test/verify/yosupo-number-of-substrings.test.cpp

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• Last update: 2022-09-11 00:53:50+09:00
• Problem: https://judge.yosupo.jp/problem/number_of_substrings

Depends on

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

Code

#define PROBLEM "https://judge.yosupo.jp/problem/number_of_substrings"

#include "../../template/template.hpp"

#include "../../string/lcp-array.hpp"

int main() {
  string S;
  cin >> S;
  int N = (int) S.size();
  SuffixArray sa(S);
  auto lcp = lcp_array(sa);
  cout << 1LL * N * (N + 1) / 2 - accumulate(begin(lcp), end(lcp), 0LL) << "\n";
}

#line 1 "test/verify/yosupo-number-of-substrings.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/number_of_substrings"

#line 1 "template/template.hpp"
#include<bits/stdc++.h>

using namespace std;

using int64 = long long;
const int mod = 1e9 + 7;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 >& p) {
  os << p.first << " " << p.second;
  return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
  is >> p.first >> p.second;
  return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for(int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for(auto &e : t) fill_v(e, v);
}

template< typename F >
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};
 
template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}
#line 4 "test/verify/yosupo-number-of-substrings.test.cpp"

#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 6 "test/verify/yosupo-number-of-substrings.test.cpp"

int main() {
  string S;
  cin >> S;
  int N = (int) S.size();
  SuffixArray sa(S);
  auto lcp = lcp_array(sa);
  cout << 1LL * N * (N + 1) / 2 - accumulate(begin(lcp), end(lcp), 0LL) << "\n";
}

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