test/yosupo/static_rmq-sparse_table.test.cpp

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• Last update: 2024-08-04 01:08:37+09:00
• Problem: https://judge.yosupo.jp/problem/staticrmq

Code

#define PROBLEM "https://judge.yosupo.jp/problem/staticrmq"

#include "include/mtl/sparse_table.hpp"
#include <iostream>
using namespace std;

int fmin(int a, int b) {return min(a,b);}

int main() {
  int n,q; cin>>n>>q;
  vector<int> A(n);
  for (int i = 0; i < n; i++) cin>>A[i];
  SparseTable<int, fmin> st(A.begin(), A.end());
  while (q--) {
    int l,r; cin>>l>>r;
    cout<<st.query(l,r)<<endl;
  }
}

#line 1 "test/yosupo/static_rmq-sparse_table.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/staticrmq"

#line 2 "include/mtl/bit_manip.hpp"
#include <cstdint>
#include <cassert>
#if __cplusplus >= 202002L
#ifndef MTL_CPP20
#define MTL_CPP20
#endif
#include <bit>
#endif

namespace bm {

/// Count 1s for each 8 bits
inline constexpr uint64_t popcnt_e8(uint64_t x) {
  x = (x & 0x5555555555555555) + ((x>>1) & 0x5555555555555555);
  x = (x & 0x3333333333333333) + ((x>>2) & 0x3333333333333333);
  x = (x & 0x0F0F0F0F0F0F0F0F) + ((x>>4) & 0x0F0F0F0F0F0F0F0F);
  return x;
}
/// Count 1s
inline constexpr unsigned popcnt(uint64_t x) {
#ifdef MTL_CPP20
  return std::popcount(x);
#else
  return (popcnt_e8(x) * 0x0101010101010101) >> 56;
#endif
}
/// Alias to mtl::popcnt(x)
constexpr unsigned popcount(uint64_t x) {
  return popcnt(x);
}
/// Count trailing 0s. s.t. *11011000 -> 3
inline constexpr unsigned ctz(uint64_t x) {
#ifdef MTL_CPP20
  return std::countr_zero(x);
#else
  return popcnt((x & (-x)) - 1);
#endif
}
/// Alias to mtl::ctz(x)
constexpr unsigned countr_zero(uint64_t x) {
  return ctz(x);
}
/// Count trailing 1s. s.t. *11011011 -> 2
inline constexpr unsigned cto(uint64_t x) {
#ifdef MTL_CPP20
  return std::countr_one(x);
#else
  return ctz(~x);
#endif
}
/// Alias to mtl::cto(x)
constexpr unsigned countr_one(uint64_t x) {
  return cto(x);
}
inline constexpr unsigned ctz8(uint8_t x) {
  return x == 0 ? 8 : popcnt_e8((x & (-x)) - 1);
}
/// [00..0](8bit) -> 0, [**..*](not only 0) -> 1
inline constexpr uint8_t summary(uint64_t x) {
  constexpr uint64_t hmask = 0x8080808080808080ull;
  constexpr uint64_t lmask = 0x7F7F7F7F7F7F7F7Full;
  auto a = x & hmask;
  auto b = x & lmask;
  b = hmask - b;
  b = ~b;
  auto c = (a | b) & hmask;
  c *= 0x0002040810204081ull;
  return uint8_t(c >> 56);
}
/// Extract target area of bits
inline constexpr uint64_t bextr(uint64_t x, unsigned start, unsigned len) {
  uint64_t mask = len < 64 ? (1ull<<len)-1 : 0xFFFFFFFFFFFFFFFFull;
  return (x >> start) & mask;
}
/// 00101101 -> 00111111 -count_1s-> 6
inline constexpr unsigned log2p1(uint8_t x) {
  if (x & 0x80)
    return 8;
  uint64_t p = uint64_t(x) * 0x0101010101010101ull;
  p -= 0x8040201008040201ull;
  p = ~p & 0x8080808080808080ull;
  p = (p >> 7) * 0x0101010101010101ull;
  p >>= 56;
  return p;
}
/// 00101100 -mask_mssb-> 00100000 -to_index-> 5
inline constexpr unsigned mssb8(uint8_t x) {
  assert(x != 0);
  return log2p1(x) - 1;
}
/// 00101100 -mask_lssb-> 00000100 -to_index-> 2
inline constexpr unsigned lssb8(uint8_t x) {
  assert(x != 0);
  return popcnt_e8((x & -x) - 1);
}
/// Count leading 0s. 00001011... -> 4
inline constexpr unsigned clz(uint64_t x) {
#ifdef MTL_CPP20
  return std::countl_zero(x);
#else
  if (x == 0)
    return 64;
  auto i = mssb8(summary(x));
  auto j = mssb8(bextr(x, 8 * i, 8));
  return 63 - (8 * i + j);
#endif
}
/// Alias to mtl::clz(x)
constexpr unsigned countl_zero(uint64_t x) {
  return clz(x);
}
/// Count leading 1s. 11110100... -> 4
inline constexpr unsigned clo(uint64_t x) {
#ifdef MTL_CPP20
  return std::countl_one(x);
#else
  return clz(~x);
#endif
}
/// Alias to mtl::clo(x)
constexpr unsigned countl_one(uint64_t x) {
  return clo(x);
}

