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#include "utils/left_to_right_maxima.hpp"
#pragma once
#include <stack>
#include <tuple>
#include <utility>
#include <vector>
#include "../utils/macros.hpp"
#include "../data_structure/sparse_table.hpp"
#include "../monoids/min.hpp"
/**
* @brief Length of Left-to-right Maxima (前処理 $O(n \log n)$ + $O(1)$)
* @description computes the lengths of the left-to-right maxima for the given interval
* @note the left-to-right maxima for a sequence $a$ means the subsubsequence of the elements $a_i$ which satisfy $\forall j \lt i. a_j \lt a_i$.
*/
class left_to_right_maxima {
std::vector<int> depth;
sparse_table<min_monoid<int> > table;
public:
left_to_right_maxima() = default;
int operator () (int l, int r) const {
assert (0 <= l and l <= r and r <= (int)depth.size());
if (l == r) return 0;
return depth[l] - table.range_get(l, r) + 1;
}
private:
left_to_right_maxima(const std::vector<int> & depth_)
: depth(depth_), table(ALL(depth_)) {
}
public:
/**
* @note this is just a constructor, but is needed to specify template arguments.
*/
template <class T, class Comparator = std::less<T>, class RandomAccessIterator>
static left_to_right_maxima construct(RandomAccessIterator first, RandomAccessIterator last, const Comparator & cmp = Comparator()) {
int n = std::distance(first, last);
// make a forest
std::vector<int> parent(n, -1);
std::stack<int> stk;
REP (i, n) {
while (not stk.empty() and cmp(*(first + stk.top()), *(first + i))) {
parent[stk.top()] = i;
stk.pop();
}
stk.push(i);
}
// calculate depths
std::vector<int> depth(n);
REP_R (i, n) {
if (parent[i] != -1) {
depth[i] = depth[parent[i]] + 1;
}
}
return left_to_right_maxima(depth);
}
};
#line 2 "utils/left_to_right_maxima.hpp"
#include <stack>
#include <tuple>
#include <utility>
#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 2 "data_structure/sparse_table.hpp"
#include <cassert>
#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 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 9 "utils/left_to_right_maxima.hpp"
/**
* @brief Length of Left-to-right Maxima (前処理 $O(n \log n)$ + $O(1)$)
* @description computes the lengths of the left-to-right maxima for the given interval
* @note the left-to-right maxima for a sequence $a$ means the subsubsequence of the elements $a_i$ which satisfy $\forall j \lt i. a_j \lt a_i$.
*/
class left_to_right_maxima {
std::vector<int> depth;
sparse_table<min_monoid<int> > table;
public:
left_to_right_maxima() = default;
int operator () (int l, int r) const {
assert (0 <= l and l <= r and r <= (int)depth.size());
if (l == r) return 0;
return depth[l] - table.range_get(l, r) + 1;
}
private:
left_to_right_maxima(const std::vector<int> & depth_)
: depth(depth_), table(ALL(depth_)) {
}
public:
/**
* @note this is just a constructor, but is needed to specify template arguments.
*/
template <class T, class Comparator = std::less<T>, class RandomAccessIterator>
static left_to_right_maxima construct(RandomAccessIterator first, RandomAccessIterator last, const Comparator & cmp = Comparator()) {
int n = std::distance(first, last);
// make a forest
std::vector<int> parent(n, -1);
std::stack<int> stk;
REP (i, n) {
while (not stk.empty() and cmp(*(first + stk.top()), *(first + i))) {
parent[stk.top()] = i;
stk.pop();
}
stk.push(i);
}
// calculate depths
std::vector<int> depth(n);
REP_R (i, n) {
if (parent[i] != -1) {
depth[i] = depth[parent[i]] + 1;
}
}
return left_to_right_maxima(depth);
}
};