C++ Library for Competitive Programming
#include "emthrm/data_structure/sparse_table.hpp"
$\langle O(N\log{N}), O(1) \rangle$
template <typename Band>
struct SparseTable;
Band
:帯である要素型名前 | 効果・戻り値 |
---|---|
SparseTable(); |
デフォルトコンストラクタ |
explicit SparseTable(const std::vector<Band>& a, const BinOp bin_op); |
$A$ に対して二項演算 $\mathrm{binOp}$ のオブジェクトを構築する。 |
void init(const std::vector<Band>& a, const BinOp bin_op_); |
$A$ によって初期化する。 |
Band query(const int left, const int right) const; |
$[\mathrm{left}, \mathrm{right})$ における演算を行った解 |
名前 | 効果・戻り値 |
---|---|
BinOp |
std::function<Band(Band, Band)> |
https://judge.yosupo.jp/submission/2719
#ifndef EMTHRM_DATA_STRUCTURE_SPARSE_TABLE_HPP_
#define EMTHRM_DATA_STRUCTURE_SPARSE_TABLE_HPP_
#include <algorithm>
#include <bit>
#include <cassert>
#include <functional>
#include <vector>
namespace emthrm {
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;
};
} // namespace emthrm
#endif // EMTHRM_DATA_STRUCTURE_SPARSE_TABLE_HPP_
#line 1 "include/emthrm/data_structure/sparse_table.hpp"
#include <algorithm>
#include <bit>
#include <cassert>
#include <functional>
#include <vector>
namespace emthrm {
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;
};
} // namespace emthrm