Submission #679628

#	Time	Username	Problem	Language	Result	Execution time	Memory
679628		peijar	Three Friends (BOI14_friends)	C++17	35 / 100	1051 ms	262144 KiB

friends

#include <bits/stdc++.h>
#define int long long
using namespace std;

namespace std {
template <typename T> ostream &operator<<(ostream &out, const vector<T> &vec) {
  out << "[";
  for (int i = 0; i < (int)vec.size(); ++i) {
    out << vec[i];
    if (i + 1 < (int)vec.size())
      out << ", ";
  }
  return out << "]";
}
} // namespace std

void dbg_out() { cout << endl; }
template <typename Head, typename... Tail> void dbg_out(Head H, Tail... T) {
  cout << ' ' << H;
  dbg_out(T...);
}

#ifdef DEBUG
#define dbg(...) cout << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)
#else
#define dbg(...)
#endif

/*
 * sa[i] = starting index of i-th smallest suffix
 * sa.len() = n+ 1, sa[0] = n
 * lcp[i] = lcp(sa[i], sa[i-1]), lcp[0] = 0, len(sa) = n+1
 */

template <class T> struct RMQ {
  vector<vector<T>> jmp;
  RMQ(const vector<T> &V) : jmp(1, V) {
    for (int pw = 1, k = 1; pw * 2 <= (int)V.size(); pw *= 2, ++k) {
      jmp.emplace_back((int)V.size() - pw * 2 + 1);
      for (int j = 0; j < (int)jmp[k].size(); ++j)
        jmp[k][j] = min(jmp[k - 1][j], jmp[k - 1][j + pw]);
    }
  }
  T query(int a, int b) { // [a, b)
    assert(a < b);
    int dep = 31 - __builtin_clz(b - a);
    return min(jmp[dep][a], jmp[dep][b - (1 << dep)]);
  }
};

vector<int> sa_is(const vector<int> &s, int lim = 256) {
  int n = s.size();
  if (!n)
    return {};
  vector<int> sa(n);
  vector<bool> ls(n);
  for (int i = n - 2; i >= 0; --i)
    ls[i] = s[i] == s[i + 1] ? ls[i + 1] : s[i] < s[i + 1];
  vector<int> sum_l(lim), sum_s(lim);
  for (int i = 0; i < n; ++i)
    (ls[i] ? sum_l[s[i] + 1] : sum_s[s[i]])++;
  for (int i = 0; i < lim; ++i) {
    if (i)
      sum_l[i] += sum_s[i - 1];
    sum_s[i] += sum_l[i];
  }
  auto induce = [&](const vector<int> &lms) {
    fill(sa.begin(), sa.end(), -1);
    vector<int> buf = sum_s;
    for (int d : lms)
      if (d != n)
        sa[buf[s[d]]++] = d;
    buf = sum_l;
    sa[buf[s[n - 1]]++] = n - 1;
    for (int i = 0; i < n; ++i) {
      int v = sa[i] - 1;
      if (v >= 0 && !ls[v])
        sa[buf[s[v]]++] = v;
    }
    buf = sum_l;
    for (int i = n - 1; i >= 0; --i) {
      int v = sa[i] - 1;
      if (v >= 0 && ls[v])
        sa[--buf[s[v] + 1]] = v;
    }
  };
  vector<int> lms_map(n + 1, -1), lms;
  int m = 0;
  for (int i = 1; i < n; ++i)
    if (!ls[i - 1] && ls[i])
      lms_map[i] = m++, lms.push_back(i);
  induce(lms);
  vector<int> sorted_lms;
  for (auto &v : sa)
    if (lms_map[v] != -1)
      sorted_lms.push_back(v);
  vector<int> rec_s(m);
  int rec_upper = 0;
  for (int i = 1; i < m; ++i) {
    int l = sorted_lms[i - 1], r = sorted_lms[i];
    int end_l = lms_map[l] + 1 < m ? lms[lms_map[l] + 1] : n;
    int end_r = lms_map[r] + 1 < m ? lms[lms_map[r] + 1] : n;
    bool same = 0;
    if (end_l - l == end_r - r) {
      for (; l < end_l && s[l] == s[r]; ++l, ++r)
        ;
      if (l != n && s[l] == s[r])
        same = 1;
    }
    rec_s[lms_map[sorted_lms[i]]] = (rec_upper += !same);
  }
  vector<int> rec_sa = sa_is(rec_s, rec_upper + 1);
  for (int i = 0; i < m; ++i)
    sorted_lms[i] = lms[rec_sa[i]];
  induce(sorted_lms);
  return sa;
}

struct SuffixArray {
  vector<int> sa, lcp, rank;
  string s;
  RMQ<int> rmq;

  SuffixArray(string &_s, int lim = 256) : rmq({}) {
    s = _s;
    vector<int> S;
    for (char c : _s)
      S.push_back(c);
    int n = s.size() + 1, k = 0, a, b;
    auto SA = sa_is(S, lim);
    vector<int> y(n);
    sa = lcp = rank = y;
    sa[0] = n - 1;
    for (int i = 1; i < n; ++i)
      sa[i] = SA[i - 1];

    for (int i = 1; i < n; ++i)
      rank[sa[i]] = i;
    for (int i = 0, j; i < n - 1; lcp[rank[i++]] = k)
      for (k &&k--, j = sa[rank[i] - 1]; s[i + k] == s[j + k]; k++)
        ;
    rmq = RMQ<int>(lcp);
  }

  int getLCP(int i, int j) {
    if (i == j)
      return s.size() - i;
    i = rank[i];
    j = rank[j];
    if (i > j)
      swap(i, j);
    return rmq.query(i + 1, j + 1);
  }
};

bool get(string U) {
  int N = U.size() / 2;
  SuffixArray suffix(U);
  for (int skip = N; skip < 2 * N + 1; ++skip) {
    if (suffix.getLCP(0, N) < skip - N)
      continue;
    if (skip < 2 * N and suffix.getLCP(skip - N, skip + 1) < N - (skip - N))
      continue;
    return true;
  }
  return false;
}

signed main(void) {
  ios_base::sync_with_stdio(false);
  cin.tie(0);

  int N;
  string U;
  cin >> N >> U;

  if (N % 2 == 0) {
    cout << "NOT POSSIBLE\n";
    return 0;
  }

  string T = U;
  reverse(T.begin(), T.end());
  bool okL = get(U);
  bool okR = get(T);
  N /= 2;
  string L = U.substr(0, N);
  string R = U.substr(N + 1, N);
  dbg(L, R);
  dbg(okL, okR);

  if (!okL and !okR) {
    cout << "NOT POSSIBLE\n";
    return 0;
  }
  if (okL and okR and L != R) {
    cout << "NOT UNIQUE\n";
    return 0;
  }
  cout << (okL ? L : R) << endl;
}

Compilation message (stderr)

friends.cpp: In constructor 'SuffixArray::SuffixArray(std::string&, long long int)':
friends.cpp:129:34: warning: unused variable 'a' [-Wunused-variable]
  129 |     int n = s.size() + 1, k = 0, a, b;
      |                                  ^
friends.cpp:129:37: warning: unused variable 'b' [-Wunused-variable]
  129 |     int n = s.size() + 1, k = 0, a, b;
      |                                     ^

• Subtask 1: 35 / 35
• Subtask 2: 0 / 65