tests/manacher.test.cpp

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Last update: 2025-01-22 03:51:11+00:00
Problem: https://onlinejudge.u-aizu.ac.jp/problems/2934

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Code

// competitive-verifier: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/2934

#include <iostream>
#include <string>
#include <vector>
#include <utility>
#include <iterator>
#include <cstdlib>
#include "atcoder/string.hpp"
#include "tools/manacher.hpp"

int main() {
  std::cin.tie(nullptr);
  std::ios_base::sync_with_stdio(false);

  int N;
  std::string T;
  std::cin >> N >> T;

  std::vector<std::pair<int, int>> R;
  tools::manacher(T.begin(), T.end(), std::back_inserter(R));
  const auto Z = atcoder::z_algorithm(T);

  std::cout << [&]() {
    for (int i = 1; i < N; ++i) {
      if (R[i * 2 + 1].first == 0 && [&]() {
        for (int j = 0; j < N; j += R[i * 2 + 1].second - R[i * 2 + 1].first - 1) {
          if (Z[j] < N - j) {
            return false;
          }
        }
        return true;
      }()) {
        return (R[i * 2 + 1].second - R[i * 2 + 1].first + 1) / 2;
      }
    }
    for (int i = 0; i < N; ++i) {
      if (R[i * 2 + 1].second == N) {
        return (N + R[i * 2 + 1].first + 1) / 2;
      }
    }
    std::exit(EXIT_FAILURE);
  }() << '\n';

  return 0;
}

#line 1 "tests/manacher.test.cpp"
// competitive-verifier: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/2934

#include <iostream>
#include <string>
#include <vector>
#include <utility>
#include <iterator>
#include <cstdlib>
#line 1 "lib/ac-library/atcoder/string.hpp"



#include <algorithm>
#include <cassert>
#include <numeric>
#line 9 "lib/ac-library/atcoder/string.hpp"

namespace atcoder {

namespace internal {

std::vector<int> sa_naive(const std::vector<int>& s) {
    int n = int(s.size());
    std::vector<int> sa(n);
    std::iota(sa.begin(), sa.end(), 0);
    std::sort(sa.begin(), sa.end(), [&](int l, int r) {
        if (l == r) return false;
        while (l < n && r < n) {
            if (s[l] != s[r]) return s[l] < s[r];
            l++;
            r++;
        }
        return l == n;
    });
    return sa;
}

std::vector<int> sa_doubling(const std::vector<int>& s) {
    int n = int(s.size());
    std::vector<int> sa(n), rnk = s, tmp(n);
    std::iota(sa.begin(), sa.end(), 0);
    for (int k = 1; k < n; k *= 2) {
        auto cmp = [&](int x, int y) {
            if (rnk[x] != rnk[y]) return rnk[x] < rnk[y];
            int rx = x + k < n ? rnk[x + k] : -1;
            int ry = y + k < n ? rnk[y + k] : -1;
            return rx < ry;
        };
        std::sort(sa.begin(), sa.end(), cmp);
        tmp[sa[0]] = 0;
        for (int i = 1; i < n; i++) {
            tmp[sa[i]] = tmp[sa[i - 1]] + (cmp(sa[i - 1], sa[i]) ? 1 : 0);
        }
        std::swap(tmp, rnk);
    }
    return sa;
}

// SA-IS, linear-time suffix array construction
// Reference:
// G. Nong, S. Zhang, and W. H. Chan,
// Two Efficient Algorithms for Linear Time Suffix Array Construction
template <int THRESHOLD_NAIVE = 10, int THRESHOLD_DOUBLING = 40>
std::vector<int> sa_is(const std::vector<int>& s, int upper) {
    int n = int(s.size());
    if (n == 0) return {};
    if (n == 1) return {0};
    if (n == 2) {
        if (s[0] < s[1]) {
            return {0, 1};
        } else {
            return {1, 0};
        }
    }
    if (n < THRESHOLD_NAIVE) {
        return sa_naive(s);
    }
    if (n < THRESHOLD_DOUBLING) {
        return sa_doubling(s);
    }

