#884257 (C++23) No.2361 Many String Compare Queries

提出ソース
結果

問題	No.2361 Many String Compare Queries
ユーザー	👑 emthrm
提出日時	2023-06-23 23:04:03
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	1,020 ms / 2,500 ms
コード長	15,849 bytes
コンパイル時間	4,305 ms
コンパイル使用メモリ	285,732 KB
実行使用メモリ	43,700 KB
最終ジャッジ日時	2024-07-01 02:51:14
合計ジャッジ時間	11,961 ms
ジャッジサーバーID （参考情報）	judge3 / judge5
このコードへのチャレンジ
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 6,816 KB
testcase_01	AC	2 ms 6,944 KB
testcase_02	AC	2 ms 6,940 KB
testcase_03	AC	2 ms 6,944 KB
testcase_04	AC	2 ms 6,940 KB
testcase_05	AC	2 ms 6,940 KB
testcase_06	AC	2 ms 6,944 KB
testcase_07	AC	2 ms 6,940 KB
testcase_08	AC	1,020 ms 43,440 KB
testcase_09	AC	1,016 ms 43,440 KB
testcase_10	AC	1,020 ms 43,548 KB
testcase_11	AC	790 ms 43,692 KB
testcase_12	AC	813 ms 43,700 KB
testcase_13	AC	750 ms 43,240 KB
testcase_14	AC	698 ms 42,904 KB
testcase_15	AC	693 ms 42,380 KB
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ソースコード

raw source code
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 998244353;
// constexpr int MOD = 1000000007;
constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};
constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U>
inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U>
inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;

template <typename Band>
struct SparseTable {
  using BinOp = std::function<Band(Band, Band)>;

  SparseTable() = default;

  explicit SparseTable(const std::vector<Band>& a, const BinOp bin_op) {
    init(a, bin_op);
  }

  void init(const std::vector<Band>& a, const BinOp bin_op_) {
    bin_op = bin_op_;
    const int n = a.size();
    assert(n > 0);
    lg.assign(n + 1, 0);
    for (int i = 2; i <= n; ++i) {
      lg[i] = lg[i >> 1] + 1;
    }
    const int table_h = std::countr_zero(std::bit_floor(a.size())) + 1;
    data.assign(table_h, std::vector<Band>(n));
    std::copy(a.begin(), a.end(), data.front().begin());
    for (int i = 1; i < table_h; ++i) {
      for (int j = 0; j + (1 << i) <= n; ++j) {
        data[i][j] = bin_op(data[i - 1][j], data[i - 1][j + (1 << (i - 1))]);
      }
    }
  }

  Band query(const int left, const int right) const {
    assert(left < right);
    const int h = lg[right - left];
    return bin_op(data[h][left], data[h][right - (1 << h)]);
  }

 private:
  BinOp bin_op;
  std::vector<int> lg;
  std::vector<std::vector<Band>> data;
};

template <typename T = std::string>
struct SuffixArray {
  std::vector<int> sa, rank;

  template <typename U = char>
  explicit SuffixArray(const T& s_, const U sentinel = 0) : s(s_) {
    const int n = s.size();
    s.push_back(sentinel);
    sa.resize(n + 1);
    std::iota(sa.rbegin(), sa.rend(), 0);
    std::ranges::stable_sort(
        sa, {}, [this](const int index) -> int { return s[index]; });
    rank.resize(n + 1);
    for (int i = 0; i <= n; ++i) {
      rank[i] = s[i];
    }
    std::vector<int> tmp(n + 1), prev_sa(n + 1);
    for (int len = 1; len <= n; len <<= 1) {
      tmp[sa[0]] = 0;
      for (int i = 1; i <= n; ++i) {
        if (rank[sa[i - 1]] == rank[sa[i]] && sa[i - 1] + len <= n &&
            rank[sa[i - 1] + (len >> 1)] == rank[sa[i] + (len >> 1)]) {
          tmp[sa[i]] = tmp[sa[i - 1]];
        } else {
          tmp[sa[i]] = i;
        }
      }
      rank.swap(tmp);
      std::iota(tmp.begin(), tmp.end(), 0);
      std::copy(sa.begin(), sa.end(), prev_sa.begin());
      for (int i = 0; i <= n; ++i) {
        const int idx = prev_sa[i] - len;
        if (idx >= 0) sa[tmp[rank[idx]]++] = idx;
      }
    }
    for (int i = 0; i <= n; ++i) {
      rank[sa[i]] = i;
    }
  }

