Sparse-Table(スパーステーブル) (structure/others/sparse-table.hpp)

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• Last update: 2024-04-24 02:34:04+09:00
• Include: #include "structure/others/sparse-table.hpp"

概要

冪等半群に対する区間クエリを, 前計算 $\Theta (n \log n)$, クエリ $\Theta (1)$ で処理する.

• SparseTable(v, f): 配列 v, 演算 $f$ で初期化する.
• fold(l, r): 区間 $[l, r)$ の演算結果を返す.

計算量

• SparseTable(v): $\Theta (N \log N)$
• fold(l, r): $\Theta (1)$

Required by

• PMORMQ-Lowest-Common-Ancestor(最小共通祖先) (graph/tree/pmormq-lowest-common-ancestor.hpp)
• RMQ-Lowest-Common-Ancestor(最小共通祖先) (graph/tree/rmq-lowest-common-ancestor.hpp)
• Plus-Minus-One-RMQ (structure/others/plus-minus-one-rmq.hpp)

Verified with

• test/verify/aoj-grl-5-c-3.test.cpp
• test/verify/aoj-grl-5-c-4.test.cpp
• test/verify/yosupo-lca-2.test.cpp
• test/verify/yosupo-lca.test.cpp
• test/verify/yosupo-staticrmq-4.test.cpp
• test/verify/yosupo-staticrmq.test.cpp

Code

/**
 * @brief Sparse-Table(スパーステーブル)
 * 
 */
template< typename T, typename F >
struct SparseTable {
  F f;
  vector< vector< T > > st;
  vector< int > lookup;

  SparseTable() = default;

  explicit SparseTable(const vector< T > &v, const F &f) : f(f) {
    const int n = (int) v.size();
    const int b = 32 - __builtin_clz(n);
    st.assign(b, vector< T >(n));
    for(int i = 0; i < v.size(); i++) {
      st[0][i] = v[i];
    }
    for(int i = 1; i < b; i++) {
      for(int j = 0; j + (1 << i) <= n; j++) {
        st[i][j] = f(st[i - 1][j], st[i - 1][j + (1 << (i - 1))]);
      }
    }
    lookup.resize(v.size() + 1);
    for(int i = 2; i < lookup.size(); i++) {
      lookup[i] = lookup[i >> 1] + 1;
    }
  }

  inline T fold(int l, int r) const {
    int b = lookup[r - l];
    return f(st[b][l], st[b][r - (1 << b)]);
  }
};

template< typename T, typename F >
SparseTable< T, F > get_sparse_table(const vector< T > &v, const F &f) {
  return SparseTable< T, F >(v, f);
}

#line 1 "structure/others/sparse-table.hpp"
/**
 * @brief Sparse-Table(スパーステーブル)
 * 
 */
template< typename T, typename F >
struct SparseTable {
  F f;
  vector< vector< T > > st;
  vector< int > lookup;

  SparseTable() = default;

  explicit SparseTable(const vector< T > &v, const F &f) : f(f) {
    const int n = (int) v.size();
    const int b = 32 - __builtin_clz(n);
    st.assign(b, vector< T >(n));
    for(int i = 0; i < v.size(); i++) {
      st[0][i] = v[i];
    }
    for(int i = 1; i < b; i++) {
      for(int j = 0; j + (1 << i) <= n; j++) {
        st[i][j] = f(st[i - 1][j], st[i - 1][j + (1 << (i - 1))]);
      }
    }
    lookup.resize(v.size() + 1);
    for(int i = 2; i < lookup.size(); i++) {
      lookup[i] = lookup[i >> 1] + 1;
    }
  }

  inline T fold(int l, int r) const {
    int b = lookup[r - l];
    return f(st[b][l], st[b][r - (1 << b)]);
  }
};

template< typename T, typename F >
SparseTable< T, F > get_sparse_table(const vector< T > &v, const F &f) {
  return SparseTable< T, F >(v, f);
}

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