結果

問題 No.1078 I love Matrix Construction
ユーザー KoD
提出日時 2020-09-27 11:00:51
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 377 ms / 2,000 ms
コード長 12,244 bytes
コンパイル時間 1,404 ms
コンパイル使用メモリ 100,808 KB
最終ジャッジ日時 2025-01-14 22:45:23
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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ファイルパターン 結果
other AC * 22
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ソースコード

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#line 1 "main.cpp"
/**
 * @title Template
 */
#include <iostream>
#include <algorithm>
#include <utility>
#include <numeric>
#include <vector>
#include <array>
#include <cassert>
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/chmin_chmax.cpp"
template <class T, class U>
constexpr bool chmin(T &lhs, const U &rhs) {
  if (lhs > rhs) { lhs = rhs; return true; }
  return false;
}
template <class T, class U>
constexpr bool chmax(T &lhs, const U &rhs) {
  if (lhs < rhs) { lhs = rhs; return true; }
  return false;
}
/**
 * @title Chmin/Chmax
 */
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/range.cpp"
#line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/other/range.cpp"
class range {
public:
  class iterator {
  private:
    int64_t M_position;
  public:
    constexpr iterator(int64_t position) noexcept: M_position(position) { }
    constexpr void operator ++ () noexcept { ++M_position; }
    constexpr bool operator != (iterator other) const noexcept { return M_position != other.M_position; }
    constexpr int64_t operator * () const noexcept { return M_position; }
  };
  class reverse_iterator {
  private:
    int64_t M_position;
  
  public:
    constexpr reverse_iterator(int64_t position) noexcept: M_position(position) { }
    constexpr void operator ++ () noexcept { --M_position; }
    constexpr bool operator != (reverse_iterator other) const noexcept { return M_position != other.M_position; }
    constexpr int64_t operator * () const noexcept { return M_position; }
  };
  
private:
  const iterator M_first, M_last;
public:
  constexpr range(int64_t first, int64_t last) noexcept: M_first(first), M_last(std::max(first, last)) { }
  constexpr iterator begin() const noexcept { return M_first; }
  constexpr iterator end() const noexcept { return M_last; }
  constexpr reverse_iterator rbegin() const noexcept { return reverse_iterator(*M_last - 1); } 
  constexpr reverse_iterator rend() const noexcept { return reverse_iterator(*M_first - 1); } 
};
/**
 * @title Range
 */
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/rev.cpp"
#include <type_traits>
#include <iterator>
#line 6 "/Users/kodamankod/Desktop/cpp_programming/Library/other/rev.cpp"
template <class T>
class rev_impl {
public:
  using iterator = decltype(std::rbegin(std::declval<T>()));
private:
  const iterator M_begin;
  const iterator M_end;
public:
  constexpr rev_impl(T &&cont) noexcept: M_begin(std::rbegin(cont)), M_end(std::rend(cont)) { }
  constexpr iterator begin() const noexcept { return M_begin; }
  constexpr iterator end() const noexcept { return M_end; }
};
template <class T>
constexpr decltype(auto) rev(T &&cont) {
  return rev_impl<T>(std::forward<T>(cont));
}
/**
 * @title Reverser
 */
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/graph/two_sat.cpp"
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/graph/network.cpp"
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/adjust_index.cpp"
#include <cstddef>
#line 5 "/Users/kodamankod/Desktop/cpp_programming/Library/other/adjust_index.cpp"
class adjust_index {
private:
  const size_t M_stuff, M_size;
public:
  explicit adjust_index(const size_t stuff, const size_t size): 
    M_stuff(stuff), M_size(size) 
  { }
  size_t operator [] (const size_t index) const {
    assert(index < M_size);
    return M_stuff + index;
  }
  size_t to_index(const size_t fixed) const {
    assert(fixed >= M_stuff);
    assert(fixed < M_size + M_stuff);
    return fixed - M_stuff;
  }
  size_t size() const {
    return M_size;
  }
};
/**
 * @title Index Adjustment
 */
#line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/graph/network.cpp"
#line 6 "/Users/kodamankod/Desktop/cpp_programming/Library/graph/network.cpp"
#include <cstdint>
#line 10 "/Users/kodamankod/Desktop/cpp_programming/Library/graph/network.cpp"
#include <type_traits>
#line 12 "/Users/kodamankod/Desktop/cpp_programming/Library/graph/network.cpp"
template <class Edge>
class network {
public:
  using vertex_type = typename Edge::vertex_type;
  using edge_type   = Edge;
  using size_type   = size_t;
protected:
  std::vector<std::vector<edge_type>> M_graph;
public:
  explicit network() = default;
  explicit network(const size_type size) { add_vertices<false>(size); }
  template <bool ReturnsIndex = true>
  typename std::enable_if<ReturnsIndex, vertex_type>::type add_vertex() {
    vertex_type res = M_graph.size();
    M_graph.push_back({ });
    return res;
  }
  template <bool ReturnsIndex = true>
  typename std::enable_if<!ReturnsIndex, void>::type add_vertex() {
    M_graph.push_back({ });
  }
  template <bool ReturnsIndices = true>
  typename std::enable_if<ReturnsIndices, adjust_index>::type 
  add_vertices(const size_type size) {
    size_type cur = M_graph.size();
    M_graph.resize(cur + size);
    return adjust_index(cur, size);
  }
  template <bool ReturnsIndices = true>
  typename std::enable_if<!ReturnsIndices, void>::type 
  add_vertices(const size_type size) {
    size_type cur = M_graph.size();
    M_graph.resize(cur + size);
  }
  
