tests/graph/scc/abc296-e.test.cpp

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• Last update: 2025-03-03 00:33:48+09:00
• Problem: https://atcoder.jp/contests/abc296/tasks/abc296_e

Depends on

• library/_internal/graph-base.hpp
• 有向グラフ (library/data-structure/digraph.hpp)
• 無向グラフ (library/data-structure/graph.hpp)
• SCC (Strongly Connected Components) (library/graph/scc.hpp)

Code

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); ++i)
using ll = long long;
using ull = unsigned long long;

#include "../../../cpp/library/data-structure/digraph.hpp"
#include "../../../cpp/library/graph/scc.hpp"
#define PROBLEM "https://atcoder.jp/contests/abc296/tasks/abc296_e"

int main() {
  cin.tie(nullptr)->sync_with_stdio(false);
  int n;
  cin >> n;
  vector<int> a(n);
  rep(i, n) cin >> a[i], a[i]--;
  asalib::graph::digraph Graph(n);
  rep(i, n) Graph.add_edge(i, a[i]);
  auto scc = Graph.scc();
  int ans = 0;
  for (auto& v : scc) {
    if (v.size() == 1 && a[v[0]] != v[0]) continue;
    ans += v.size();
  }
  cout << ans << endl;
  return 0;
}

#line 1 "tests/graph/scc/abc296-e.test.cpp"
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); ++i)
using ll = long long;
using ull = unsigned long long;

#line 2 "library/data-structure/digraph.hpp"

#line 4 "library/data-structure/digraph.hpp"
#include <optional>
#line 6 "library/data-structure/digraph.hpp"
using namespace std;

#line 2 "library/_internal/graph-base.hpp"

#include <concepts>
#include <type_traits>
using namespace std;

namespace asalib {
  namespace _internal {
    class graph_base {};
    class notweighted_graph_base: public graph_base {};
    class weighted_graph_base: public graph_base {};

    template<typename T>
    concept is_graph = is_base_of_v<graph_base, T>;

    template<typename T>
    concept notweighted_graph = is_base_of_v<notweighted_graph_base, T>;

    template<typename T>
    concept weighted_graph = is_base_of_v<weighted_graph_base, T>;

    using adjlist_t = vector<vector<pair<size_t, size_t>>>;
    using edgelist_t = vector<pair<size_t, size_t>>;
  }  // namespace _internal
}  // namespace asalib
#line 2 "library/data-structure/graph.hpp"

#line 6 "library/data-structure/graph.hpp"
using namespace std;

#line 9 "library/data-structure/graph.hpp"

namespace asalib {
  namespace graph {
    class graph: public _internal::notweighted_graph_base {
      public:
      graph(): n_vertex(0), n_edge(0) {}
      explicit graph(size_t n_vertex): n_vertex(n_vertex), n_edge(0) {
        adj_list.reserve(n_vertex);
        adj_list.resize(n_vertex);
      }

      void add_edge(size_t v1, size_t v2) {
        assert(0 <= v1 && v1 < n_vertex);
        assert(0 <= v2 && v2 < n_vertex);
        adj_list[v1].push_back({ v2, n_edge });
        adj_list[v2].push_back({ v1, n_edge });
        edge_list.push_back({ v1, v2 });
        ++n_edge;
      }

      // (v1, v2)
      pair<size_t, size_t> get_edge(size_t edgeId) const {
        assert(0 <= edgeId && edgeId < n_edge);
        return edge_list[edgeId];
      }

      // (v2, edgeId)
      vector<pair<size_t, size_t>> get_adj(size_t vertex) const {
        assert(0 <= vertex && vertex < n_vertex);
        return adj_list[vertex];
      }

