test/yukicoder/274.2sat.test.cpp

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• Last update: 2024-09-20 12:04:43+09:00
• Problem: https://yukicoder.me/problems/no/274

Depends on

• グラフ (src/Graph/Graph.hpp)
• 強連結成分分解 (src/Graph/StronglyConnectedComponents.hpp)
• CSR 表現を用いた二次元配列 他 (src/Internal/ListRange.hpp)
• 2-SAT (src/Misc/TwoSatisfiability.hpp)

Code

// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/274
// competitive-verifier: TLE 1
// competitive-verifier: MLE 256
#include <iostream>
#include "src/Misc/TwoSatisfiability.hpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N, M;
 cin >> N >> M;
 int L[N], R[N];
 for (int i= 0; i < N; ++i) cin >> L[i] >> R[i];
 TwoSatisfiability sat(N);
 for (int i= N; i--;)
  for (int j= i; j--;) {
   if (!(R[i] < L[j] || R[j] < L[i])) sat.add_nand(i, j), sat.add_nand(sat.neg(i), sat.neg(j));
   if (!(R[i] < M - 1 - R[j] || M - 1 - L[j] < L[i])) sat.add_nand(sat.neg(i), j), sat.add_nand(i, sat.neg(j));
  }
 cout << (sat.solve().empty() ? "NO" : "YES") << '\n';
 return 0;
}