    std::vector<int> sa(n);
    std::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]);
    }
    std::vector<int> sum_l(upper + 1), sum_s(upper + 1);
    for (int i = 0; i < n; i++) {
        if (!ls[i]) {
            sum_s[s[i]]++;
        } else {
            sum_l[s[i] + 1]++;
        }
    }
    for (int i = 0; i <= upper; i++) {
        sum_s[i] += sum_l[i];
        if (i < upper) sum_l[i + 1] += sum_s[i];
    }

    auto induce = [&](const std::vector<int>& lms) {
        std::fill(sa.begin(), sa.end(), -1);
        std::vector<int> buf(upper + 1);
        std::copy(sum_s.begin(), sum_s.end(), buf.begin());
        for (auto d : lms) {
            if (d == n) continue;
            sa[buf[s[d]]++] = d;
        }
        std::copy(sum_l.begin(), sum_l.end(), buf.begin());
        sa[buf[s[n - 1]]++] = n - 1;
        for (int i = 0; i < n; i++) {
            int v = sa[i];
            if (v >= 1 && !ls[v - 1]) {
                sa[buf[s[v - 1]]++] = v - 1;
            }
        }
        std::copy(sum_l.begin(), sum_l.end(), buf.begin());
        for (int i = n - 1; i >= 0; i--) {
            int v = sa[i];
            if (v >= 1 && ls[v - 1]) {
                sa[--buf[s[v - 1] + 1]] = v - 1;
            }
        }
    };

    std::vector<int> lms_map(n + 1, -1);
    int m = 0;
    for (int i = 1; i < n; i++) {
        if (!ls[i - 1] && ls[i]) {
            lms_map[i] = m++;
        }
    }
    std::vector<int> lms;
    lms.reserve(m);
    for (int i = 1; i < n; i++) {
        if (!ls[i - 1] && ls[i]) {
            lms.push_back(i);
        }
    }

    induce(lms);

    if (m) {
        std::vector<int> sorted_lms;
        sorted_lms.reserve(m);
        for (int v : sa) {
            if (lms_map[v] != -1) sorted_lms.push_back(v);
        }
        std::vector<int> rec_s(m);
        int rec_upper = 0;
        rec_s[lms_map[sorted_lms[0]]] = 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 = true;
            if (end_l - l != end_r - r) {
                same = false;
            } else {
                while (l < end_l) {
                    if (s[l] != s[r]) {
                        break;
                    }
                    l++;
                    r++;
                }
                if (l == n || s[l] != s[r]) same = false;
            }
            if (!same) rec_upper++;
            rec_s[lms_map[sorted_lms[i]]] = rec_upper;
        }

        auto rec_sa =
            sa_is<THRESHOLD_NAIVE, THRESHOLD_DOUBLING>(rec_s, rec_upper);

        for (int i = 0; i < m; i++) {
            sorted_lms[i] = lms[rec_sa[i]];
        }
        induce(sorted_lms);
    }
    return sa;
}

}  // namespace internal

std::vector<int> suffix_array(const std::vector<int>& s, int upper) {
    assert(0 <= upper);
    for (int d : s) {
        assert(0 <= d && d <= upper);
    }
    auto sa = internal::sa_is(s, upper);
    return sa;
}

template <class T> std::vector<int> suffix_array(const std::vector<T>& s) {
    int n = int(s.size());
    std::vector<int> idx(n);
    iota(idx.begin(), idx.end(), 0);
    sort(idx.begin(), idx.end(), [&](int l, int r) { return s[l] < s[r]; });
    std::vector<int> s2(n);
    int now = 0;
    for (int i = 0; i < n; i++) {
        if (i && s[idx[i - 1]] != s[idx[i]]) now++;
        s2[idx[i]] = now;
    }
    return internal::sa_is(s2, now);
}

std::vector<int> suffix_array(const std::string& s) {
    int n = int(s.size());
    std::vector<int> s2(n);
    for (int i = 0; i < n; i++) {
        s2[i] = s[i];
    }
    return internal::sa_is(s2, 255);
}

