competitive-programming-library

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:heavy_check_mark: Length of Left-to-right Maxima (前処理 $O(n \log n)$ + $O(1)$)
(utils/left_to_right_maxima.hpp)

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Code

#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);
    }
};
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