library

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:heavy_check_mark: test/library_checker/datastructure/staticrmq.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/staticrmq"
#include "my_template.hpp"
#include "other/io.hpp"

#include "alg/monoid/min.hpp"
#include "ds/static_range_product.hpp"

signed main() {
  using Mono = Monoid_Min<u32>;
  using ST = Sparse_Table<Mono>;
  INT(N, Q);
  Static_Range_Product<Mono, ST> X(N, [&](int i) -> u32 {
    u32 x;
    read(x);
    return x;
  });
  FOR(Q) {
    u32 L, R;
    read(L, R);
    print(X.prod(L, R));
  }
  return 0;
}
#line 1 "test/library_checker/datastructure/staticrmq.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/staticrmq"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

// 参考 https://codeforces.com/blog/entry/96344
// bmi,bmi2,lzcnt は ucup でコンパイルエラー
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,popcnt")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) \
  for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sm = 0;
  for (auto &&a: A) sm += a;
  return sm;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
  sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}
#endif
#line 1 "other/io.hpp"
#define FASTIO
#include <unistd.h>


// https://judge.yosupo.jp/submission/21623

namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf

uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
  char num[10000][4];
  constexpr Pre() : num() {
    for (int i = 0; i < 10000; i++) {
      int n = i;
      for (int j = 3; j >= 0; j--) {
        num[i][j] = n % 10 | '0';
        n /= 10;
      }
    }
  }
} constexpr pre;

inline void load() {
  memcpy(ibuf, ibuf + pil, pir - pil);
  pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
  pil = 0;
  if (pir < SZ) ibuf[pir++] = '\n';
}

inline void flush() {
  fwrite(obuf, 1, por, stdout);
  por = 0;
}

void rd(char &c) {
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
}

void rd(string &x) {
  x.clear();
  char c;
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
  do {
    x += c;
    if (pil == pir) load();
    c = ibuf[pil++];
  } while (!isspace(c));
}

template <typename T>
void rd_real(T &x) {
  string s;
  rd(s);
  x = stod(s);
}

template <typename T>
void rd_integer(T &x) {
  if (pil + 100 > pir) load();
  char c;
  do
    c = ibuf[pil++];
  while (c < '-');
  bool minus = 0;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (c == '-') { minus = 1, c = ibuf[pil++]; }
  }
  x = 0;
  while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (minus) x = -x;
  }
}

void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }

template <class T, class U>
void rd(pair<T, U> &p) {
  return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
  if constexpr (N < std::tuple_size<T>::value) {
    auto &x = std::get<N>(t);
    rd(x);
    rd_tuple<N + 1>(t);
  }
}
template <class... T>
void rd(tuple<T...> &tpl) {
  rd_tuple(tpl);
}

template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
  for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
  for (auto &d: x) rd(d);
}

void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
  rd(h), read(t...);
}

void wt(const char c) {
  if (por == SZ) flush();
  obuf[por++] = c;
}
void wt(const string s) {
  for (char c: s) wt(c);
}
void wt(const char *s) {
  size_t len = strlen(s);
  for (size_t i = 0; i < len; i++) wt(s[i]);
}

template <typename T>
void wt_integer(T x) {
  if (por > SZ - 100) flush();
  if (x < 0) { obuf[por++] = '-', x = -x; }
  int outi;
  for (outi = 96; x >= 10000; outi -= 4) {
    memcpy(out + outi, pre.num[x % 10000], 4);
    x /= 10000;
  }
  if (x >= 1000) {
    memcpy(obuf + por, pre.num[x], 4);
    por += 4;
  } else if (x >= 100) {
    memcpy(obuf + por, pre.num[x] + 1, 3);
    por += 3;
  } else if (x >= 10) {
    int q = (x * 103) >> 10;
    obuf[por] = q | '0';
    obuf[por + 1] = (x - q * 10) | '0';
    por += 2;
  } else
    obuf[por++] = x | '0';
  memcpy(obuf + por, out + outi + 4, 96 - outi);
  por += 96 - outi;
}

template <typename T>
void wt_real(T x) {
  ostringstream oss;
  oss << fixed << setprecision(15) << double(x);
  string s = oss.str();
  wt(s);
}

void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }

template <class T, class U>
void wt(const pair<T, U> val) {
  wt(val.first);
  wt(' ');
  wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
  if constexpr (N < std::tuple_size<T>::value) {
    if constexpr (N > 0) { wt(' '); }
    const auto x = std::get<N>(t);
    wt(x);
    wt_tuple<N + 1>(t);
  }
}
template <class... T>
void wt(tuple<T...> tpl) {
  wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}
template <class T>
void wt(const vector<T> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}

void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  wt(head);
  if (sizeof...(Tail)) wt(' ');
  print(forward<Tail>(tail)...);
}

