Longest common substring (tools/longest_common_substring.hpp)

• View this file on GitHub
• View document part on GitHub
• Last update: 2025-01-25 08:45:50+09:00
• Include: #include "tools/longest_common_substring.hpp"

template <typename InputIterator>
std::tuple<std::size_t, std::size_t, std::size_t, std::size_t> longest_common_substring(InputIterator S_begin, InputIterator S_end, InputIterator T_begin, InputIterator T_end);

It returns $(a, b, c, d)$ when a longest common continuous subsequence of $S$ and $T$ can be taken as $(S_a, \ldots, S_{b - 1})$ and $(T_c, \ldots, T_{d - 1})$. If the longest common continuous subsequence is empty, it returns $(0, 0, 0, 0)$.

Constraints

• S_begin $\leq$ S_end
• T_begin $\leq$ T_end
• std::decay_t<decltype(*std::declval<InputIterator>())> is char, int, unsigned int, long long or unsigned long long.

Time Complexity

• (std::decay_t<decltype(*std::declval<InputIterator>())> is char): $O(|S| + |T|)$
• (otherwise): $O((|S| + |T|) \log (|S| + |T|))$

License

• CC0

Author

• anqooqie

Depends on

• chmax function (tools/chmax.hpp)
• Minimum excluded value (tools/mex.hpp)

Verified with

• tests/longest_common_substring.test.cpp

Code

#ifndef TOOLS_LONGEST_COMMON_SUBSTRING_HPP
#define TOOLS_LONGEST_COMMON_SUBSTRING_HPP

#include <tuple>
#include <cstddef>
#include <type_traits>
#include <string>
#include <vector>
#include <algorithm>
#include <iterator>
#include "atcoder/string.hpp"
#include "tools/mex.hpp"
#include "tools/chmax.hpp"

namespace tools {
  template <typename InputIterator>
  ::std::tuple<::std::size_t, ::std::size_t, ::std::size_t, ::std::size_t> longest_common_substring(const InputIterator S_begin, const InputIterator S_end, const InputIterator T_begin, const InputIterator T_end) {
    using Z = ::std::decay_t<decltype(*::std::declval<InputIterator>())>;
    using Container = ::std::conditional_t<::std::is_same_v<Z, char>, ::std::string, ::std::vector<Z>>;

    Container ST(S_begin, S_end);
    const int N = ST.size();
    ::std::copy(T_begin, T_end, ::std::back_inserter(ST));
    const int M = ST.size() - N;

    ST.push_back(::tools::mex(ST.begin(), ST.end()));
    ::std::rotate(::std::next(ST.begin(), N), ::std::prev(ST.end()), ST.end());

    const auto sa = ::atcoder::suffix_array(ST);
    const auto lcpa = ::atcoder::lcp_array(ST, sa);

    int a = 0;
    int c = 0;
    int l = 0;
    const auto is_in_S = [&](const int i) { return i < N; };
    const auto is_in_T = [&](const int i) { return N + 1 <= i; };

    for (int i = 1; i < N + M + 1; ++i) {
      if (is_in_S(sa[i]) && is_in_T(sa[i - 1])) {
        if (::tools::chmax(l, lcpa[i - 1])) {
          a = sa[i];
          c = sa[i - 1] - (N + 1);
        }
      } else if (is_in_T(sa[i]) && is_in_S(sa[i - 1])) {
        if (::tools::chmax(l, lcpa[i - 1])) {
          a = sa[i - 1];
          c = sa[i] - (N + 1);
        }
      }
    }

    return ::std::make_tuple(a, a + l, c, c + l);
  }
}

#endif

#line 1 "tools/longest_common_substring.hpp"



#include <tuple>
#include <cstddef>
#include <type_traits>
#include <string>
#include <vector>
#include <algorithm>
#include <iterator>
#line 1 "lib/ac-library/atcoder/string.hpp"



#line 5 "lib/ac-library/atcoder/string.hpp"
#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/mex.hpp"



#line 5 "tools/mex.hpp"
#include <utility>
#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 1 "tools/chmax.hpp"



#line 6 "tools/chmax.hpp"

namespace tools {

  template <typename M, typename N>
  bool chmax(M& lhs, const N& rhs) {
    bool updated;
    if constexpr (::std::is_integral_v<M> && ::std::is_integral_v<N>) {
      updated = ::std::cmp_less(lhs, rhs);
    } else {
      updated = lhs < rhs;
    }
    if (updated) lhs = rhs;
    return updated;
  }
}


#line 14 "tools/longest_common_substring.hpp"

namespace tools {
  template <typename InputIterator>
  ::std::tuple<::std::size_t, ::std::size_t, ::std::size_t, ::std::size_t> longest_common_substring(const InputIterator S_begin, const InputIterator S_end, const InputIterator T_begin, const InputIterator T_end) {
    using Z = ::std::decay_t<decltype(*::std::declval<InputIterator>())>;
    using Container = ::std::conditional_t<::std::is_same_v<Z, char>, ::std::string, ::std::vector<Z>>;

    Container ST(S_begin, S_end);
    const int N = ST.size();
    ::std::copy(T_begin, T_end, ::std::back_inserter(ST));
    const int M = ST.size() - N;

    ST.push_back(::tools::mex(ST.begin(), ST.end()));
    ::std::rotate(::std::next(ST.begin(), N), ::std::prev(ST.end()), ST.end());

    const auto sa = ::atcoder::suffix_array(ST);
    const auto lcpa = ::atcoder::lcp_array(ST, sa);

    int a = 0;
    int c = 0;
    int l = 0;
    const auto is_in_S = [&](const int i) { return i < N; };
    const auto is_in_T = [&](const int i) { return N + 1 <= i; };

    for (int i = 1; i < N + M + 1; ++i) {
      if (is_in_S(sa[i]) && is_in_T(sa[i - 1])) {
        if (::tools::chmax(l, lcpa[i - 1])) {
          a = sa[i];
          c = sa[i - 1] - (N + 1);
        }
      } else if (is_in_T(sa[i]) && is_in_S(sa[i - 1])) {
        if (::tools::chmax(l, lcpa[i - 1])) {
          a = sa[i - 1];
          c = sa[i] - (N + 1);
        }
      }
    }

    return ::std::make_tuple(a, a + l, c, c + l);
  }
}

Back to top page