  std::vector<int> match(T* t) const {
    const int lb = lower_bound(t);
    ++t->back();
    const int ub = lower_bound(t);
    --t->back();
    std::vector<int> res(ub - lb);
    std::copy(sa.begin() + lb, sa.begin() + ub, res.begin());
    std::sort(res.begin(), res.end());
    return res;
  }

 private:
  T s;

  int lower_bound(const T* t) const {
    const int s_size = s.size(), t_size = t->size();
    int lb = 0, ub = s_size;
    while (ub - lb > 1) {
      const int mid = std::midpoint(lb, ub);
      int s_idx = sa[mid], t_idx = 0;
      bool finished = false;
      for (; s_idx < s_size && t_idx < t_size; ++s_idx, ++t_idx) {
        if (s[s_idx] != (*t)[t_idx]) {
          (s[s_idx] < (*t)[t_idx] ? lb : ub) = mid;
          finished = true;
          break;
        }
      }
      if (!finished) (s_idx == s_size && t_idx < t_size ? lb : ub) = mid;
    }
    return ub;
  }
};

template <typename T = std::string>
struct LongestCommonPrefix : SuffixArray<T> {
  std::vector<int> lcp_array;

  explicit LongestCommonPrefix(const T& s) : SuffixArray<T>(s) {
    const int n = s.size();
    lcp_array.resize(n);
    for (int i = 0, common = 0; i < n; ++i) {
      const int j = this->sa[this->rank[i] - 1];
      if (common > 0) --common;
      while (i + common < n && j + common < n &&
             s[i + common] == s[j + common]) {
        ++common;
      }
      lcp_array[this->rank[i] - 1] = common;
    }
    st.init(lcp_array, [](const int a, const int b) -> int {
      return std::min(a, b);
    });
  }

  int query(int i, int j) const {
    assert(i != j);
    i = this->rank[i];
    j = this->rank[j];
    if (i > j) std::swap(i, j);
    return st.query(i, j);
  }

 private:
  SparseTable<int> st;
};

template <typename T>
requires requires {
  typename T::Monoid;
  typename T::OperatorMonoid;
  {T::m_id()} -> std::same_as<typename T::Monoid>;
  {T::o_id()} -> std::same_as<typename T::OperatorMonoid>;
  {T::m_merge(std::declval<typename T::Monoid>(),
              std::declval<typename T::Monoid>())}
      -> std::same_as<typename T::Monoid>;
  {T::o_merge(std::declval<typename T::OperatorMonoid>(),
              std::declval<typename T::OperatorMonoid>())}
      -> std::same_as<typename T::OperatorMonoid>;
  {T::apply(std::declval<typename T::Monoid>(),
            std::declval<typename T::OperatorMonoid>())}
      -> std::same_as<typename T::Monoid>;
}
struct LazySegmentTree {
  using Monoid = typename T::Monoid;
  using OperatorMonoid = typename T::OperatorMonoid;

  explicit LazySegmentTree(const int n)
      : LazySegmentTree(std::vector<Monoid>(n, T::m_id())) {}

  explicit LazySegmentTree(const std::vector<Monoid>& a)
      : n(a.size()), height(std::countr_zero(std::bit_ceil(a.size()))),
        p2(1 << height) {
    lazy.assign(p2, T::o_id());
    data.assign(p2 << 1, T::m_id());
    std::copy(a.begin(), a.end(), data.begin() + p2);
    for (int i = p2 - 1; i > 0; --i) {
      data[i] = T::m_merge(data[i << 1], data[(i << 1) + 1]);
    }
  }

