#511788 (C++17) No.1031 いたずら好きなお姉ちゃん

• 問題: No.1031 いたずら好きなお姉ちゃん
• ユーザー: kimiyuki
• 提出日時: 2020-07-15 05:14:53
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 139 ms / 3,500 ms
• コード長: 6,930 bytes
• コンパイル時間: 1,123 ms
• コンパイル使用メモリ: 88,668 KB
• 実行使用メモリ: 29,832 KB
• 最終ジャッジ日時: 2024-11-20 18:31:23
• 合計ジャッジ時間: 8,992 ms
• ジャッジサーバーID （参考情報）: judge5 / judge2

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,248 KB
testcase_02	AC	1 ms; 5,248 KB
testcase_03	AC	6 ms; 5,248 KB
testcase_04	AC	6 ms; 5,248 KB
testcase_05	AC	6 ms; 5,248 KB
testcase_06	AC	7 ms; 5,248 KB
testcase_07	AC	6 ms; 5,248 KB
testcase_08	AC	6 ms; 5,248 KB
testcase_09	AC	6 ms; 5,248 KB
testcase_10	AC	6 ms; 5,248 KB
testcase_11	AC	113 ms; 16,084 KB
testcase_12	AC	102 ms; 15,972 KB
testcase_13	AC	133 ms; 18,888 KB
testcase_14	AC	113 ms; 16,724 KB
testcase_15	AC	126 ms; 17,912 KB
testcase_16	AC	113 ms; 15,880 KB
testcase_17	AC	118 ms; 17,948 KB
testcase_18	AC	121 ms; 17,364 KB
testcase_19	AC	136 ms; 18,128 KB
testcase_20	AC	137 ms; 18,736 KB
testcase_21	AC	129 ms; 17,480 KB
testcase_22	AC	102 ms; 15,800 KB
testcase_23	AC	119 ms; 16,148 KB
testcase_24	AC	131 ms; 18,032 KB
testcase_25	AC	124 ms; 19,808 KB
testcase_26	AC	127 ms; 17,656 KB
testcase_27	AC	108 ms; 16,476 KB
testcase_28	AC	134 ms; 18,940 KB
testcase_29	AC	129 ms; 18,932 KB
testcase_30	AC	129 ms; 18,764 KB
testcase_31	AC	134 ms; 18,928 KB
testcase_32	AC	139 ms; 18,824 KB
testcase_33	AC	131 ms; 18,836 KB
testcase_34	AC	131 ms; 29,832 KB
testcase_35	AC	90 ms; 24,824 KB
testcase_36	AC	91 ms; 23,476 KB
testcase_37	AC	91 ms; 25,044 KB
testcase_38	AC	86 ms; 22,644 KB
testcase_39	AC	91 ms; 21,272 KB
testcase_40	AC	85 ms; 21,120 KB
testcase_41	AC	88 ms; 22,568 KB
testcase_42	AC	89 ms; 22,612 KB
testcase_43	AC	86 ms; 20,732 KB
testcase_44	AC	92 ms; 19,644 KB
testcase_45	AC	86 ms; 19,756 KB
testcase_46	AC	98 ms; 23,556 KB
testcase_47	AC	104 ms; 21,600 KB
testcase_48	AC	110 ms; 24,916 KB
testcase_49	AC	97 ms; 22,504 KB
testcase_50	AC	99 ms; 22,928 KB
testcase_51	AC	108 ms; 22,744 KB
testcase_52	AC	109 ms; 23,492 KB
testcase_53	AC	109 ms; 23,484 KB
testcase_54	AC	2 ms; 5,248 KB
testcase_55	AC	2 ms; 5,248 KB

ソースコード

#line 1 "main.cpp"
#define PROBLEM
#line 2 "/home/user/Library/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 "/home/user/Library/graph/cartesian_tree.hpp"
#include <functional>
#include <vector>
#line 5 "/home/user/Library/graph/cartesian_tree.hpp"

