test/graph/scc.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_1_C

Depends on

• arith/sat.hpp
• graph.hpp
• graph/bellman_ford.hpp
• graph/csr.hpp
• graph/ford_fulkerson.hpp
• graph/scc.hpp
• graph/traits.hpp
• prelude.hpp
• range.hpp

Code

// competitive-verifier: PROBLEM https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_1_C

#include "graph/bellman_ford.hpp"
#include "graph/ford_fulkerson.hpp"
#include "graph/scc.hpp"
#include "prelude.hpp"

int n, m;
vector<pair<int, ll>> G[100];

int main() {
  scanf("%d%d", &n, &m);
  rep(_, m) {
    int u, v;
    int w;
    scanf("%d%d%d", &u, &v, &w);
    G[u].emplace_back(v, w);
  }
  scc scc(G);
  for (auto& vs : scc.groups())
    if (bellman_ford(G, vs[0]).first) return printf("NEGATIVE CYCLE\n"), 0;
  auto d = ford_fulkerson(G);
  rep(v, n) rep(i, n) printf(
      "%s%c", d[v][i] == LONG_LONG_MAX ? "INF" : to_string(d[v][i]).c_str(),
      " \n"[i == n - 1]);
}

#line 1 "test/graph/scc.test.cpp"
// competitive-verifier: PROBLEM https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_1_C

#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 "graph/bellman_ford.hpp"

// (fail, dist)
template <class G>
pair<bool, vector<weight_t<G>>> bellman_ford(G& graph, int s) {
  const weight_t<G> inf = numeric_limits<weight_t<G>>::max();
  graph_trait<G> g(graph);
  vector<weight_t<G>> dist(g.size(), inf);
  dist[s] = 0;
  bool success = false;
  rep(t, g.size()) {
    bool updated = false;
    rep(v, g.size()) if (dist[v] != inf) g.adj(v, [&](auto&& e) {
      if (dist[e.to] > dist[v] + e.w())
        updated = true,
        dist[e.to] = dist[v] + e.w();
    });
    if (!updated) {
      success = true;
      break;
    }
  }
  for (auto& d : dist) if (d >= inf / 2) d = numeric_limits<weight_t<G>>::max();
  return {!success, move(dist)};
}
#line 3 "arith/sat.hpp"

template <class T, class U>
auto sat_add(T a, U b) {
  using V = common_type_t<T, U>;
  V res;
  return __builtin_add_overflow((V)a, (V)b, &res)
             ? (a < 0 ? numeric_limits<V>::min() : numeric_limits<V>::max())
             : res;
}
template <class T, class U>
auto sat_sub(T a, U b) {
  using V = common_type_t<T, U>;
  V res;
  return __builtin_sub_overflow((V)a, (V)b, &res)
             ? (a < 0 ? numeric_limits<V>::min() : numeric_limits<V>::max())
             : res;
}
template <class T, class U>
auto sat_mul(T a, U b) {
  using V = common_type_t<T, U>;
  V res;
  return __builtin_mul_overflow((V)a, (V)b, &res)
             ? ((a < 0) == (b < 0) ? numeric_limits<V>::max()
                                   : numeric_limits<V>::min())
             : res;
}
#line 4 "graph/ford_fulkerson.hpp"

template <class G>
vector<vector<weight_t<G>>> ford_fulkerson(const G& graph) {
  const weight_t<G> inf = numeric_limits<weight_t<G>>::max();
  graph_trait<G> g(graph);
  vector<vector<weight_t<G>>> res(g.size(), vector<weight_t<G>>(g.size(), inf));
  rep(v, g.size()) {
    res[v][v] = weight_t<G>(0);
    g.adj(v, [&](auto&& e) { res[v][e.to] = e.w(); });
  }
  rep(k, g.size()) rep(u, g.size()) rep(v, g.size())
    res[u][v] = min(res[u][v], sat_add(res[u][k], res[k][v]));
  rep(u, g.size()) rep(v, g.size())
    res[u][v] = res[u][v] >= inf / 2 ? inf : res[u][v];
  return res;
}
#line 3 "graph/scc.hpp"