  void set(int idx, const Monoid val) {
    idx += p2;
    for (int i = height; i > 0; --i) {
      propagate(idx >> i);
    }
    data[idx] = val;
    for (int i = 1; i <= height; ++i) {
      const int current_idx = idx >> i;
      data[current_idx] =
          T::m_merge(data[current_idx << 1], data[(current_idx << 1) + 1]);
    }
  }

  void apply(int idx, const OperatorMonoid val) {
    idx += p2;
    for (int i = height; i > 0; --i) {
      propagate(idx >> i);
    }
    data[idx] = T::apply(data[idx], val);
    for (int i = 1; i <= height; ++i) {
      const int current_idx = idx >> i;
      data[current_idx] =
          T::m_merge(data[current_idx << 1], data[(current_idx << 1) + 1]);
    }
  }

  void apply(int left, int right, const OperatorMonoid val) {
    if (right <= left) [[unlikely]] return;
    left += p2;
    right += p2;
    const int ctz_left = std::countr_zero(static_cast<unsigned int>(left));
    for (int i = height; i > ctz_left; --i) {
      propagate(left >> i);
    }
    const int ctz_right = std::countr_zero(static_cast<unsigned int>(right));
    for (int i = height; i > ctz_right; --i) {
      propagate(right >> i);
    }
    for (int l = left, r = right; l < r; l >>= 1, r >>= 1) {
      if (l & 1) apply_sub(l++, val);
      if (r & 1) apply_sub(--r, val);
    }
    for (int i = left >> (ctz_left + 1); i > 0; i >>= 1) {
      data[i] = T::m_merge(data[i << 1], data[(i << 1) + 1]);
    }
    for (int i = right >> (ctz_right + 1); i > 0; i >>= 1) {
      data[i] = T::m_merge(data[i << 1], data[(i << 1) + 1]);
    }
  }

  Monoid get(int left, int right) {
    if (right <= left) [[unlikely]] return T::m_id();
    left += p2;
    right += p2;
    const int ctz_left = std::countr_zero(static_cast<unsigned int>(left));
    for (int i = height; i > ctz_left; --i) {
      propagate(left >> i);
    }
    const int ctz_right = std::countr_zero(static_cast<unsigned int>(right));
    for (int i = height; i > ctz_right; --i) {
      propagate(right >> i);
    }
    Monoid res_l = T::m_id(), res_r = T::m_id();
    for (; left < right; left >>= 1, right >>= 1) {
      if (left & 1) res_l = T::m_merge(res_l, data[left++]);
      if (right & 1) res_r = T::m_merge(data[--right], res_r);
    }
    return T::m_merge(res_l, res_r);
  }

  Monoid operator[](const int idx) {
    const int node = idx + p2;
    for (int i = height; i > 0; --i) {
      propagate(node >> i);
    }
    return data[node];
  }

  template <typename G>
  int find_right(int left, const G g) {
    if (left >= n) [[unlikely]] return n;
    left += p2;
    for (int i = height; i > 0; --i) {
      propagate(left >> i);
    }
    Monoid val = T::m_id();
    do {
      while (!(left & 1)) left >>= 1;
      Monoid nxt = T::m_merge(val, data[left]);
      if (!g(nxt)) {
        while (left < p2) {
          propagate(left);
          left <<= 1;
          nxt = T::m_merge(val, data[left]);
          if (g(nxt)) {
            val = nxt;
            ++left;
          }
        }
        return left - p2;
      }
      val = nxt;
      ++left;
    } while (!std::has_single_bit(static_cast<unsigned int>(left)));
    return n;
  }