// Reference:
// T. Kasai, G. Lee, H. Arimura, S. Arikawa, and K. Park,
// Linear-Time Longest-Common-Prefix Computation in Suffix Arrays and Its
// Applications
template <class T>
std::vector<int> lcp_array(const std::vector<T>& s,
                           const std::vector<int>& sa) {
    int n = int(s.size());
    assert(n >= 1);
    std::vector<int> rnk(n);
    for (int i = 0; i < n; i++) {
        rnk[sa[i]] = i;
    }
    std::vector<int> lcp(n - 1);
    int h = 0;
    for (int i = 0; i < n; i++) {
        if (h > 0) h--;
        if (rnk[i] == 0) continue;
        int j = sa[rnk[i] - 1];
        for (; j + h < n && i + h < n; h++) {
            if (s[j + h] != s[i + h]) break;
        }
        lcp[rnk[i] - 1] = h;
    }
    return lcp;
}

std::vector<int> lcp_array(const std::string& s, const std::vector<int>& sa) {
    int n = int(s.size());
    std::vector<int> s2(n);
    for (int i = 0; i < n; i++) {
        s2[i] = s[i];
    }
    return lcp_array(s2, sa);
}

// Reference:
// D. Gusfield,
// Algorithms on Strings, Trees, and Sequences: Computer Science and
// Computational Biology
template <class T> std::vector<int> z_algorithm(const std::vector<T>& s) {
    int n = int(s.size());
    if (n == 0) return {};
    std::vector<int> z(n);
    z[0] = 0;
    for (int i = 1, j = 0; i < n; i++) {
        int& k = z[i];
        k = (j + z[j] <= i) ? 0 : std::min(j + z[j] - i, z[i - j]);
        while (i + k < n && s[k] == s[i + k]) k++;
        if (j + z[j] < i + z[i]) j = i;
    }
    z[0] = n;
    return z;
}

std::vector<int> z_algorithm(const std::string& s) {
    int n = int(s.size());
    std::vector<int> s2(n);
    for (int i = 0; i < n; i++) {
        s2[i] = s[i];
    }
    return z_algorithm(s2);
}

}  // namespace atcoder


#line 1 "tools/manacher.hpp"



#line 6 "tools/manacher.hpp"
#include <cstddef>
#line 1 "tools/mex.hpp"



#include <type_traits>
#line 10 "tools/mex.hpp"

namespace tools {

  template <typename InputIterator>
  ::std::decay_t<decltype(*::std::declval<InputIterator>())> mex(InputIterator begin, InputIterator end) {
    using T = ::std::decay_t<decltype(*::std::declval<InputIterator>())>;
    const ::std::vector<T> orig(begin, end);
    const ::std::size_t n = orig.size();

    assert(::std::all_of(orig.begin(), orig.end(), [](const auto& o) { return o >= 0; }));

    ::std::vector<bool> exists(n, false);
    for (const ::std::size_t o : orig) {
      if (o < n) {
        exists[o] = true;
      }
    }
    for (::std::size_t i = 0; i < n; ++i) {
      if (!exists[i]) {
        return i;
      }
    }
    return n;
  }
}


#line 10 "tools/manacher.hpp"

namespace tools {
  template <typename InputIterator, typename OutputIterator>
  void manacher(const InputIterator begin, const InputIterator end, const OutputIterator result) {
    using T = typename ::std::iterator_traits<InputIterator>::value_type;
    ::std::vector<T> S(begin, end);
    const auto N = S.size();
    {
      ::std::vector<T> new_S(2 * N + 1, ::tools::mex(S.begin(), S.end()));
      for (::std::size_t i = 0; i < N; ++i) {
        new_S[2 * i + 1] = S[i];
      }
      S = ::std::move(new_S);
    }

