Longest Common Substring
(string/LongestCommonSubstring.hpp)

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• Last update: 2025-12-17 00:38:44+09:00
• Include: #include "string/LongestCommonSubstring.hpp"

概要

todo

計算量

todo

Depends on

• Monotonic Queue (Min Queue) (data-structure/others/MonotonicMinQueue.hpp)
• LCP Array (string/LCPArray.hpp)
• Suffix Array (string/SuffixArray.hpp)

Verified with

• verify/LibraryChecker/string/LongestCommonSubstring.test.cpp

Code

#include "../data-structure/others/MonotonicMinQueue.hpp"
#include "LCPArray.hpp"
vector<pair<int, int>> longest_common_substring(const vector<string>& v) {
  int siz = int(v.size());
  if (siz < 2) return {};
  string concat = "";
  for (int i = 0; i < siz; i++) {
    concat += v[i];
    if (i + 1 != siz) concat += '$';
  }
  MonotonicMinQueue<int> que;
  vector<int> sa = suffixArray(concat);
  vector<int> lcp = LCPArray(concat, sa);
  int concat_n = int(concat.size());
  int lcs_len = 0;
  int best_l = -1, best_r = -1;
  if (siz == 2) {
    int cnt_s1 = 0, cnt_s2 = 0;
    int l = 0, r = 0;
    int s1_siz = v.front().size();
    while (1) {
      while (r < concat_n and (cnt_s1 == 0 or cnt_s2 == 0)) {
        if (sa[r] < s1_siz) {
          cnt_s1++;
        } else if (sa[r] > s1_siz) {
          cnt_s2++;
        }
        if (r > 0) que.push(lcp[r - 1]);
        r++;
      }
      while (l < concat_n and (cnt_s1 > 1 or cnt_s2 > 1)) {
        if (sa[l] < s1_siz) {
          if (cnt_s1 == 1) break;
          cnt_s1--;
        } else if (sa[l] > s1_siz) {
          if (cnt_s2 == 1) break;
          cnt_s2--;
        }
        l++;
        if (!que.empty()) que.pop();
      }

      if (cnt_s1 >= 1 and cnt_s2 >= 1 and !que.empty()) {
        if (lcs_len < que.minimum()) {
          lcs_len = que.minimum();
          best_l = l;
          best_r = r;
        }
      }

      if (r == concat_n) break;
      if (sa[l] < s1_siz) {
        cnt_s1--;
      } else if (sa[l] > s1_siz) {
        cnt_s2--;
      }
      l++;
      if (!que.empty()) que.pop();
    }

    vector<pair<int, int>> res(2, {0, 0});
    if (best_l == -1) return res;
    for (int i = best_l; i < best_r; i++) {
      if (sa[i] < s1_siz) {
        res[0] = {sa[i], sa[i] + lcs_len};
      } else if (sa[i] > s1_siz) {
        res[1] = {sa[i] - s1_siz - 1, sa[i] - s1_siz - 1 + lcs_len};
      }
    }
    return res;
  } else {
    vector<pair<int, int>> res(2, {0, 0});
    // todo
    return res;
  }
}

#line 1 "data-structure/others/MonotonicMinQueue.hpp"
template <class T>
class MonotonicMinQueue {
 private:
  queue<T> que;
  deque<T> deq;

 public:
  void push(const T& x) {
    que.push(x);
    while (deq.size() > 0 and deq.back() > x) deq.pop_back();
    deq.push_back(x);
  }

  void pop() {
    if (que.front() == deq.front()) deq.pop_front();
    que.pop();
  }

  const T& front() const {
    return que.front();
  }

  bool empty() const {
    return que.empty();
  }

  const T& minimum() const {
    return deq.front();
  }
};
#line 2 "string/SuffixArray.hpp"

#define tget(i) (((t)[(i) >> 3] >> (7 - ((i) & 7))) & 1)

#define tset(i, b)                                    \
    do {                                              \
        if (b)                                        \
            (t)[(i) >> 3] |= (1 << (7 - ((i) & 7)));  \
        else                                          \
            (t)[(i) >> 3] &= ~(1 << (7 - ((i) & 7))); \
    } while (0)

