test/aoj/0575/main.test.cpp

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• Last update: 2021-04-23 23:44:44+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0575

Depends on

• Parallel binary search (Mylib/Algorithm/parallel_binary_search.cpp)
• Union-find (Mylib/DataStructure/UnionFind/unionfind.cpp)
• Dijkstra algorithm (Mylib/Graph/ShortestPath/dijkstra.cpp)
• Basic graph (Mylib/Graph/Template/graph.cpp)
• Input tuple vector (Mylib/IO/input_tuple_vector.cpp)
• Input vector (Mylib/IO/input_vector.cpp)

Code

#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0575"

#include <algorithm>
#include <iostream>
#include <utility>
#include <vector>
#include "Mylib/Algorithm/parallel_binary_search.cpp"
#include "Mylib/DataStructure/UnionFind/unionfind.cpp"
#include "Mylib/Graph/ShortestPath/dijkstra.cpp"
#include "Mylib/Graph/Template/graph.cpp"
#include "Mylib/IO/input_tuple_vector.cpp"
#include "Mylib/IO/input_vector.cpp"

namespace hl = haar_lib;

int main() {
  std::cin.tie(0);
  std::ios::sync_with_stdio(false);

  int N, M, K, Q;
  std::cin >> N >> M >> K >> Q;

  hl::graph<int> g(N);
  g.read<1, false>(M);

  auto F = hl::input_vector<int>(K);
  for (auto &x : F) x -= 1;

  auto [S, T] = hl::input_tuple_vector<int, int>(Q);
  for (auto &x : S) x -= 1;
  for (auto &x : T) x -= 1;

  auto dist = hl::dijkstra(g, {F});

  std::vector<int> dist_list;
  for (auto &x : dist) {
    dist_list.push_back(*x);
  }

  std::sort(dist_list.begin(), dist_list.end());
  dist_list.erase(std::unique(dist_list.begin(), dist_list.end()), dist_list.end());

  const int C = dist_list.size();

  std::vector<std::vector<std::pair<int, int>>> edges(C);
  for (int i = 0; i < N; ++i) {
    for (auto &e : g[i]) {
      if (*dist[e.from] <= *dist[e.to]) {
        int x = std::lower_bound(dist_list.begin(), dist_list.end(), *dist[e.from]) - dist_list.begin();
        edges[x].emplace_back(e.from, e.to);
      }
    }
  }

  hl::unionfind uf;

  auto res =
      hl::parallel_binary_search(
          C,
          Q,
          [&]() { uf = hl::unionfind(N); },
          [&](int i) {
            for (auto [x, y] : edges[C - 1 - i]) {
              uf.merge(x, y);
            }
          },
          [&](int i) -> bool {
            return uf.is_same(S[i], T[i]);
          });

  for (auto x : res) {
    std::cout << dist_list[C - x - 1] << "\n";
  }

  return 0;
}

#line 1 "test/aoj/0575/main.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0575"

#include <algorithm>
#include <iostream>
#include <utility>
#include <vector>
#line 2 "Mylib/Algorithm/parallel_binary_search.cpp"
#include <cmath>
#line 4 "Mylib/Algorithm/parallel_binary_search.cpp"

namespace haar_lib {
  template <typename Init, typename Process, typename Checker>
  std::vector<int> parallel_binary_search(int M, int Q, Init init, Process process, Checker checker) {
    std::vector<int> lb(Q, -1), ub(Q, M);

    while (1) {
      bool check = true;
      std::vector<std::vector<int>> mids(M);
      for (int i = 0; i < Q; ++i) {
        if (std::abs(lb[i] - ub[i]) > 1) {
          check   = false;
          int mid = (lb[i] + ub[i]) / 2;
          mids[mid].push_back(i);
        }
      }

      if (check) break;

      init();

      for (int i = 0; i < M; ++i) {
        process(i);
        for (int j : mids[i]) {
          if (checker(j)) {
            ub[j] = i;
          } else {
            lb[j] = i;
          }
        }
      }
    }

    return ub;
  }
}  // namespace haar_lib
#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/ShortestPath/dijkstra.cpp"
#include <functional>
#include <optional>
#include <queue>
#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 8 "Mylib/Graph/ShortestPath/dijkstra.cpp"

namespace haar_lib {
  template <typename T>
  auto dijkstra(const graph<T> &graph, std::vector<int> src) {
    using P = std::pair<T, int>;