inline constexpr unsigned clz8(uint8_t x) {
  return x == 0 ? 8 : 7 - mssb8(x);
}
inline constexpr uint64_t bit_reverse(uint64_t x) {
  x = ((x & 0x00000000FFFFFFFF) << 32) | ((x & 0xFFFFFFFF00000000) >> 32);
  x = ((x & 0x0000FFFF0000FFFF) << 16) | ((x & 0xFFFF0000FFFF0000) >> 16);
  x = ((x & 0x00FF00FF00FF00FF) << 8) | ((x & 0xFF00FF00FF00FF00) >> 8);
  x = ((x & 0x0F0F0F0F0F0F0F0F) << 4) | ((x & 0xF0F0F0F0F0F0F0F0) >> 4);
  x = ((x & 0x3333333333333333) << 2) | ((x & 0xCCCCCCCCCCCCCCCC) >> 2);
  x = ((x & 0x5555555555555555) << 1) | ((x & 0xAAAAAAAAAAAAAAAA) >> 1);
  return x;
}

/// Check if x is power of 2. 00100000 -> true, 00100001 -> false
constexpr bool has_single_bit(uint64_t x) noexcept {
#ifdef MTL_CPP20
  return std::has_single_bit(x);
#else
  return x != 0 && (x & (x - 1)) == 0;
#endif
}

/// Bit width needs to represent x. 00110110 -> 6
constexpr int bit_width(uint64_t x) noexcept {
#ifdef MTL_CPP20
  return std::bit_width(x);
#else
  return 64 - clz(x);
#endif
}

/// Ceil power of 2. 00110110 -> 01000000
constexpr uint64_t bit_ceil(uint64_t x) {
#ifdef MTL_CPP20
  return std::bit_ceil(x);
#else
  if (x == 0) return 1;
  return 1ull << bit_width(x - 1);
#endif
}

/// Floor power of 2. 00110110 -> 00100000
constexpr uint64_t bit_floor(uint64_t x) {
#ifdef MTL_CPP20
  return std::bit_floor(x);
#else
  if (x == 0) return 0;
  return 1ull << (bit_width(x) - 1);
#endif
}