  template <typename G>
  int find_left(int right, const G g) {
    if (right <= 0) [[unlikely]] return -1;
    right += p2;
    for (int i = height; i > 0; --i) {
      propagate((right - 1) >> i);
    }
    Monoid val = T::m_id();
    do {
      --right;
      while (right > 1 && (right & 1)) right >>= 1;
      Monoid nxt = T::m_merge(data[right], val);
      if (!g(nxt)) {
        while (right < p2) {
          propagate(right);
          right = (right << 1) + 1;
          nxt = T::m_merge(data[right], val);
          if (g(nxt)) {
            val = nxt;
            --right;
          }
        }
        return right - p2;
      }
      val = nxt;
    } while (!std::has_single_bit(static_cast<unsigned int>(right)));
    return -1;
  }

 private:
  const int n, height, p2;
  std::vector<Monoid> data;
  std::vector<OperatorMonoid> lazy;

  void apply_sub(const int idx, const OperatorMonoid& val) {
    data[idx] = T::apply(data[idx], val);
    if (idx < p2) lazy[idx] = T::o_merge(lazy[idx], val);
  }

  void propagate(const int idx) {
    // assert(1 <= idx && idx < p2);
    apply_sub(idx << 1, lazy[idx]);
    apply_sub((idx << 1) + 1, lazy[idx]);
    lazy[idx] = T::o_id();
  }
};

namespace monoid {

template <typename T>
struct RangeMinimumAndUpdateQuery {
  using Monoid = T;
  using OperatorMonoid = T;
  static constexpr Monoid m_id() { return std::numeric_limits<Monoid>::max(); }
  static constexpr OperatorMonoid o_id() {
    return std::numeric_limits<OperatorMonoid>::max();
  }
  static Monoid m_merge(const Monoid& a, const Monoid& b) {
    return std::min(a, b);
  }
  static OperatorMonoid o_merge(const OperatorMonoid& a,
                                const OperatorMonoid& b) {
    return b == o_id() ? a : b;
  }
  static Monoid apply(const Monoid& a, const OperatorMonoid& b) {
    return b == o_id() ? a : b;
  }
};

template <typename T>
struct RangeMaximumAndUpdateQuery {
  using Monoid = T;
  using OperatorMonoid = T;
  static constexpr Monoid m_id() {
    return std::numeric_limits<Monoid>::lowest();
  }
  static constexpr OperatorMonoid o_id() {
    return std::numeric_limits<OperatorMonoid>::lowest();
  }
  static Monoid m_merge(const Monoid& a, const Monoid& b) {
    return std::max(a, b);
  }
  static OperatorMonoid o_merge(const OperatorMonoid& a,
                                const OperatorMonoid& b) {
    return b == o_id() ? a : b;
  }
  static Monoid apply(const Monoid& a, const OperatorMonoid& b) {
    return b == o_id()? a : b;
  }
};

template <typename T, T Inf>
struct RangeMinimumAndAddQuery {
  using Monoid = T;
  using OperatorMonoid = T;
  static constexpr Monoid m_id() { return Inf; }
  static constexpr OperatorMonoid o_id() { return 0; }
  static Monoid m_merge(const Monoid& a, const Monoid& b) {
    return std::min(a, b);
  }
  static OperatorMonoid o_merge(const OperatorMonoid& a,
                                const OperatorMonoid& b) {
    return a + b;
  }
  static Monoid apply(const Monoid& a, const OperatorMonoid& b) {
    return a + b;
  }
};

template <typename T, T Inf>
struct RangeMaximumAndAddQuery {
  using Monoid = T;
  using OperatorMonoid = T;
  static constexpr Monoid m_id() { return -Inf; }
  static constexpr OperatorMonoid o_id() { return 0; }
  static Monoid m_merge(const Monoid& a, const Monoid& b) {
    return std::max(a, b);
  }
  static OperatorMonoid o_merge(const OperatorMonoid& a,
                                const OperatorMonoid& b) {
    return a + b;
  }
  static Monoid apply(const Monoid& a, const OperatorMonoid& b) {
    return a + b;
  }
};