  void add_edge(const edge_type &edge) {
    M_graph[edge.source].push_back(edge);
  }
  template <class... Args>
  void emplace_edge(const vertex_type src, Args&&... args) {
    M_graph[src].emplace_back(src, std::forward<Args>(args)...);
  }
  std::vector<edge_type> &operator [] (const vertex_type vert) {
    assert(vert < size());
    return M_graph[vert];
  }
  const std::vector<edge_type> &operator [] (const vertex_type vert) const {
    assert(vert < size());
    return M_graph[vert];
  }
  size_type size() const {
    return M_graph.size();
  }
  bool empty() const {
    return M_graph.empty();
  }
  void clear() {
    M_graph.clear();
    M_graph.shrink_to_fit();
  }
};
class base_edge {
public:
  using vertex_type = uint32_t;
  const vertex_type source, dest;
  explicit base_edge(const vertex_type source, const vertex_type dest): 
    source(source), dest(dest) 
  { }
  base_edge reverse() const {
    return base_edge(dest, source);
  }
};
template <class Flow>
class flow_edge: public base_edge {
public:
  using vertex_type = typename base_edge::vertex_type;
  using flow_type   = Flow;
  flow_type flow;
  const flow_type capacity;
  explicit flow_edge(const base_edge &edge, const flow_type capacity):
    base_edge(edge), flow(0), capacity(capacity)
  { }
  explicit flow_edge(const base_edge &edge, const flow_type flow, const flow_type capacity):
    base_edge(edge), flow(flow), capacity(capacity)
  { }
  explicit flow_edge(const vertex_type source, const vertex_type dest, const flow_type capacity):
    base_edge(source, dest), flow(0), capacity(capacity)
  { }
  explicit flow_edge(const vertex_type source, const vertex_type dest, const flow_type flow, const flow_type capacity):
    base_edge(source, dest), flow(flow), capacity(capacity)
  { }
  flow_edge reverse() const {
    return flow_edge(static_cast<base_edge>(*this).reverse(), capacity - flow, capacity);
  }
};
/**
 * @title Network
 */
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/graph/scc.cpp"
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/fix_point.cpp"
#line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/other/fix_point.cpp"
template <class Func>
struct fix_point_impl: private Func {
  explicit constexpr fix_point_impl(Func &&func): Func(std::forward<Func>(func)) { }
  template <class... Args>
  constexpr decltype(auto) operator () (Args &&... args) const {
    return Func::operator()(*this, std::forward<Args>(args)...);
  }
};
template <class Func>
constexpr decltype(auto) fix_point(Func &&func) {
  return fix_point_impl<Func>(std::forward<Func>(func));
}
/**
 * @title Lambda Recursion
 */
#line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/graph/scc.cpp"
#line 6 "/Users/kodamankod/Desktop/cpp_programming/Library/graph/scc.cpp"
#include <stack>
template <class Network>
class strongly_connected_components {
public:
  using network_type = Network;
  using vertex_type  = typename Network::vertex_type;
  using edge_type    = typename Network::edge_type;
  using size_type    = typename Network::size_type;
private:
  std::vector<std::vector<vertex_type>> graph;
  std::vector<std::vector<vertex_type>> revgraph;
public:
  explicit strongly_connected_components(const network_type &net) {
    graph.resize(net.size());
    revgraph.resize(net.size());
    for (size_type src = 0; src < net.size(); ++src) {
      for (const auto &edge: net[src]) {
        graph[src].push_back(edge.dest);
        revgraph[edge.dest].push_back(src);
      }
    }
  }
  std::vector<std::vector<vertex_type>> decompose() const {
