Longest Common Substring (string/longest-common-substring.hpp)

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• Last update: 2024-05-27 02:13:15+09:00
• Include: #include "string/longest-common-substring.hpp"

与えられた 2 つの文字列の最長共通部分文字列を求めます。

longest_common_substring

template< typename S >
tuple< int, int, int, int > longest_common_substring(const S& s, const S& t, bool compress = false)

$s$ と $t$ の最長共通部分列を $S[a, b)$、$T[c, d)$ とします。このとき、$\{a, b, c, d\}$ を返します。

S の値域が広い場合は、compress = true を与える必要があります。

計算量

$n = \max(|s|, |t|)$ とします。

• compress = false: $O(n)$
• compress = true: $O(n \log n)$

Depends on

• LCP Array (string/lcp-array.hpp)
• Suffix Array(接尾辞配列) (string/suffix-array.hpp)

Verified with

• test/verify/yosupo-longest-common-substring.test.cpp

Code

#include "lcp-array.hpp"

template <typename S>
tuple<int, int, int, int> longest_common_substring(const S& s, const S& t,
                                                   bool compress = false) {
  int n = (int)s.size(), m = (int)t.size();
  auto dummy =
      max(*max_element(s.begin(), s.end()), *max_element(t.begin(), t.end()));
  S st;
  st.reserve(n + 1 + m);
  for (auto& x : s) st.push_back(x);
  st.push_back(dummy + 1);
  for (auto& x : t) st.push_back(x);
  SuffixArray sa(st, compress);
  auto lcp = lcp_array(sa);
  tuple<int, int, int, int> res{0, 0, 0, 0};
  int ret = 0;
  for (int i = 0; i < (int)st.size() - 1; i++) {
    int x = sa[i], y = sa[i + 1];
    if (x > y) swap(x, y);
    if (x < n and n < y and ret < lcp[i + 1]) {
      y -= n + 1;
      ret = lcp[i + 1];
      res = {x, x + ret, y, y + ret};
    }
  }
  return res;
}

#line 1 "string/suffix-array.hpp"
/**
 * @brief Suffix Array(接尾辞配列)
 */
template <typename T>
struct SuffixArray : vector<int> {
 private:
  vector<int> sa_is(const vector<int> &s) const {
    const int n = (int)s.size();
    vector<int> ret(n);

    vector<int> is_s(n), is_lms(n);
    int m = 0;
    for (int i = n - 2; i >= 0; i--) {
      is_s[i] = (s[i] > s[i + 1]) or (s[i] == s[i + 1] and is_s[i + 1]);
      m += (is_lms[i + 1] = is_s[i] and not is_s[i + 1]);
    }

    auto induced_sort = [&](const vector<int> &lms) {
      int upper = *max_element(s.begin(), s.end());
      vector<int> l(upper + 2), r(upper + 2);
      for (auto &&v : s) {
        ++l[v + 1];
        ++r[v];
      }
      partial_sum(l.begin(), l.end(), l.begin());
      partial_sum(r.begin(), r.end(), r.begin());
      fill(ret.begin(), ret.end(), -1);
      for (int i = (int)lms.size() - 1; i >= 0; i--) {
        ret[--r[s[lms[i]]]] = lms[i];
      }
      for (auto &&v : ret) {
        if (v >= 1 and is_s[v - 1]) ret[l[s[v - 1]]++] = v - 1;
      }
      fill(r.begin(), r.end(), 0);
      for (auto &&v : s) ++r[v];
      partial_sum(r.begin(), r.end(), r.begin());
      for (int k = (int)ret.size() - 1, i = ret[k]; k >= 1; i = ret[--k]) {
        if (i >= 1 and not is_s[i - 1]) {
          ret[--r[s[i - 1]]] = i - 1;
        }
      }
    };

    vector<int> lms;
    lms.reserve(m);
    for (int i = 1; i < n; i++) {
      if (is_lms[i]) lms.push_back(i);
    }

    induced_sort(lms);

    vector<int> new_lms;
    new_lms.reserve(m);
    for (int i = 0; i < n; i++) {
      if (not is_s[ret[i]] and ret[i] > 0 and is_s[ret[i] - 1]) {
        new_lms.push_back(ret[i]);
      }
    }

    auto is_same = [&](int a, int b) {
      if (s[a++] != s[b++]) return false;
      for (;; ++a, ++b) {
        if (s[a] != s[b]) return false;
        if (is_lms[a] or is_lms[b]) return is_lms[a] and is_lms[b];
      }
    };

    int rank = 0;
    ret[n - 1] = 0;
    for (int i = 1; i < m; i++) {
      if (not is_same(new_lms[i - 1], new_lms[i])) ++rank;
      ret[new_lms[i]] = rank;
    }