template <typename T>
struct RangeSumAndUpdateQuery {
  using Monoid = struct { T sum; int len; };
  using OperatorMonoid = T;
  static std::vector<Monoid> init(const int n) {
    return std::vector<Monoid>(n, Monoid{0, 1});
  }
  static constexpr Monoid m_id() { return {0, 0}; }
  static constexpr OperatorMonoid o_id() {
    return std::numeric_limits<OperatorMonoid>::max();
  }
  static Monoid m_merge(const Monoid& a, const Monoid& b) {
    return Monoid{a.sum + b.sum, a.len + b.len};
  }
  static OperatorMonoid o_merge(const OperatorMonoid& a,
                                const OperatorMonoid& b) {
    return b == o_id() ? a : b;
  }
  static Monoid apply(const Monoid& a, const OperatorMonoid& b) {
    return Monoid{b == o_id() ? a.sum : b * a.len, a.len};
  }
};

template <typename T>
struct RangeSumAndAddQuery {
  using Monoid = struct { T sum; int len; };
  using OperatorMonoid = T;
  static std::vector<Monoid> init(const int n) {
    return std::vector<Monoid>(n, Monoid{0, 1});
  }
  static constexpr Monoid m_id() { return {0, 0}; }
  static constexpr OperatorMonoid o_id() { return 0; }
  static Monoid m_merge(const Monoid& a, const Monoid& b) {
    return Monoid{a.sum + b.sum, a.len + b.len};
  }
  static OperatorMonoid o_merge(const OperatorMonoid& a,
                                const OperatorMonoid& b) {
    return a + b;
  }
  static Monoid apply(const Monoid& a, const OperatorMonoid& b) {
    return Monoid{a.sum + b * a.len, a.len};
  }
};

}  // namespace monoid

int main() {
  int n, q; string s; cin >> n >> q >> s;
  LongestCommonPrefix lcp(s);
  vector<ll> sum(n + 1, 0);
  REP(i, n + 1) sum[i] = n - lcp.sa[i];
  REP(i, n) sum[i + 1] += sum[i];
  vector<vector<pair<int, int>>> queries(n + 1);
  vector<ll> ans(q, 0);
  REP(i, q) {
    int l, r; cin >> l >> r; --l; --r;
    int lb = 0, ub = lcp.rank[l];
    while (ub - lb > 1) {
      const int mid = midpoint(lb, ub);
      (lcp.query(lcp.sa[mid], l) >= r - l + 1 ? ub : lb) = mid;
    }
    ans[i] = ll{lcp.rank[l] - lb} * (r - l);
    if (lb > 0) ans[i] += sum[lb];
    queries[lcp.rank[l]].emplace_back(i, r - l);
  }
  LazySegmentTree<monoid::RangeSumAndUpdateQuery<ll>> seg(monoid::RangeSumAndUpdateQuery<ll>::init(n + 1));
  // REP(i, n) cout << lcp.lcp_array[i] << " \n"[i + 1 == n];
  for (int i = n - 1; i >= 0; --i) {
    int lb = i, ub = n;
    while (ub - lb > 1) {
      const int mid = midpoint(lb, ub);
      (seg[mid].sum > lcp.lcp_array[i] ? lb : ub) = mid;
    }
    seg.apply(i, lb + 1, lcp.lcp_array[i]);
    // REP(i, n) cout << seg[i].sum << " \n"[i + 1 == n];
    for (const auto& [id, mn] : queries[i]) {
      int lb = i - 1, ub = n;
      while (ub - lb > 1) {
        const int mid = midpoint(lb, ub);
        (seg[mid].sum > mn ? lb : ub) = mid;
      }
      ans[id] += (lb - i + 1LL) * mn;
      ans[id] += seg.get(lb + 1, n).sum;
    }
  }
  REP(i, q) cout << ans[i] << '\n';
  return 0;
}
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結果

テストケース

ソースコード