#define chr(i) (cs == sizeof(int) ? ((int *)s)[i] : ((unsigned char *)s)[i])
#define isLMS(i) (i > 0 and tget(i) and !tget(i - 1))

void getBuckets(unsigned char *s, int *bkt, int n, int K, int cs, bool end) {
    int sum = 0;
    for (int i = 0; i <= K; i++) {
        bkt[i] = 0;
    }
    for (int i = 0; i < n; i++) {
        bkt[chr(i)]++;
    }
    for (int i = 0; i <= K; i++) {
        sum += bkt[i];
        bkt[i] = end ? sum : sum - bkt[i];
    }
}

void induceSAl(unsigned char *t, int *SA, unsigned char *s, int *bkt, int n, int K, int cs, bool end) {
    getBuckets(s, bkt, n, K, cs, end);
    for (int i = 0; i < n; i++) {
        int j = SA[i] - 1;
        if (j >= 0 and !tget(j)) {
            SA[bkt[chr(j)]++] = j;
        }
    }
}

void induceSAs(unsigned char *t, int *SA, unsigned char *s, int *bkt, int n, int K, int cs, bool end) {
    getBuckets(s, bkt, n, K, cs, end);
    for (int i = n - 1; i >= 0; i--) {
        int j = SA[i] - 1;
        if (j >= 0 and tget(j)) {
            SA[--bkt[chr(j)]] = j;
        }
    }
}

void SA_IS(unsigned char *s, int *SA, int n, int K, int cs) {
    unsigned char *t = (unsigned char *)malloc(n / 8 + 1);
    tset(n - 2, 0);
    tset(n - 1, 1);
    for (int i = n - 3; i >= 0; i--) {
        tset(i, (chr(i) < chr(i + 1) or (chr(i) == chr(i + 1) and tget(i + 1) == 1)) ? 1 : 0);
    }

    int *bkt = (int *)malloc(sizeof(int) * (K + 1));
    getBuckets(s, bkt, n, K, cs, true);
    for (int i = 0; i < n; i++) {
        SA[i] = -1;
    }
    for (int i = 1; i < n; i++) {
        if (isLMS(i)) {
            SA[--bkt[chr(i)]] = i;
        }
    }
    induceSAl(t, SA, s, bkt, n, K, cs, false);
    induceSAs(t, SA, s, bkt, n, K, cs, true);
    free(bkt);

    int n1 = 0;
    for (int i = 0; i < n; i++) {
        if (isLMS(SA[i])) {
            SA[n1++] = SA[i];
        }
    }

    for (int i = n1; i < n; i++) {
        SA[i] = -1;
    }
    int name = 0;
    int prev = -1;
    for (int i = 0; i < n1; i++) {
        int pos = SA[i];
        bool diff = false;
        for (int d = 0; d < n; d++) {
            if (prev == -1 or chr(pos + d) != chr(prev + d) or tget(pos + d) != tget(prev + d)) {
                diff = true;
                break;
            } else if (d > 0 and (isLMS(pos + d) or isLMS(prev + d))) {
                break;
            }
        }
        if (diff) {
            name++;
            prev = pos;
        }
        pos = (pos % 2 == 0) ? pos / 2 : (pos - 1) / 2;
        SA[n1 + pos] = name - 1;
    }
    for (int i = n - 1, j = n - 1; i >= n1; i--) {
        if (SA[i] >= 0) {
            SA[j--] = SA[i];
        }
    }

    int *SA1 = SA;
    int *s1 = SA + n - n1;
    if (name < n1) {
        SA_IS((unsigned char *)s1, SA1, n1, name - 1, sizeof(int));
    } else {
        for (int i = 0; i < n1; i++) {
            SA1[s1[i]] = i;
        }
    }
    bkt = (int *)malloc(sizeof(int) * (K + 1));
    getBuckets(s, bkt, n, K, cs, true);
    for (int i = 1, j = 0; i < n; i++) {
        if (isLMS(i)) {
            s1[j++] = i;
        }
    }
    for (int i = 0; i < n1; i++) {
        SA1[i] = s1[SA1[i]];
    }
    for (int i = n1; i < n; i++) {
        SA[i] = -1;
    }
    for (int i = n1 - 1; i >= 0; i--) {
        int j = SA[i];
        SA[i] = -1;
        SA[--bkt[chr(j)]] = j;
    }
    induceSAl(t, SA, s, bkt, n, K, cs, false);
    induceSAs(t, SA, s, bkt, n, K, cs, true);
    free(bkt);
    free(t);
}

