cnt;
};
#line 4 "graph/kruskal.hpp"

template <class weight_t>
vector<tuple<int, int, weight_t>> kruskal(int n, vector<tuple<int, int, weight_t>> edges) {
  sort(all(edges), [&](auto&& a, auto&& b) { return get<2>(a) < get<2>(b); });
  dsu dsu(n);
  vector<tuple<int, int, weight_t>> res;
  for (auto [u, v, w] : edges)
    if (dsu.unite(u, v)) res.emplace_back(u, v, w);
  return res;
}

// G: undirected
// forest if not connected
template <class G>
vector<tuple<int, int, weight_t<G>>> kruskal(const G& graph) {
  graph_trait<G> g(graph);
  vector<tuple<int, int, weight_t<G>>> edges;
  rep(v, g.size()) g.adj(v, [&](auto&& e) {
    if (e.to > v) edges.emplace_back(v, e.to, e.w());
  });
  return kruskal(g.size(), move(edges));
}

#line 4 "test/graph/kruskal.test.cpp"

int main() {
  int n, m; scanf("%d%d", &n, &m);
  vector<tuple<int, int, int>> edges(m);
  rep(i, m) {
    int s, t, w; scanf("%d%d%d", &s, &t, &w);
    edges[i] = {s, t, w};
  }
  ll tot = 0;
  for (auto [u, v, w] : kruskal(n, edges)) tot += w;
  printf("%lld\n", tot);
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-12	00_sample1.in	AC	96 ms	8 MB
g++-12	00_sample2.in	AC	12 ms	8 MB
g++-12	critical1.in	AC	12 ms	8 MB
g++-12	critical2.in	AC	18 ms	10 MB
g++-12	critical3.in	AC	64 ms	11 MB
g++-12	out1.in	AC	12 ms	9 MB
g++-12	out10.in	AC	68 ms	12 MB
g++-12	out11.in	AC	29 ms	10 MB
g++-12	out12.in	AC	41 ms	10 MB
g++-12	out13.in	AC	35 ms	10 MB
g++-12	out14.in	AC	39 ms	10 MB
g++-12	out15.in	AC	31 ms	10 MB
g++-12	out2.in	AC	12 ms	9 MB
g++-12	out3.in	AC	12 ms	9 MB
g++-12	out4.in	AC	12 ms	9 MB
g++-12	out5.in	AC	12 ms	9 MB
g++-12	out6.in	AC	68 ms	12 MB
g++-12	out7.in	AC	68 ms	12 MB
g++-12	out8.in	AC	70 ms	12 MB
g++-12	out9.in	AC	68 ms	12 MB

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