      // ---------- prototype ---------- //
      optional<pair<vector<size_t>, vector<size_t>>> cycle() const;
      bool is_connected() const;
      optional<pair<vector<size_t>, vector<size_t>>> eulerian_walk() const;

      private:
      size_t n_vertex, n_edge;
      asalib::_internal::adjlist_t adj_list;
      asalib::_internal::edgelist_t edge_list;
    };
  }  // namespace graph
}  // namespace asalib
#line 10 "library/data-structure/digraph.hpp"

namespace asalib {
  namespace graph {
    class digraph: public _internal::notweighted_graph_base {
      public:
      digraph(): n_vertex(0), n_edge(0) {}
      explicit digraph(size_t n_vertex): n_vertex(n_vertex), n_edge(0) {
        adj_list.reserve(n_vertex);
        adj_list.resize(n_vertex);
        adj_list_rev.reserve(n_vertex);
        adj_list_rev.resize(n_vertex);
        underlying_graph = graph(n_vertex);
      }

      void add_edge(size_t from, size_t to) {
        assert(0 <= from && from < n_vertex);
        assert(0 <= to && to < n_vertex);
        adj_list[from].push_back({ to, n_edge });
        adj_list_rev[to].push_back({ from, n_edge });
        edge_list.push_back({ from, to });
        underlying_graph.add_edge(from, to);
        ++n_edge;
      }

      // (from, to)
      pair<size_t, size_t> get_edge(size_t edgeId) const {
        assert(0 <= edgeId && edgeId < n_edge);
        return edge_list[edgeId];
      }

      // (to, edgeId)
      vector<pair<size_t, size_t>> get_adj(size_t vertex) const {
        assert(0 <= vertex && vertex < n_vertex);
        return adj_list[vertex];
      }

      // (from, edgeId)
      vector<pair<size_t, size_t>> get_adjrev(size_t vertex) const {
        assert(0 <= vertex && vertex < n_vertex);
        return adj_list_rev[vertex];
      }

      // ---------- prototype ---------- //
      vector<vector<size_t>> scc() const;
      optional<pair<vector<size_t>, vector<size_t>>> cycle() const;
      bool is_connected() const;
      optional<pair<vector<size_t>, vector<size_t>>> eulerian_walk() const;

      private:
      size_t n_vertex, n_edge;
      asalib::_internal::adjlist_t adj_list, adj_list_rev;
      asalib::_internal::edgelist_t edge_list;
      graph underlying_graph;
    };
  }  // namespace graph
}  // namespace asalib
#line 2 "library/graph/scc.hpp"

#line 5 "library/graph/scc.hpp"
using namespace std;

#line 8 "library/graph/scc.hpp"

namespace asalib {
  namespace graph {
    vector<vector<size_t>> digraph::scc() const {
      constexpr size_t Unvisited = -1;
      vector<bool> visited(n_vertex, false);
      size_t order_num = 0;
      vector<size_t> ord2pt(n_vertex, Unvisited);

      function<void(size_t)> visit1 = [&](size_t v) {
        visited[v] = true;
        for (auto [w, _] : adj_list[v]) {
          if (!visited[w]) visit1(w);
        }
        ord2pt[order_num++] = v;
      };

      for (size_t v = 0; v < n_vertex; ++v) {
        if (!visited[v]) visit1(v);
      }

      visited.assign(n_vertex, false);
      size_t comp_num = 0;
      vector<size_t> comp(n_vertex, Unvisited);

      function<void(size_t)> visit2 = [&](size_t v) {
        visited[v] = true;
        for (auto [w, _] : adj_list_rev[v]) {
          if (!visited[w]) visit2(w);
        }
        comp[v] = comp_num;
      };

      for (int i = n_vertex - 1; i >= 0; --i) {
        if (!visited[ord2pt[i]]) visit2(ord2pt[i]), ++comp_num;
      }

      vector<vector<size_t>> res(comp_num);
      for (size_t v = 0; v < n_vertex; ++v) {
        res[comp[v]].push_back(v);
      }
      return res;
    }
  }  // namespace graph
}  // namespace asalib
#line 9 "tests/graph/scc/abc296-e.test.cpp"
#define PROBLEM "https://atcoder.jp/contests/abc296/tasks/abc296_e"

int main() {
  cin.tie(nullptr)->sync_with_stdio(false);
  int n;
  cin >> n;
  vector<int> a(n);
  rep(i, n) cin >> a[i], a[i]--;
  asalib::graph::digraph Graph(n);
  rep(i, n) Graph.add_edge(i, a[i]);
  auto scc = Graph.scc();
  int ans = 0;
  for (auto& v : scc) {
    if (v.size() == 1 && a[v[0]] != v[0]) continue;
    ans += v.size();
  }
  cout << ans << endl;
  return 0;
}

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