    const int n = graph.size();
    std::vector<std::optional<T>> dist(n);

    std::vector<bool> check(n, false);
    std::priority_queue<P, std::vector<P>, std::greater<P>> pq;

    for (auto s : src) {
      dist[s] = 0;
      pq.emplace(0, s);
    }

    while (not pq.empty()) {
      const auto [d, i] = pq.top();
      pq.pop();

      if (check[i]) continue;
      check[i] = true;

      for (auto &e : graph[i]) {
        if (not dist[e.to]) {
          dist[e.to] = d + e.cost;
          pq.emplace(*dist[e.to], e.to);
        } else {
          if (*dist[e.to] > d + e.cost) {
            dist[e.to] = d + e.cost;
            if (not check[e.to]) pq.emplace(*dist[e.to], e.to);
          }
        }
      }
    }

    return dist;
  }
}  // namespace haar_lib
#line 2 "Mylib/IO/input_tuple_vector.cpp"
#include <initializer_list>
#line 4 "Mylib/IO/input_tuple_vector.cpp"
#include <tuple>
#line 7 "Mylib/IO/input_tuple_vector.cpp"

namespace haar_lib {
  template <typename T, size_t... I>
  void input_tuple_vector_init(T &val, int N, std::index_sequence<I...>) {
    (void) std::initializer_list<int>{(void(std::get<I>(val).resize(N)), 0)...};
  }

  template <typename T, size_t... I>
  void input_tuple_vector_helper(T &val, int i, std::index_sequence<I...>) {
    (void) std::initializer_list<int>{(void(std::cin >> std::get<I>(val)[i]), 0)...};
  }

  template <typename... Args>
  auto input_tuple_vector(int N) {
    std::tuple<std::vector<Args>...> ret;

    input_tuple_vector_init(ret, N, std::make_index_sequence<sizeof...(Args)>());
    for (int i = 0; i < N; ++i) {
      input_tuple_vector_helper(ret, i, std::make_index_sequence<sizeof...(Args)>());
    }

    return ret;
  }
}  // namespace haar_lib
#line 4 "Mylib/IO/input_vector.cpp"

namespace haar_lib {
  template <typename T>
  std::vector<T> input_vector(int N) {
    std::vector<T> ret(N);
    for (int i = 0; i < N; ++i) std::cin >> ret[i];
    return ret;
  }

  template <typename T>
  std::vector<std::vector<T>> input_vector(int N, int M) {
    std::vector<std::vector<T>> ret(N);
    for (int i = 0; i < N; ++i) ret[i] = input_vector<T>(M);
    return ret;
  }
}  // namespace haar_lib
#line 13 "test/aoj/0575/main.test.cpp"

namespace hl = haar_lib;

int main() {
  std::cin.tie(0);
  std::ios::sync_with_stdio(false);

  int N, M, K, Q;
  std::cin >> N >> M >> K >> Q;

  hl::graph<int> g(N);
  g.read<1, false>(M);

  auto F = hl::input_vector<int>(K);
  for (auto &x : F) x -= 1;

  auto [S, T] = hl::input_tuple_vector<int, int>(Q);
  for (auto &x : S) x -= 1;
  for (auto &x : T) x -= 1;

  auto dist = hl::dijkstra(g, {F});

  std::vector<int> dist_list;
  for (auto &x : dist) {
    dist_list.push_back(*x);
  }

  std::sort(dist_list.begin(), dist_list.end());
  dist_list.erase(std::unique(dist_list.begin(), dist_list.end()), dist_list.end());

  const int C = dist_list.size();

  std::vector<std::vector<std::pair<int, int>>> edges(C);
  for (int i = 0; i < N; ++i) {
    for (auto &e : g[i]) {
      if (*dist[e.from] <= *dist[e.to]) {
        int x = std::lower_bound(dist_list.begin(), dist_list.end(), *dist[e.from]) - dist_list.begin();
        edges[x].emplace_back(e.from, e.to);
      }
    }
  }

  hl::unionfind uf;

  auto res =
      hl::parallel_binary_search(
          C,
          Q,
          [&]() { uf = hl::unionfind(N); },
          [&](int i) {
            for (auto [x, y] : edges[C - 1 - i]) {
              uf.merge(x, y);
            }
          },
          [&](int i) -> bool {
            return uf.is_same(S[i], T[i]);
          });

  for (auto x : res) {
    std::cout << dist_list[C - x - 1] << "\n";
  }

  return 0;
}

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