    if (rank + 1 < m) {
      vector<int> new_s(m);
      for (int i = 0; i < m; i++) {
        new_s[i] = ret[lms[i]];
      }
      auto lms_sa = sa_is(new_s);
      for (int i = 0; i < m; i++) {
        new_lms[i] = lms[lms_sa[i]];
      }
    }

    induced_sort(new_lms);

    return ret;
  }

 public:
  T vs;

  explicit SuffixArray(const T &vs, bool compress = false) : vs(vs) {
    vector<int> new_vs(vs.size() + 1);
    if (compress) {
      T xs = vs;
      sort(xs.begin(), xs.end());
      xs.erase(unique(xs.begin(), xs.end()), xs.end());
      for (int i = 0; i < (int)vs.size(); i++) {
        new_vs[i] =
            std::lower_bound(xs.begin(), xs.end(), vs[i]) - xs.begin() + 1;
      }
    } else {
      auto d = *min_element(vs.begin(), vs.end());
      for (int i = 0; i < (int)vs.size(); i++) {
        new_vs[i] = vs[i] - d + 1;
      }
    }
    auto ret = sa_is(new_vs);
    assign(ret.begin(), ret.end());
  }

  void output() const {
    for (int i = 0; i < size(); i++) {
      cout << i << ":[" << (*this)[i] << "]";
      for (int j = (*this)[i]; j < (int)vs.size(); j++) cout << " " << vs[j];
      cout << "\n";
    }
  }

  bool lt_substr(const string &t, int si = 0, int ti = 0) {
    int sn = (int)vs.size(), tn = (int)t.size();
    while (si < sn && ti < tn) {
      if (vs[si] < t[ti]) return true;
      if (vs[si] > t[ti]) return false;
      ++si, ++ti;
    }
    return si >= sn && ti < tn;
  }

  // t <= s[i,N) なる最小の i を返す O(|t| log |s|)
  int lower_bound(const T &t) {
    int ng = 0, ok = (int)size();
    while (ok - ng > 1) {
      int mid = (ok + ng) / 2;
      if (lt_substr(t, at(mid)))
        ng = mid;
      else
        ok = mid;
    }
    return ok;
  }

  // O(|t| log |s|)
  pair<int, int> equal_range(T &t) {
    int low = lower_bound(t);
    int ng = low - 1, ok = (int)size();
    t.back()++;
    while (ok - ng > 1) {
      int mid = (ok + ng) / 2;
      if (lt_substr(t, at(mid)))
        ng = mid;
      else
        ok = mid;
    }
    t.back()--;
    return {low, ok};
  }
};

template <>
void SuffixArray<string>::output() const {
  for (int i = 0; i < (int)size(); i++) {
    cout << i << ":[" << (*this)[i] << "] " << vs.substr((*this)[i]) << "\n";
  }
}
#line 2 "string/lcp-array.hpp"

/**
 * @brief LCP Array
 */
template <typename T>
vector<int> lcp_array(const SuffixArray<T> &sa) {
  int n = (int)sa.size() - 1;
  vector<int> lcp(n + 1), rank(n + 1);
  for (int i = 0; i <= n; i++) {
    rank[sa[i]] = i;
  }
  int h = 0;
  for (int i = 0; i <= n; i++) {
    if (rank[i] < n) {
      int j = sa[rank[i] + 1];
      for (; j + h < n && i + h < n; h++) {
        if (sa.vs[j + h] != sa.vs[i + h]) break;
      }
      lcp[rank[i] + 1] = h;
      if (h > 0) h--;
    }
  }
  return lcp;
}
#line 2 "string/longest-common-substring.hpp"

template <typename S>
tuple<int, int, int, int> longest_common_substring(const S& s, const S& t,
                                                   bool compress = false) {
  int n = (int)s.size(), m = (int)t.size();
  auto dummy =
      max(*max_element(s.begin(), s.end()), *max_element(t.begin(), t.end()));
  S st;
  st.reserve(n + 1 + m);
  for (auto& x : s) st.push_back(x);
  st.push_back(dummy + 1);
  for (auto& x : t) st.push_back(x);
  SuffixArray sa(st, compress);
  auto lcp = lcp_array(sa);
  tuple<int, int, int, int> res{0, 0, 0, 0};
  int ret = 0;
  for (int i = 0; i < (int)st.size() - 1; i++) {
    int x = sa[i], y = sa[i + 1];
    if (x > y) swap(x, y);
    if (x < n and n < y and ret < lcp[i + 1]) {
      y -= n + 1;
      ret = lcp[i + 1];
      res = {x, x + ret, y, y + ret};
    }
  }
  return res;
}

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