    std::vector<bool> visited(graph.size());
    std::stack<vertex_type> topological;
    const auto sort = fix_point([&](auto dfs, const vertex_type u) -> void {
      if (visited[u]) return;
      visited[u] = true;
      for (const auto v: graph[u]) {
        dfs(v);
      }
      topological.push(u);
    });
    for (vertex_type src = 0; src < graph.size(); ++src) {
      sort(src);
    }
    std::vector<std::vector<vertex_type>> group;
    const auto decompose = fix_point([&](const auto dfs, const vertex_type u) -> void {
      if (visited[u]) return;
      visited[u] = true;
      group.back().push_back(u);
      for (const auto v: revgraph[u]) {
        dfs(v);
      }
    });
    std::fill(visited.begin(), visited.end(), false);
    while (!topological.empty()) {
      const auto u = topological.top();
      topological.pop();
      if (!visited[u]) {
        group.push_back({ });
        decompose(u);
      }
    }
    return group;
  }
};
/**
 * @title Strongly Connected Components
 */
#line 5 "/Users/kodamankod/Desktop/cpp_programming/Library/graph/two_sat.cpp"
#line 10 "/Users/kodamankod/Desktop/cpp_programming/Library/graph/two_sat.cpp"
class two_sat {
public:
  using size_type = size_t;
private:
  network<base_edge> graph;
public:
  explicit two_sat() = default;
  explicit two_sat(const size_type size): graph(size * 2) { }
  void add_clause(const size_type i, const bool f, const size_type j, const bool g) {
    assert(i < size());
    assert(j < size());
    graph.emplace_edge(2 * i + (f ? 0 : 1), 2 * j + (g ? 1 : 0));
    graph.emplace_edge(2 * j + (g ? 0 : 1), 2 * i + (f ? 1 : 0));
  }
  std::pair<bool, std::vector<bool>> satisfy() const {
    const auto groups = strongly_connected_components(graph).decompose();
    std::vector<size_type> id(graph.size());
    std::vector<bool> res(size());
    for (size_type i = 0; i < groups.size(); ++i) {
      for (const auto x: groups[i]) {
        id[x] = i;
      }
    }
    for (size_type i = 0; i < size(); ++i) {
      if (id[2 * i] == id[2 * i + 1]) {
        return { false, { } };
      }
      res[i] = id[2 * i] < id[2 * i + 1];
    }
    return { true, res };
  }
  size_type size() const {
    return graph.size() / 2;
  }
};
/**
 * @title Two Sat
 */
#line 18 "main.cpp"
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
constexpr i32 inf32 = (i32(1) << 30) - 1;
constexpr i64 inf64 = (i64(1) << 62) - 1;
int main() {
  size_t N;
  std::cin >> N;
  std::vector<size_t> S(N), T(N);
  std::vector<u32> U(N);
  for (auto &x: S) {
    std::cin >> x;
    --x;
  }
  for (auto &x: T) {
    std::cin >> x;
    --x;
  }
  for (auto &x: U) {
    std::cin >> x;
  }
  two_sat sat(N * N);
  for (auto i: range(0, N)) {
    for (auto j: range(0, N)) {
      const auto u = S[i] * N + j;
      const auto v = j * N + T[i];
      switch (U[i]) {
        case 0:
          sat.add_clause(u, true, v, true);
          break;
        case 1:
          sat.add_clause(u, false, v, true); 
          break;
        case 2:
          sat.add_clause(u, true, v, false); 
          break;
        case 3:
          sat.add_clause(u, false, v, false);
          break;
        default:
          break;
      }
    }
  }
  const auto [satisfiable, answer] = sat.satisfy();
  if (!satisfiable) {
    std::cout << "-1\n";
  }
  else {
    for (auto i: range(0, N)) {
      for (auto j: range(0, N)) {
        std::cout << answer[i * N + j] << (j + 1 == N ? '\n' : ' ');
      }
    }
  }
  return 0;
}
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