# competitive-programming-library

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# data_structure/sparse_table.yosupo.test.cpp

## Code

#define PROBLEM "https://judge.yosupo.jp/problem/staticrmq"
#include "data_structure/sparse_table.hpp"

#include "utils/macros.hpp"
#include "monoids/min.hpp"
#include <cstdio>
#include <vector>
using namespace std;

int main() {
// input a sequence
int n, q; scanf("%d%d", &n, &q);
vector<int> a(n);
REP (i, n) {
scanf("%d", &a[i]);
}

// construct the sparse table
sparse_table<min_monoid<int> > st(ALL(a));

while (q --) {
int l, r; scanf("%d%d", &l, &r);
}
return 0;
}



#line 1 "data_structure/sparse_table.yosupo.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/staticrmq"
#line 2 "data_structure/sparse_table.hpp"
#include <cassert>
#include <vector>
#line 2 "utils/macros.hpp"
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) std::begin(x), std::end(x)
#line 5 "data_structure/sparse_table.hpp"

/**
* @brief Sparse Table (idempotent monoid)
* @note the unit is required just for convenience
* @note $O(N \log N)$ space
*/
template <class IdempotentMonoid>
struct sparse_table {
typedef typename IdempotentMonoid::value_type value_type;
std::vector<std::vector<value_type> > table;
IdempotentMonoid mon;
sparse_table() = default;

/**
* @note $O(N \log N)$ time
*/
template <class InputIterator>
sparse_table(InputIterator first, InputIterator last, const IdempotentMonoid & mon_ = IdempotentMonoid())
: mon(mon_) {
table.emplace_back(first, last);
int n = table[0].size();
int log_n = 32 - __builtin_clz(n);
table.resize(log_n, std::vector<value_type>(n));
REP (k, log_n - 1) {
REP (i, n) {
table[k + 1][i] = i + (1ll << k) < n ?
mon.mult(table[k][i], table[k][i + (1ll << k)]) :
table[k][i];
}
}
}

/**
* @note $O(1)$
*/
value_type range_get(int l, int r) const {
if (l == r) return mon.unit();  // if there is no unit, remove this line
assert (0 <= l and l < r and r <= (int)table[0].size());
int k = 31 - __builtin_clz(r - l);  // log2
return mon.mult(table[k][l], table[k][r - (1ll << k)]);
}
};
#line 3 "data_structure/sparse_table.yosupo.test.cpp"

#line 2 "monoids/min.hpp"
#include <algorithm>
#include <limits>

template <class T>
struct min_monoid {
typedef T value_type;
value_type unit() const { return std::numeric_limits<T>::max(); }
value_type mult(value_type a, value_type b) const { return std::min(a, b); }
};
#line 6 "data_structure/sparse_table.yosupo.test.cpp"
#include <cstdio>
#line 8 "data_structure/sparse_table.yosupo.test.cpp"
using namespace std;

int main() {
// input a sequence
int n, q; scanf("%d%d", &n, &q);
vector<int> a(n);
REP (i, n) {
scanf("%d", &a[i]);
}

// construct the sparse table
sparse_table<min_monoid<int> > st(ALL(a));