結果

問題 No.1955 Not Prime
ユーザー RVindicatio
提出日時 2022-05-22 22:20:26
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 77 ms / 2,000 ms
コード長 4,830 bytes
コンパイル時間 15,183 ms
コンパイル使用メモリ 303,480 KB
最終ジャッジ日時 2025-01-29 13:56:33
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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ファイルパターン 結果
other AC * 26
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ソースコード

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プレゼンテーションモードにする

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>
using namespace std;
using ll = long long;
const int INF = 1e9;
const ll inf = 1LL<<60;
namespace internal {
template <class E> struct csr {
    std::vector<int> start;
    std::vector<E> elist;
    csr(int n, const std::vector<std::pair<int, E>>& edges)
        : start(n + 1), elist(edges.size()) {
        for (auto e : edges) {
            start[e.first + 1]++;
        }
        for (int i = 1; i <= n; i++) {
            start[i] += start[i - 1];
        }
        auto counter = start;
        for (auto e : edges) {
            elist[counter[e.first]++] = e.second;
        }
    }
};
// Reference:
// R. Tarjan,
// Depth-First Search and Linear Graph Algorithms
struct scc_graph {
  public:
    scc_graph(int n) : _n(n) {}
    int num_vertices() { return _n; }
    void add_edge(int from, int to) { edges.push_back({from, {to}}); }
    // @return pair of (# of scc, scc id)
    std::pair<int, std::vector<int>> scc_ids() {
        auto g = csr<edge>(_n, edges);
        int now_ord = 0, group_num = 0;
        std::vector<int> visited, low(_n), ord(_n, -1), ids(_n);
        visited.reserve(_n);
        auto dfs = [&](auto self, int v) -> void {
            low[v] = ord[v] = now_ord++;
            visited.push_back(v);
            for (int i = g.start[v]; i < g.start[v + 1]; i++) {
                auto to = g.elist[i].to;
                if (ord[to] == -1) {
                    self(self, to);
                    low[v] = std::min(low[v], low[to]);
                } else {
                    low[v] = std::min(low[v], ord[to]);
                }
            }
            if (low[v] == ord[v]) {
                while (true) {
                    int u = visited.back();
                    visited.pop_back();
                    ord[u] = _n;
                    ids[u] = group_num;
                    if (u == v) break;
                }
                group_num++;
            }
        };
        for (int i = 0; i < _n; i++) {
            if (ord[i] == -1) dfs(dfs, i);
        }
        for (auto& x : ids) {
            x = group_num - 1 - x;
        }
        return {group_num, ids};
    }
    std::vector<std::vector<int>> scc() {
        auto ids = scc_ids();
        int group_num = ids.first;
        std::vector<int> counts(group_num);
        for (auto x : ids.second) counts[x]++;
        std::vector<std::vector<int>> groups(ids.first);
        for (int i = 0; i < group_num; i++) {
            groups[i].reserve(counts[i]);
        }
        for (int i = 0; i < _n; i++) {
            groups[ids.second[i]].push_back(i);
        }
        return groups;
    }
  private:
    int _n;
    struct edge {
        int to;
    };
    std::vector<std::pair<int, edge>> edges;
};
}  // namespace internal
struct two_sat {
  public:
    two_sat() : _n(0), scc(0) {}
    two_sat(int n) : _n(n), _answer(n), scc(2 * n) {}
    void add_clause(int i, bool f, int j, bool g) {
        assert(0 <= i && i < _n);
        assert(0 <= j && j < _n);
        scc.add_edge(2 * i + (f ? 0 : 1), 2 * j + (g ? 1 : 0));
        scc.add_edge(2 * j + (g ? 0 : 1), 2 * i + (f ? 1 : 0));
    }
    bool satisfiable() {
        auto id = scc.scc_ids().second;
        for (int i = 0; i < _n; i++) {
            if (id[2 * i] == id[2 * i + 1]) return false;
            _answer[i] = id[2 * i] < id[2 * i + 1];
        }
        return true;
    }
    std::vector<bool> answer() { return _answer; }
  private:
    int _n;
    std::vector<bool> _answer;
    internal::scc_graph scc;
};
void solve() {
  vector<bool> era(1000100, true);
  era[0] = era[1] = true;
  for (int i=2; i<1000100; i++) if (era[i]) {
    for (int x=2*i; x<1000100; x+=i) era[x] = false;
  }
  auto check = [&](int x, int y) -> bool {
    string s = to_string(x) + to_string(y);
    return era[stoi(s)];
  };
  int n; cin >> n;
  two_sat ts(n);
  vector<int> a(n), b(n);
  for (int i=0; i<n; i++) cin >> a[i] >> b[i];
  for (int i=0; i<n; i++) {
    if (check(a[i], b[i]) && check(b[i], a[i])) {
      cout << "No" << '\n';
      return;
    }
    if (!check(a[i], b[i]) && check(b[i], a[i])) ts.add_clause(i, 0, i, 0);
    if (!check(b[i], a[i]) && check(a[i], b[i])) ts.add_clause(i, 1, i, 1);
    for (int j=i+1; j<n; j++) {
      if (check(a[i], b[j]) || check(a[j], b[i])) ts.add_clause(i, 1, j, 1);
      if (check(a[i], a[j]) || check(b[j], b[i])) ts.add_clause(i, 1, j, 0);
      if (check(b[i], b[j]) || check(a[j], a[i])) ts.add_clause(i, 0, j, 1);
      if (check(b[i], a[j]) || check(b[j], a[i])) ts.add_clause(i, 0, j, 0);
    }
  }
  cout << (ts.satisfiable() ? "Yes" : "No") << '\n';
}
int main() {
  ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  // int t; cin >> t;
  /*while (t--)*/ solve();
}
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