template <class G>
class scc {
 public:
  scc(const G& graph) : g(graph), id_(g.size()), n_cpnts(0) {
    vector<char> visited(g.size(), false);
    vector<int> post_ord;
    post_ord.reserve(g.size());
    vector<vector<int>> rev_graph(g.size());
    auto dfs = [&](auto&& f, int v) -> void {
      visited[v] = true;
      g.adj(v, [&](int u) {
        rev_graph[u].push_back(v);
        if (!visited[u]) f(f, u);
      });
      post_ord.push_back(v);
    };
    rep(v, g.size()) if (!visited[v]) dfs(dfs, v);
    reverse(all(post_ord));
    fill(all(visited), false);
    auto dfs2 = [&](auto&& f, int v) -> void {
      visited[v] = true;
      id_[v] = n_cpnts;
      for (auto u : rev_graph[v])
        if (!visited[u]) f(f, u);
    };
    for (auto v : post_ord)
      if (!visited[v]) dfs2(dfs2, v), n_cpnts++;
  }
  // which component v belongs to
  int operator()(int v) const { return id_[v]; }
  int group_of(int v) const { return id_[v]; }
  int n_groups() const { return n_cpnts; }

  vector<vector<int>> groups() const {
    vector<vector<int>> res(n_cpnts);
    rep(v, g.size()) res[id_[v]].push_back(v);
    return res;
  }

  template <class G1 = G, enable_if_t<!is_weighted_v<G1>>* = nullptr>
  vector<vector<vector<int>>> components() const {
    vector<int> v;
    return components(v);
  }
  template <class G1 = G, enable_if_t<!is_weighted_v<G1>>* = nullptr>
  vector<vector<vector<int>>> components(vector<int>& mapping) const {
    vector<int> sizes(n_cpnts, 0);
    mapping.resize(g.size());
    rep(v, g.size()) mapping[v] = sizes[id_[v]]++;
    vector<vector<vector<int>>> res(n_cpnts);
    rep(i, n_cpnts) res[i].resize(sizes[i]);
    rep(v, g.size()) g.adj(v, [&](int u) {
      if (id_[v] == id_[u]) res[id_[v]][mapping[v]].push_back(mapping[u]);
    });
    return res;
  }

  template <class G1 = G, enable_if_t<is_weighted_v<G1>>* = nullptr>
  vector<vector<vector<pair<int, weight_t<G>>>>> components() const {
    vector<int> v;
    return components(v);
  }
  template <class G1 = G, enable_if_t<is_weighted_v<G1>>* = nullptr>
  vector<vector<vector<pair<int, weight_t<G>>>>> components(
      vector<int>& mapping) const {
    vector<int> sizes(n_cpnts, 0);
    mapping.resize(g.size());
    rep(v, g.size()) mapping[v] = sizes[id_[v]]++;
    vector<vector<vector<pair<int, weight_t<G>>>>> res(n_cpnts);
    rep(i, n_cpnts) res[i].resize(sizes[i]);
    rep(v, g.size()) g.adj(v, [&](auto&& e) {
      if (id_[v] == id_[e.to])
        res[id_[v]][mapping[v]].emplace_back(mapping[e.to], e.w());
    });
    return res;
  }

  template <class G1 = G, enable_if_t<!is_weighted_v<G1>>* = nullptr>
  vector<vector<int>> contract() const {
    vector<vector<int>> res(n_cpnts);
    rep(v, g.size()) g.adj(v, [&](int u) {
      if (id_[v] != id_[u]) res[id_[v]].push_back(id_[u]);
    });
    return res;
  }

  template <class G1 = G, enable_if_t<is_weighted_v<G1>>* = nullptr>
  vector<vector<pair<int, weight_t<G>>>> contract() const {
    vector<vector<pair<int, weight_t<G>>>> res(n_cpnts);
    rep(v, g.size()) g.adj(v, [&](auto&& e) {
      if (id_[v] != id_[e.to]) res[v].emplace_back(e.to, e.w());
    });
    return res;
  }

 private:
  graph_trait<G> g;
  vector<int> id_;
  int n_cpnts;
};
#line 7 "test/graph/scc.test.cpp"