#line 1 "test/yukicoder/274.2sat.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/274
// competitive-verifier: TLE 1
// competitive-verifier: MLE 256
#include <iostream>
#line 2 "src/Graph/StronglyConnectedComponents.hpp"
#include <algorithm>
#line 2 "src/Internal/ListRange.hpp"
#include <vector>
#line 4 "src/Internal/ListRange.hpp"
#include <iterator>
#include <type_traits>
#define _LR(name, IT, CT) \
 template <class T> struct name { \
  using Iterator= typename std::vector<T>::IT; \
  Iterator bg, ed; \
  Iterator begin() const { return bg; } \
  Iterator end() const { return ed; } \
  size_t size() const { return std::distance(bg, ed); } \
  CT &operator[](int i) const { return bg[i]; } \
 }
_LR(ListRange, iterator, T);
_LR(ConstListRange, const_iterator, const T);
#undef _LR
template <class T> struct CSRArray {
 std::vector<T> dat;
 std::vector<int> p;
 size_t size() const { return p.size() - 1; }
 ListRange<T> operator[](int i) { return {dat.begin() + p[i], dat.begin() + p[i + 1]}; }
 ConstListRange<T> operator[](int i) const { return {dat.cbegin() + p[i], dat.cbegin() + p[i + 1]}; }
};
template <template <class> class F, class T> std::enable_if_t<std::disjunction_v<std::is_same<F<T>, ListRange<T>>, std::is_same<F<T>, ConstListRange<T>>, std::is_same<F<T>, CSRArray<T>>>, std::ostream &> operator<<(std::ostream &os, const F<T> &r) {
 os << '[';
 for (int _= 0, __= r.size(); _ < __; ++_) os << (_ ? ", " : "") << r[_];
 return os << ']';
}
#line 3 "src/Graph/Graph.hpp"
struct Edge: std::pair<int, int> {
 using std::pair<int, int>::pair;
 Edge &operator--() { return --first, --second, *this; }
 int to(int v) const { return first ^ second ^ v; }
 friend std::istream &operator>>(std::istream &is, Edge &e) { return is >> e.first >> e.second, is; }
};
struct Graph: std::vector<Edge> {
 size_t n;
 Graph(size_t n= 0, size_t m= 0): vector(m), n(n) {}
 size_t vertex_size() const { return n; }
 size_t edge_size() const { return size(); }
 size_t add_vertex() { return n++; }
 size_t add_edge(int s, int d) { return emplace_back(s, d), size() - 1; }
 size_t add_edge(Edge e) { return emplace_back(e), size() - 1; }
#define _ADJ_FOR(a, b) \
 for (auto [u, v]: *this) a; \
 for (size_t i= 0; i < n; ++i) p[i + 1]+= p[i]; \
 for (int i= size(); i--;) { \
  auto [u, v]= (*this)[i]; \
  b; \
 }
#define _ADJ(a, b) \
 vector<int> p(n + 1), c(size() << !dir); \
 if (!dir) { \
  _ADJ_FOR((++p[u], ++p[v]), (c[--p[u]]= a, c[--p[v]]= b)) \
 } else if (dir > 0) { \
  _ADJ_FOR(++p[u], c[--p[u]]= a) \
 } else { \
  _ADJ_FOR(++p[v], c[--p[v]]= b) \
 } \
 return {c, p}
 CSRArray<int> adjacency_vertex(int dir) const { _ADJ(v, u); }
 CSRArray<int> adjacency_edge(int dir) const { _ADJ(i, i); }
#undef _ADJ
#undef _ADJ_FOR
};
#line 4 "src/Graph/StronglyConnectedComponents.hpp"
class StronglyConnectedComponents {
 std::vector<int> m, q, b;
public:
 StronglyConnectedComponents(const Graph &g) {
  const int n= g.vertex_size();
  m.assign(n, -2), b.resize(n);
  {
   auto adj= g.adjacency_vertex(1);
   std::vector<int> c(adj.p.begin(), adj.p.begin() + n);
   for (int s= 0, k= n, p; s < n; ++s)
    if (m[s] == -2)
     for (m[p= s]= -1; p >= 0;) {
      if (c[p] == adj.p[p + 1]) b[--k]= p, p= m[p];
      else if (int w= adj.dat[c[p]++]; m[w] == -2) m[w]= p, p= w;
     }
  }
  auto adj= g.adjacency_vertex(-1);
  std::vector<char> z(n);
  int k= 0, p= 0;
  q= {0};
  for (int s: b)
   if (!z[s]) {
    for (z[m[k++]= s]= 1; p < k; ++p)
     for (int u: adj[m[p]])
      if (!z[u]) z[m[k++]= u]= 1;
    q.push_back(k);
   }
  for (int i= q.size() - 1; i--;)
   while (k > q[i]) b[m[--k]]= i;
 }
 size_t size() const { return q.size() - 1; }
 ConstListRange<int> block(int k) const { return {m.cbegin() + q[k], m.cbegin() + q[k + 1]}; }