/**
 * @brief Cartesian tree ($O(n)$)
 * @note the smallest value is the root
 * @note if a is not distinct, the way for tie-break is undefined
 * @return the binary tree as the list of parents
 */
template <class T, class Comparator = std::less<int> >
std::vector<int> construct_cartesian_tree(const std::vector<T> & a, const Comparator & cmp = Comparator()) {
    int n = a.size();
    std::vector<int> parent(n, -1);
    REP3 (i, 1, n) {
        int p = i - 1;
        int l = -1;
        while (p != -1 and cmp(a[i], a[p])) {
            int pp = parent[p];
            if (l != -1) {
                parent[l] = p;
            }
            parent[p] = i;
            p = pp;
        }
        parent[i] = p;
    }
    return parent;
}
#line 2 "/home/user/Library/graph/format.hpp"
#include <cassert>
#include <utility>
#line 6 "/home/user/Library/graph/format.hpp"

std::pair<std::vector<std::vector<int> >, int> children_from_parent(const std::vector<int> & parent) {
    int n = parent.size();
    std::vector<std::vector<int> > children(n);
    int root = -1;
    REP (x, n) {
        if (parent[x] == -1) {
            assert (root == -1);
            root = x;
        } else {
            children[parent[x]].push_back(x);
        }
    }
    assert (root != -1);
    return std::make_pair(children, root);
}

std::vector<std::vector<int> > adjacent_list_from_children(const std::vector<std::vector<int> > & children) {
    int n = children.size();
    std::vector<std::vector<int> > g(n);
    REP (x, n) {
        for (int y : children[x]) {
            g[x].push_back(y);
            g[y].push_back(x);
        }
    }
    return g;
}
#line 2 "/home/user/Library/graph/subtree.hpp"
#include <algorithm>
#line 4 "/home/user/Library/graph/subtree.hpp"

struct subtree_info_t {
    int parent;  // in the entire tree
    int depth;  // in the entire tree
    int size;  // of the subtree
    int height;  // of the subtree
};

/**
 * @brief subtree info / それぞれの部分木の size とか height とかをまとめて求めておいてくれるやつ
 * @arg g must be a tree
 * @note O(n) time
 * @note O(n) space on heap
 */
std::vector<subtree_info_t> prepare_subtree_info(std::vector<std::vector<int> > const & g, int root) {
    int n = g.size();
    std::vector<subtree_info_t> info(n, (subtree_info_t) { -1, -1, -1, -1 });
    std::vector<int> topological(n);
    topological[0] = root;
    info[root].parent = root;
    info[root].depth = 0;
    int r = 1;
    for (int l = 0; l < r; ++ l) {
        int i = topological[l];
        for (int j : g[i]) if (j != info[i].parent) {
            topological[r ++] = j;
            info[j].parent = i;
            info[j].depth = info[i].depth + 1;
        }
    }
    while ((-- r) >= 0) {
        int i = topological[r];
        info[i].size = 1;
        info[i].height = 0;
        for (int j : g[i]) if (j != info[i].parent) {
            info[i].size += info[j].size;
            info[i].height = std::max(info[i].height, info[j].height + 1);
        }
    }
    info[root].parent = -1;
    return info;
}
#line 5 "/home/user/Library/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 "/home/user/Library/monoids/min.hpp"
#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 8 "main.cpp"
#include <cstdio>
#line 12 "main.cpp"
using namespace std;

int64_t solve1(int n, const vector<int> & p) {
    // prepare a data structure for LIS
    vector<int> depth(n);
    {
        vector<int> parent = construct_cartesian_tree<int, greater<int> >(p);
        vector<vector<int> > children; int root; tie(children, root) = children_from_parent(parent);
        auto g = adjacent_list_from_children(children);
        auto info = prepare_subtree_info(g, root);
        REP (x, n) {
            depth[x] = info[x].depth;
        }
    }
    sparse_table<min_monoid<int> > table(ALL(depth));
    auto lis = [&](int l, int r) {
        if (l == r) return 0;
        return depth[l] - table.range_get(l, r) + 1;
    };

    // fold the Cartesian tree
    vector<int> parent = construct_cartesian_tree(p);
    vector<vector<int> > children; int root; tie(children, root) = children_from_parent(parent);
    int64_t ans = 0;
    auto go = [&](auto && go, int l, int m, int r) -> void {
        if (l == r) {
            return;
        }
        ans += lis(m + 1, r);
        for (int x : children[m]) {
            if (x < m) {
                go(go, l, x, m);
            } else {
                go(go, m + 1, x, r);
            }
        }
    };
    go(go, 0, root, n);
    return ans;
}

int64_t solve(int n, vector<int> p) {
    int64_t ans = solve1(n, p);
    reverse(ALL(p));
    return ans + solve1(n, p);
}

int main() {
    int n; scanf("%d", &n);
    vector<int> p(n);
    REP (i, n) {
        scanf("%d", &p[i]);
    }
    long long ans = solve(n, p);
    printf("%lld\n", ans);
    return 0;
}