Problem p02557 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
#include <stdio.h>
using namespace std;
const int nax = 4e5 + 10;
namespace atcoder {
// Reference:
// B. Aspvall, M. Plass, and R. Tarjan,
// A Linear-Time Algorithm for Testing the Truth of Certain Quantified Boolean
// Formulas
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;
};
} // namespace atcoder
using two_sat = atcoder::two_sat;

using two_sat = atcoder::two_sat;
int a[nax];
int b[nax];
int first[nax];
int last[nax];

pair<int, int> ban[nax];
int top_ban = 0;
int n;

int main() {
  scanf("%d", &n);

  for (int i = 1; i <= n; ++i) {
    scanf("%d", a + i);
    if (!first[a[i]])
      first[a[i]] = i;
    last[a[i]] = i;
  }

  for (int i = 1; i <= n; ++i) {
    scanf("%d", b + i);
  }

  for (int i = 1; i <= n; ++i) {
    int x = first[b[i]], y = last[b[i]];
    if (x == 0)
      continue;
    int ban_l, ban_r;
    if (i <= x) {
      ban_l = x - i;
      ban_r = ban_l + y - x;
    } else {
      x += n;
      y += n;
      ban_l = x - i;
      ban_r = ban_l + y - x;
    }

    if (ban_r >= n) {
      ban[++top_ban] = make_pair(0, ban_r - n);
      ban[++top_ban] = make_pair(ban_l, n - 1);
    } else
      ban[++top_ban] = make_pair(ban_l, ban_r);
  }

  /**
      if matching exist, it's one of cyclic shift
      not we can express it as some boolean clause?
      ban range has logical expression as
      not(x >= a && x <= b)
      = not(x >= a) || (x >= b - 1)
      not just and all of these clause
      and add some additional clause
      if (x >= a)-> (x >= a - 1)
      equivalent to not(x >= a) or x >= a - 1;
  */

  two_sat sat(n);
  for (int i = 1; i < n; ++i) {
    sat.add_clause(i, false, i - 1, true);
  }

  for (int i = 1; i <= top_ban; ++i) {
    auto [l, r] = ban[i];
    //     cout << l << ' ' << r << '\\n';
    if (r == n - 1)
      sat.add_clause(l, false, l, false);
    else
      sat.add_clause(l, false, r + 1, true);
  }
  sat.add_clause(0, true, 0, true);

  if (!sat.satisfiable())
    return !printf("No");

  vector<bool> answer = sat.answer();

  int last_true = 0;

  for (const auto &it : answer) {
    //      cout << it << ' ';
  }
  //  cout << '\\n';

  for (int i = 0; i < n; ++i) {
    if (answer[i]) {
      last_true = i;
    } else
      break;
  }

  // cerr << "LAST TRUE " << last_true << '\\n';
  printf("Yes\\n");

  for (int i = 1; i <= n; ++i) {
    int pos = i - last_true;
    if (pos <= 0)
      pos += n;
    printf("%d ", b[pos]);
  }
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
#include <stdio.h>
using namespace std;
const int nax = 4e5 + 10;
int a[nax];
int b[nax];
int c[nax];
int n;

int main() {
  scanf("%d", &n);

  for (int i = 0; i < n; ++i) {
    scanf("%d", a + i);
  }

  for (int i = 0; i < n; ++i) {
    scanf("%d", b + i);
  }

  for (int shift = 0; shift < n; ++shift) {
    for (int i = 0; i < n; ++i)
      c[i] = b[(i + shift) % n];
    bool ok = true;
    for (int i = 0; i < n; ++i) {
      ok &= c[i] != a[i];
      if (!ok)
        break;
    }
    if (ok) {
      puts("Yes");
      for (int i = 0; i < n; ++i)
        printf("%d ", c[i]);
      return 0;
    }
  }
  puts("No");
}