データ構造/disjoint sparse table
(test/data_structure/disjoint_sparse_table.test.cpp)

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• Last update: 2023-02-25 01:48:23+09:00
• Problem: https://judge.yosupo.jp/problem/staticrmq

Depends on

• disjoint sparse table (include/emthrm/data_structure/disjoint_sparse_table.hpp)

Code

/*
 * @title データ構造/disjoint sparse table
 *
 * verification-helper: PROBLEM https://judge.yosupo.jp/problem/staticrmq
 */

#include <algorithm>
#include <iostream>
#include <vector>

#include "emthrm/data_structure/disjoint_sparse_table.hpp"

int main() {
  int n, q;
  std::cin >> n >> q;
  std::vector<int> a(n);
  for (int i = 0; i < n; ++i) {
    std::cin >> a[i];
  }
  emthrm::DisjointSparseTable disjoint_sparse_table(
      a, [](const int a, const int b) -> int { return std::min(a, b); });
  while (q--) {
    int l, r;
    std::cin >> l >> r;
    std::cout << disjoint_sparse_table.query(l, r) << '\n';
  }
  return 0;
}

#line 1 "test/data_structure/disjoint_sparse_table.test.cpp"
/*
 * @title データ構造/disjoint sparse table
 *
 * verification-helper: PROBLEM https://judge.yosupo.jp/problem/staticrmq
 */

#include <algorithm>
#include <iostream>
#include <vector>

#line 1 "include/emthrm/data_structure/disjoint_sparse_table.hpp"



#line 5 "include/emthrm/data_structure/disjoint_sparse_table.hpp"
#include <bit>
#include <cassert>
#line 8 "include/emthrm/data_structure/disjoint_sparse_table.hpp"

namespace emthrm {

template <typename Semigroup, typename BinOp>
struct DisjointSparseTable {
  explicit DisjointSparseTable(const std::vector<Semigroup>& a,
                               const BinOp bin_op = BinOp())
      : bin_op(bin_op) {
    const int table_h = std::max(std::countr_zero(std::bit_ceil(a.size())), 1);
    lg.assign(1 << table_h, 0);
    for (int i = 2; i < (1 << table_h); ++i) {
      lg[i] = lg[i >> 1] + 1;
    }
    const int n = a.size();
    data.assign(table_h, std::vector<Semigroup>(n));
    std::copy(a.begin(), a.end(), data.front().begin());
    for (int i = 1; i < table_h; ++i) {
      const int shift = 1 << i;
      for (int left = 0; left < n; left += shift << 1) {
        const int mid = std::min(left + shift, n);
        data[i][mid - 1] = a[mid - 1];
        for (int j = mid - 2; j >= left; --j) {
          data[i][j] = bin_op(a[j], data[i][j + 1]);
        }
        if (n <= mid) break;
        const int right = std::min(mid + shift, n);
        data[i][mid] = a[mid];
        for (int j = mid + 1; j < right; ++j) {
          data[i][j] = bin_op(data[i][j - 1], a[j]);
        }
      }
    }
  }

  Semigroup query(const int left, int right) const {
    assert(left < right);
    if (left == --right) return data[0][left];
    const int h = lg[left ^ right];
    return bin_op(data[h][left], data[h][right]);
  }

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

}  // namespace emthrm


#line 12 "test/data_structure/disjoint_sparse_table.test.cpp"

int main() {
  int n, q;
  std::cin >> n >> q;
  std::vector<int> a(n);
  for (int i = 0; i < n; ++i) {
    std::cin >> a[i];
  }
  emthrm::DisjointSparseTable disjoint_sparse_table(
      a, [](const int a, const int b) -> int { return std::min(a, b); });
  while (q--) {
    int l, r;
    std::cin >> l >> r;
    std::cout << disjoint_sparse_table.query(l, r) << '\n';
  }
  return 0;
}

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