// gcc expansion. called automaticall after main.

void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio

using fastio::read;
using fastio::print;
using fastio::flush;

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define U32(...)   \
  u32 __VA_ARGS__; \
  read(__VA_ARGS__)
#define U64(...)   \
  u64 __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)   \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 4 "test/library_checker/datastructure/staticrmq.test.cpp"

#line 2 "alg/monoid/min.hpp"

template <typename E>
struct Monoid_Min {
  using X = E;
  using value_type = X;
  static constexpr X op(const X &x, const X &y) noexcept { return min(x, y); }
  static constexpr X unit() { return infty<E>; }
  static constexpr bool commute = true;
};
#line 2 "ds/sparse_table/sparse_table.hpp"

// 冪等なモノイドであることを仮定。disjoint sparse table より x 倍高速
template <class Monoid>
struct Sparse_Table {
  using MX = Monoid;
  using X = typename MX::value_type;
  int n, log;
  vvc<X> dat;

  Sparse_Table() {}
  Sparse_Table(int n) { build(n); }
  template <typename F>
  Sparse_Table(int n, F f) {
    build(n, f);
  }
  Sparse_Table(const vc<X>& v) { build(v); }

  void build(int m) {
    build(m, [](int i) -> X { return MX::unit(); });
  }
  void build(const vc<X>& v) {
    build(len(v), [&](int i) -> X { return v[i]; });
  }
  template <typename F>
  void build(int m, F f) {
    n = m, log = 1;
    while ((1 << log) < n) ++log;
    dat.resize(log);
    dat[0].resize(n);
    FOR(i, n) dat[0][i] = f(i);

    FOR(i, log - 1) {
      dat[i + 1].resize(len(dat[i]) - (1 << i));
      FOR(j, len(dat[i]) - (1 << i)) {
        dat[i + 1][j] = MX::op(dat[i][j], dat[i][j + (1 << i)]);
      }
    }
  }

  X prod(int L, int R) {
    if (L == R) return MX::unit();
    if (R == L + 1) return dat[0][L];
    int k = topbit(R - L - 1);
    return MX::op(dat[k][L], dat[k][R - (1 << k)]);
  }

  template <class F>
  int max_right(const F check, int L) {
    assert(0 <= L && L <= n && check(MX::unit()));
    if (L == n) return n;
    int ok = L, ng = n + 1;
    while (ok + 1 < ng) {
      int k = (ok + ng) / 2;
      bool bl = check(prod(L, k));
      if (bl) ok = k;
      if (!bl) ng = k;
    }
    return ok;
  }

  template <class F>
  int min_left(const F check, int R) {
    assert(0 <= R && R <= n && check(MX::unit()));
    if (R == 0) return 0;
    int ok = R, ng = -1;
    while (ng + 1 < ok) {
      int k = (ok + ng) / 2;
      bool bl = check(prod(k, R));
      if (bl) ok = k;
      if (!bl) ng = k;
    }
    return ok;
  }
};
#line 2 "ds/sparse_table/disjoint_sparse_table.hpp"

template <class Monoid>
struct Disjoint_Sparse_Table {
  using MX = Monoid;
  using X = typename MX::value_type;
  int n, log;
  vvc<X> dat;

