Disjoint-Sparse-Table (structure/others/disjoint-sparse-table.hpp)

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

概要

更新がない場合の半群に対する区間クエリを, 前計算 $O(n \log n)$, クエリ $O(1)$ で処理する.

使い方

• DisjointSparseTable(v, f): 配列 v で初期化する. f は半群をマージする二項演算である.
• fold(l, r): 区間 $[l, r)$ を演算した結果を返す.

計算量

• DisjointSparseTable(v, f): $O(N \log N)$
• fold(l, r): $O(1)$

Verified with

• test/verify/yosupo-staticrmq-2.test.cpp

Code

/**
 * @brief Disjoint-Sparse-Table
 * 
 */
template< typename Semigroup, typename F >
struct DisjointSparseTable {
  const F f;
  vector< vector< Semigroup > > st;
  vector< int > lookup;

  DisjointSparseTable(const vector< Semigroup > &v, const F &f) : f(f) {
    int b = 0;
    while((1 << b) <= v.size()) ++b;
    st.resize(b, vector< Semigroup >(v.size(), Semigroup()));
    for(int i = 0; i < v.size(); i++) st[0][i] = v[i];
    for(int i = 1; i < b; i++) {
      int shift = 1 << i;
      for(int j = 0; j < v.size(); j += shift << 1) {
        int t = min(j + shift, (int) v.size());
        st[i][t - 1] = v[t - 1];
        for(int k = t - 2; k >= j; k--) st[i][k] = f(v[k], st[i][k + 1]);
        if(v.size() <= t) break;
        st[i][t] = v[t];
        int r = min(t + shift, (int) v.size());
        for(int k = t + 1; k < r; k++) st[i][k] = f(st[i][k - 1], v[k]);
      }
    }
    lookup.resize(1 << b);
    for(int i = 2; i < lookup.size(); i++) {
      lookup[i] = lookup[i >> 1] + 1;
    }
  }

  Semigroup fold(int l, int r) {
    if(l >= --r) return st[0][l];
    int p = lookup[l ^ r];
    return f(st[p][l], st[p][r]);
  }
};

template< typename SemiGroup, typename F >
DisjointSparseTable< SemiGroup, F > get_disjoint_sparse_table(const vector< SemiGroup >& v, const F& f) {
  return {v, f};
}

#line 1 "structure/others/disjoint-sparse-table.hpp"
/**
 * @brief Disjoint-Sparse-Table
 * 
 */
template< typename Semigroup, typename F >
struct DisjointSparseTable {
  const F f;
  vector< vector< Semigroup > > st;
  vector< int > lookup;

  DisjointSparseTable(const vector< Semigroup > &v, const F &f) : f(f) {
    int b = 0;
    while((1 << b) <= v.size()) ++b;
    st.resize(b, vector< Semigroup >(v.size(), Semigroup()));
    for(int i = 0; i < v.size(); i++) st[0][i] = v[i];
    for(int i = 1; i < b; i++) {
      int shift = 1 << i;
      for(int j = 0; j < v.size(); j += shift << 1) {
        int t = min(j + shift, (int) v.size());
        st[i][t - 1] = v[t - 1];
        for(int k = t - 2; k >= j; k--) st[i][k] = f(v[k], st[i][k + 1]);
        if(v.size() <= t) break;
        st[i][t] = v[t];
        int r = min(t + shift, (int) v.size());
        for(int k = t + 1; k < r; k++) st[i][k] = f(st[i][k - 1], v[k]);
      }
    }
    lookup.resize(1 << b);
    for(int i = 2; i < lookup.size(); i++) {
      lookup[i] = lookup[i >> 1] + 1;
    }
  }

  Semigroup fold(int l, int r) {
    if(l >= --r) return st[0][l];
    int p = lookup[l ^ r];
    return f(st[p][l], st[p][r]);
  }
};

template< typename SemiGroup, typename F >
DisjointSparseTable< SemiGroup, F > get_disjoint_sparse_table(const vector< SemiGroup >& v, const F& f) {
  return {v, f};
}

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