} // namespace bm
#line 3 "include/mtl/sparse_table.hpp"
#include <cstddef>
#include <vector>

template <class T, T (*op)(T, T)>
class SparseTable {
 public:
  using value_type = T;
 private:
  size_t size_;
  size_t log_n_;
  std::vector<std::vector<value_type>> table_;

 public:
  SparseTable() = default;
  template <class Iter>
  SparseTable(Iter begin, Iter end) : 
    size_(std::distance(begin, end)), 
    log_n_(63-bm::clz(size_)), 
    table_(log_n_+1, std::vector<value_type>(size_)) 
  {
    std::copy(begin, end, table_[0].begin());
    for (size_t log_n = 1; log_n <= log_n_; log_n++) {
      size_t width = 1ull<<log_n;
      for (size_t i = 0; i + width <= size_; i++) {
        table_[log_n][i] = op(table_[log_n-1][i],
                              table_[log_n-1][i+width/2]);
      }
    }
  }

  value_type query(size_t l, size_t r) const {
    size_t p = 63-bm::clz(r-l);
    return op(table_[p][l], table_[p][r-(1ull<<p)]);
  }
};
#line 4 "test/yosupo/static_rmq-sparse_table.test.cpp"
#include <iostream>
using namespace std;

int fmin(int a, int b) {return min(a,b);}

int main() {
  int n,q; cin>>n>>q;
  vector<int> A(n);
  for (int i = 0; i < n; i++) cin>>A[i];
  SparseTable<int, fmin> st(A.begin(), A.end());
  while (q--) {
    int l,r; cin>>l>>r;
    cout<<st.query(l,r)<<endl;
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	6 ms	3 MB
g++	max_random_00	AC	907 ms	44 MB
g++	max_random_01	AC	1015 ms	44 MB
g++	max_random_02	AC	1064 ms	44 MB
g++	max_random_03	AC	875 ms	44 MB
g++	max_random_04	AC	908 ms	44 MB
g++	random_00	AC	727 ms	35 MB
g++	random_01	AC	738 ms	41 MB
g++	random_02	AC	557 ms	7 MB
g++	random_03	AC	182 ms	39 MB
g++	random_04	AC	236 ms	26 MB
g++	small_00	AC	7 ms	3 MB
g++	small_01	AC	7 ms	3 MB
g++	small_02	AC	6 ms	3 MB
g++	small_03	AC	6 ms	3 MB
g++	small_04	AC	6 ms	3 MB
g++	small_05	AC	6 ms	3 MB
g++	small_06	AC	6 ms	3 MB
g++	small_07	AC	6 ms	3 MB
g++	small_08	AC	6 ms	3 MB
g++	small_09	AC	6 ms	3 MB
g++	small_values_00	AC	1017 ms	44 MB
g++	small_width_query_00	AC	895 ms	44 MB
g++	small_width_query_01	AC	892 ms	44 MB
g++	small_width_query_02	AC	1036 ms	44 MB
g++	small_width_query_03	AC	915 ms	44 MB
g++	small_width_query_04	AC	865 ms	44 MB
clang++	example_00	AC	6 ms	3 MB
clang++	max_random_00	AC	890 ms	44 MB
clang++	max_random_01	AC	881 ms	44 MB
clang++	max_random_02	AC	916 ms	44 MB
clang++	max_random_03	AC	876 ms	44 MB
clang++	max_random_04	AC	885 ms	44 MB
clang++	random_00	AC	723 ms	35 MB
clang++	random_01	AC	741 ms	41 MB
clang++	random_02	AC	791 ms	7 MB
clang++	random_03	AC	179 ms	39 MB
clang++	random_04	AC	296 ms	26 MB
clang++	small_00	AC	7 ms	3 MB
clang++	small_01	AC	7 ms	3 MB
clang++	small_02	AC	6 ms	3 MB
clang++	small_03	AC	6 ms	3 MB
clang++	small_04	AC	6 ms	3 MB
clang++	small_05	AC	6 ms	3 MB
clang++	small_06	AC	6 ms	3 MB
clang++	small_07	AC	7 ms	3 MB
clang++	small_08	AC	7 ms	3 MB
clang++	small_09	AC	7 ms	3 MB
clang++	small_values_00	AC	1006 ms	44 MB
clang++	small_width_query_00	AC	900 ms	44 MB
clang++	small_width_query_01	AC	864 ms	44 MB
clang++	small_width_query_02	AC	957 ms	44 MB
clang++	small_width_query_03	AC	993 ms	44 MB
clang++	small_width_query_04	AC	878 ms	44 MB

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