  Disjoint_Sparse_Table() {}
  Disjoint_Sparse_Table(int n) { build(n); }
  template <typename F>
  Disjoint_Sparse_Table(int n, F f) {
    build(n, f);
  }
  Disjoint_Sparse_Table(const vc<X>& v) { build(v); }

  void build(int m) {
    build(m, [](int i) -> X { return MX::unit(); });
  }
  void build(const vc<X>& v) {
    build(len(v), [&](int i) -> X { return v[i]; });
  }
  template <typename F>
  void build(int m, F f) {
    n = m, log = 1;
    while ((1 << log) < n) ++log;
    dat.resize(log);
    dat[0].reserve(n);
    FOR(i, n) dat[0].eb(f(i));
    FOR(i, 1, log) {
      auto& v = dat[i];
      v = dat[0];
      int b = 1 << i;
      for (int m = b; m <= n; m += 2 * b) {
        int L = m - b, R = min(n, m + b);
        FOR_R(j, L + 1, m) v[j - 1] = MX::op(v[j - 1], v[j]);
        FOR(j, m, R - 1) v[j + 1] = MX::op(v[j], v[j + 1]);
      }
    }
  }

  X prod(int L, int R) {
    if (L == R) return MX::unit();
    --R;
    if (L == R) return dat[0][L];
    int k = topbit(L ^ R);
    return MX::op(dat[k][L], dat[k][R]);
  }

  template <class F>
  int max_right(const F check, int L) {
    assert(0 <= L && L <= n && check(MX::unit()));
    if (L == n) return n;
    int ok = L, ng = n + 1;
    while (ok + 1 < ng) {
      int k = (ok + ng) / 2;
      bool bl = check(prod(L, k));
      if (bl) ok = k;
      if (!bl) ng = k;
    }
    return ok;
  }

  template <class F>
  int min_left(const F check, int R) {
    assert(0 <= R && R <= n && check(MX::unit()));
    if (R == 0) return 0;
    int ok = R, ng = -1;
    while (ng + 1 < ok) {
      int k = (ok + ng) / 2;
      bool bl = check(prod(k, R));
      if (bl) ok = k;
      if (!bl) ng = k;
    }
    return ok;
  }
};
#line 3 "ds/static_range_product.hpp"

/*
参考:https://judge.yosupo.jp/submission/106668
長さ 2^LOG のブロックに分ける.ブロック内の prefix, suffix を持つ.
ブロック積の列を ST(DST) で持つ.ブロックをまたぐ積は O(1).
短いものは O(1) を諦めて愚直ということにする.
前計算:O(Nlog(N)/2^LOG)
クエリ:O(1) / worst O(2^LOG)
*/
template <typename Monoid, typename SPARSE_TABLE, int LOG = 4>
struct Static_Range_Product {
  using MX = Monoid;
  using X = typename MX::value_type;
  int N, b_num;
  vc<X> A, pre, suf; // inclusive
  SPARSE_TABLE ST;

  Static_Range_Product() {}
  template <typename F>
  Static_Range_Product(int n, F f) {
    build(n, f);
  }
  Static_Range_Product(const vc<X>& v) { build(v); }

  void build(const vc<X>& v) {
    build(len(v), [&](int i) -> X { return v[i]; });
  }
  template <typename F>
  void build(int m, F f) {
    N = m;
    b_num = N >> LOG;
    A.resize(N);
    FOR(i, N) A[i] = f(i);
    pre = A, suf = A;
    constexpr int mask = (1 << LOG) - 1;
    FOR(i, 1, N) {
      if (i & mask) pre[i] = MX::op(pre[i - 1], A[i]);
    }
    FOR_R(i, 1, N) {
      if (i & mask) suf[i - 1] = MX::op(A[i - 1], suf[i]);
    }
    ST.build(b_num, [&](int i) -> X { return suf[i << LOG]; });
  }

  // O(1) or O(R-L)
  X prod(int L, int R) {
    if (L == R) return MX::unit();
    R -= 1;
    int a = L >> LOG, b = R >> LOG;
    if (a < b) {
      X x = ST.prod(a + 1, b);
      x = MX::op(suf[L], x);
      x = MX::op(x, pre[R]);
      return x;
    }
    X x = A[L];
    FOR(i, L + 1, R + 1) x = MX::op(x, A[i]);
    return x;
  }
};
#line 7 "test/library_checker/datastructure/staticrmq.test.cpp"

signed main() {
  using Mono = Monoid_Min<u32>;
  using ST = Sparse_Table<Mono>;
  INT(N, Q);
  Static_Range_Product<Mono, ST> X(N, [&](int i) -> u32 {
    u32 x;
    read(x);
    return x;
  });
  FOR(Q) {
    u32 L, R;
    read(L, R);
    print(X.prod(L, R));
  }
  return 0;
}
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