vector<int> suffixArray(string &str) {
    int n = str.size() + 1;
    int *sa = (int *)malloc(sizeof(int) * n);
    unsigned char *s = (unsigned char *)malloc(sizeof(unsigned char) * (n + 2));
    int k = 256;
    int cs = sizeof(unsigned char);
    for (int i = 0; i < str.size(); i++) {
        s[i] = str[i];
    }
    s[int(str.size())] = 0;
    SA_IS((unsigned char *)(s), sa, n, k, cs);
    vector<int> res(n - 1);
    for (int i = 0; i < n - 1; i++) {
        res[i] = sa[i + 1];
    }
    free(sa);
    free(s);
    return res;
}
#line 2 "string/LCPArray.hpp"
vector<int> LCPArray(const string& s, const vector<int>& sa) {
  int n = int(s.size());
  vector<int> rank(n);
  for (int i = 0; i < n; i++) rank[sa[i]] = i;
  vector<int> lcp(n - 1);
  int h = 0;
  for (int i = 0; i < n; i++) {
    if (h > 0) h--;
    if (rank[i] == 0) continue;
    int j = sa[rank[i] - 1];
    for (; j + h < n and i + h < n; h++) {
      if (s[j + h] != s[i + h]) break;
    }
    lcp[rank[i] - 1] = h;
  }
  return lcp;
}
#line 3 "string/LongestCommonSubstring.hpp"
vector<pair<int, int>> longest_common_substring(const vector<string>& v) {
  int siz = int(v.size());
  if (siz < 2) return {};
  string concat = "";
  for (int i = 0; i < siz; i++) {
    concat += v[i];
    if (i + 1 != siz) concat += '$';
  }
  MonotonicMinQueue<int> que;
  vector<int> sa = suffixArray(concat);
  vector<int> lcp = LCPArray(concat, sa);
  int concat_n = int(concat.size());
  int lcs_len = 0;
  int best_l = -1, best_r = -1;
  if (siz == 2) {
    int cnt_s1 = 0, cnt_s2 = 0;
    int l = 0, r = 0;
    int s1_siz = v.front().size();
    while (1) {
      while (r < concat_n and (cnt_s1 == 0 or cnt_s2 == 0)) {
        if (sa[r] < s1_siz) {
          cnt_s1++;
        } else if (sa[r] > s1_siz) {
          cnt_s2++;
        }
        if (r > 0) que.push(lcp[r - 1]);
        r++;
      }
      while (l < concat_n and (cnt_s1 > 1 or cnt_s2 > 1)) {
        if (sa[l] < s1_siz) {
          if (cnt_s1 == 1) break;
          cnt_s1--;
        } else if (sa[l] > s1_siz) {
          if (cnt_s2 == 1) break;
          cnt_s2--;
        }
        l++;
        if (!que.empty()) que.pop();
      }

      if (cnt_s1 >= 1 and cnt_s2 >= 1 and !que.empty()) {
        if (lcs_len < que.minimum()) {
          lcs_len = que.minimum();
          best_l = l;
          best_r = r;
        }
      }

      if (r == concat_n) break;
      if (sa[l] < s1_siz) {
        cnt_s1--;
      } else if (sa[l] > s1_siz) {
        cnt_s2--;
      }
      l++;
      if (!que.empty()) que.pop();
    }

    vector<pair<int, int>> res(2, {0, 0});
    if (best_l == -1) return res;
    for (int i = best_l; i < best_r; i++) {
      if (sa[i] < s1_siz) {
        res[0] = {sa[i], sa[i] + lcs_len};
      } else if (sa[i] > s1_siz) {
        res[1] = {sa[i] - s1_siz - 1, sa[i] - s1_siz - 1 + lcs_len};
      }
    }
    return res;
  } else {
    vector<pair<int, int>> res(2, {0, 0});
    // todo
    return res;
  }
}

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