 int operator()(int i) const { return b[i]; }
 Graph dag(const Graph &g) const {
  Graph ret(size());
  for (auto [s, d]: g)
   if (b[s] != b[d]) ret.add_edge(b[s], b[d]);
  return std::sort(ret.begin(), ret.end()), ret.erase(std::unique(ret.begin(), ret.end()), ret.end()), ret;
 }
};
#line 3 "src/Misc/TwoSatisfiability.hpp"
class TwoSatisfiability {
 int n;
 Graph g;
public:
 TwoSatisfiability(int n): n(n), g(n + n) {}
 inline int neg(int x) const { return x >= n ? x - n : x + n; }
 void add_if(int u, int v) { g.add_edge(u, v), g.add_edge(neg(v), neg(u)); }  // u -> v <=> !v -> !u
 void add_or(int u, int v) { add_if(neg(u), v); }                             // u or v <=> !u -> v
 void add_nand(int u, int v) { add_if(u, neg(v)); }                           // u nand v <=> u -> !v
 void set_true(int u) { g.add_edge(neg(u), u); }                              // u <=> !u -> u
 void set_false(int u) { g.add_edge(u, neg(u)); }                             // !u <=> u -> !u
 std::vector<bool> solve() {
  StronglyConnectedComponents scc(g);
  std::vector<bool> ret(n);
  for (int i= 0, l, r; i<n; ret[i++]= l> r)
   if (l= scc(i), r= scc(neg(i)); l == r) return {};  // no solution
  return ret;
 }
};
#line 6 "test/yukicoder/274.2sat.test.cpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N, M;
 cin >> N >> M;
 int L[N], R[N];
 for (int i= 0; i < N; ++i) cin >> L[i] >> R[i];
 TwoSatisfiability sat(N);
 for (int i= N; i--;)
  for (int j= i; j--;) {
   if (!(R[i] < L[j] || R[j] < L[i])) sat.add_nand(i, j), sat.add_nand(sat.neg(i), sat.neg(j));
   if (!(R[i] < M - 1 - R[j] || M - 1 - L[j] < L[i])) sat.add_nand(sat.neg(i), j), sat.add_nand(i, sat.neg(j));
  }
 cout << (sat.solve().empty() ? "NO" : "YES") << '\n';
 return 0;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-13	98_challenge01.txt	AC	5 ms	4 MB
g++-13	99_system_test1.txt	AC	5 ms	4 MB
g++-13	99_system_test2.txt	AC	5 ms	4 MB
g++-13	99_system_test3.txt	AC	110 ms	88 MB
g++-13	99_system_test4.txt	AC	16 ms	10 MB
g++-13	challenge01.txt	AC	5 ms	4 MB
g++-13	sample1.txt	AC	5 ms	4 MB
g++-13	sample2.txt	AC	5 ms	4 MB
g++-13	sample3.txt	AC	5 ms	4 MB
g++-13	sample4.txt	AC	5 ms	4 MB
g++-13	system_test1.txt	AC	5 ms	4 MB
g++-13	test1.txt	AC	5 ms	4 MB
g++-13	test10.txt	AC	10 ms	4 MB
g++-13	test11.txt	AC	11 ms	4 MB
g++-13	test12.txt	AC	11 ms	4 MB
g++-13	test13.txt	AC	11 ms	4 MB
g++-13	test14.txt	AC	11 ms	4 MB
g++-13	test15.txt	AC	12 ms	4 MB
g++-13	test16.txt	AC	11 ms	4 MB
g++-13	test2.txt	AC	316 ms	253 MB
g++-13	test3.txt	AC	9 ms	4 MB
g++-13	test4.txt	AC	5 ms	4 MB
g++-13	test5.txt	AC	6 ms	4 MB
g++-13	test6.txt	AC	7 ms	4 MB
g++-13	test7.txt	AC	75 ms	54 MB
g++-13	test8.txt	AC	73 ms	50 MB
g++-13	test9.txt	AC	78 ms	54 MB
clang++-18	98_challenge01.txt	AC	6 ms	4 MB
clang++-18	99_system_test1.txt	AC	5 ms	4 MB
clang++-18	99_system_test2.txt	AC	5 ms	4 MB
clang++-18	99_system_test3.txt	AC	73 ms	88 MB
clang++-18	99_system_test4.txt	AC	15 ms	10 MB
clang++-18	challenge01.txt	AC	5 ms	4 MB
clang++-18	sample1.txt	AC	5 ms	4 MB
clang++-18	sample2.txt	AC	5 ms	4 MB
clang++-18	sample3.txt	AC	5 ms	4 MB
clang++-18	sample4.txt	AC	5 ms	4 MB
clang++-18	system_test1.txt	AC	5 ms	4 MB
clang++-18	test1.txt	AC	5 ms	4 MB
clang++-18	test10.txt	AC	10 ms	4 MB
clang++-18	test11.txt	AC	11 ms	4 MB
clang++-18	test12.txt	AC	11 ms	4 MB
clang++-18	test13.txt	AC	12 ms	4 MB
clang++-18	test14.txt	AC	12 ms	4 MB
clang++-18	test15.txt	AC	13 ms	4 MB
clang++-18	test16.txt	AC	12 ms	4 MB
clang++-18	test2.txt	AC	204 ms	253 MB
clang++-18	test3.txt	AC	9 ms	4 MB
clang++-18	test4.txt	AC	5 ms	4 MB
clang++-18	test5.txt	AC	6 ms	4 MB
clang++-18	test6.txt	AC	7 ms	4 MB
clang++-18	test7.txt	AC	64 ms	53 MB
clang++-18	test8.txt	AC	63 ms	50 MB
clang++-18	test9.txt	AC	65 ms	56 MB

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