    ::std::vector<::std::size_t> R(S.size());
    {
      ::std::size_t i = 0;
      ::std::size_t j = 0;
      while (i < S.size()) {
        for (; i >= j && i + j < S.size() && S[i - j] == S[i + j]; ++j);
        R[i] = j;
        ::std::size_t k;
        for (k = 1; i >= k && k + R[i - k] < j; ++k) {
          R[i + k] = R[i - k];
        }
        i += k;
        j -= k;
      }
    }

    ::std::vector<::std::pair<::std::size_t, ::std::size_t>> new_R(S.size());
    for (::std::size_t i = 0; i <= N; ++i) {
      new_R[i * 2] = ::std::make_pair(i - (R[i * 2] - 1) / 2, i + (R[i * 2] - 1) / 2);
    }
    for (::std::size_t i = 0; i < N; ++i) {
      new_R[i * 2 + 1] = ::std::make_pair(i - (R[i * 2 + 1] / 2 - 1), i + R[i * 2 + 1] / 2);
    }
    ::std::move(new_R.begin(), new_R.end(), result);
  }
}


#line 11 "tests/manacher.test.cpp"

int main() {
  std::cin.tie(nullptr);
  std::ios_base::sync_with_stdio(false);

  int N;
  std::string T;
  std::cin >> N >> T;

  std::vector<std::pair<int, int>> R;
  tools::manacher(T.begin(), T.end(), std::back_inserter(R));
  const auto Z = atcoder::z_algorithm(T);

  std::cout << [&]() {
    for (int i = 1; i < N; ++i) {
      if (R[i * 2 + 1].first == 0 && [&]() {
        for (int j = 0; j < N; j += R[i * 2 + 1].second - R[i * 2 + 1].first - 1) {
          if (Z[j] < N - j) {
            return false;
          }
        }
        return true;
      }()) {
        return (R[i * 2 + 1].second - R[i * 2 + 1].first + 1) / 2;
      }
    }
    for (int i = 0; i < N; ++i) {
      if (R[i * 2 + 1].second == N) {
        return (N + R[i * 2 + 1].first + 1) / 2;
      }
    }
    std::exit(EXIT_FAILURE);
  }() << '\n';

  return 0;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	00_sample_01.in	AC	5 ms	4 MB
g++	00_sample_02.in	AC	4 ms	4 MB
g++	00_sample_03.in	AC	4 ms	4 MB
g++	10_random_small_00.in	AC	4 ms	4 MB
g++	11_random_large_00.in	AC	32 ms	61 MB
g++	11_random_large_01.in	AC	32 ms	57 MB
g++	12_random_max_00.in	AC	40 ms	72 MB
g++	12_random_max_01.in	AC	40 ms	72 MB
g++	20_roundtrip_small_00.in	AC	5 ms	4 MB
g++	21_roundtrip_large_00.in	AC	16 ms	27 MB
g++	21_roundtrip_large_01.in	AC	31 ms	59 MB
g++	22_roundtrip_max_00.in	AC	38 ms	72 MB
g++	22_roundtrip_max_01.in	AC	38 ms	72 MB
g++	30_large_ans_small_00.in	AC	5 ms	4 MB
g++	31_large_ans_large_00.in	AC	31 ms	59 MB
g++	31_large_ans_large_01.in	AC	36 ms	66 MB
g++	32_large_ans_max_00.in	AC	38 ms	72 MB
g++	32_large_ans_max_01.in	AC	38 ms	71 MB
g++	40_ABonly_small_00.in	AC	5 ms	4 MB
g++	41_ABonly_large_00.in	AC	19 ms	30 MB
g++	41_ABonly_large_01.in	AC	24 ms	37 MB
g++	42_ABonly_max_00.in	AC	40 ms	71 MB
g++	42_ABonly_max_01.in	AC	41 ms	71 MB
g++	99_challenge_01.in	AC	41 ms	72 MB
g++	99_challenge_02.in	AC	5 ms	4 MB
g++	99_challenge_03.in	AC	4 ms	4 MB