int n, m;
vector<pair<int, ll>> G[100];

int main() {
  scanf("%d%d", &n, &m);
  rep(_, m) {
    int u, v;
    int w;
    scanf("%d%d%d", &u, &v, &w);
    G[u].emplace_back(v, w);
  }
  scc scc(G);
  for (auto& vs : scc.groups())
    if (bellman_ford(G, vs[0]).first) return printf("NEGATIVE CYCLE\n"), 0;
  auto d = ford_fulkerson(G);
  rep(v, n) rep(i, n) printf(
      "%s%c", d[v][i] == LONG_LONG_MAX ? "INF" : to_string(d[v][i]).c_str(),
      " \n"[i == n - 1]);
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-12	00_sample_00.in	AC	27 ms	9 MB
g++-12	00_sample_01.in	AC	25 ms	9 MB
g++-12	00_sample_02.in	AC	13 ms	8 MB
g++-12	01_small_00.in	AC	25 ms	9 MB
g++-12	01_small_01.in	AC	13 ms	8 MB
g++-12	02_corner_00.in	AC	25 ms	9 MB
g++-12	02_corner_01.in	AC	25 ms	9 MB
g++-12	02_corner_02.in	AC	25 ms	9 MB
g++-12	02_corner_03.in	AC	13 ms	8 MB
g++-12	02_corner_04.in	AC	25 ms	9 MB
g++-12	02_corner_05.in	AC	25 ms	9 MB
g++-12	02_corner_06.in	AC	25 ms	9 MB
g++-12	03_medium_00.in	AC	25 ms	9 MB
g++-12	03_medium_01.in	AC	13 ms	9 MB
g++-12	04_dag_00.in	AC	25 ms	9 MB
g++-12	04_dag_01.in	AC	26 ms	9 MB
g++-12	04_dag_02.in	AC	26 ms	9 MB
g++-12	04_dag_03.in	AC	27 ms	9 MB
g++-12	04_dag_04.in	AC	28 ms	9 MB
g++-12	05_ring_00.in	AC	26 ms	9 MB
g++-12	05_ring_01.in	AC	26 ms	9 MB
g++-12	05_ring_02.in	AC	27 ms	9 MB
g++-12	05_ring_03.in	AC	27 ms	9 MB
g++-12	05_ring_04.in	AC	26 ms	9 MB
g++-12	06_grid_00.in	AC	25 ms	9 MB
g++-12	06_grid_01.in	AC	25 ms	9 MB
g++-12	06_grid_02.in	AC	25 ms	9 MB
g++-12	06_grid_03.in	AC	26 ms	9 MB
g++-12	06_grid_04.in	AC	26 ms	9 MB
g++-12	07_complete_00.in	AC	25 ms	9 MB
g++-12	07_complete_01.in	AC	26 ms	9 MB
g++-12	07_complete_02.in	AC	28 ms	9 MB
g++-12	07_complete_03.in	AC	29 ms	10 MB
g++-12	07_complete_04.in	AC	30 ms	10 MB
g++-12	08_random_00.in	AC	14 ms	9 MB
g++-12	08_random_01.in	AC	14 ms	9 MB
g++-12	08_random_02.in	AC	26 ms	9 MB
g++-12	08_random_03.in	AC	26 ms	9 MB
g++-12	08_random_04.in	AC	26 ms	9 MB
g++-12	08_random_05.in	AC	26 ms	9 MB
g++-12	08_random_06.in	AC	26 ms	9 MB
g++-12	08_random_07.in	AC	27 ms	9 MB
g++-12	08_random_08.in	AC	27 ms	9 MB
g++-12	09_maximum_00.in	AC	26 ms	9 MB
g++-12	09_maximum_01.in	AC	27 ms	9 MB
g++-12	09_maximum_02.in	AC	32 ms	10 MB
g++-12	09_maximum_03.in	AC	28 ms	9 MB
g++-12	09_maximum_04.in	AC	15 ms	9 MB
g++-12	09_maximum_05.in	AC	27 ms	10 MB
g++-12	09_maximum_06.in	AC	26 ms	9 MB

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