結果

問題 No.1031 いたずら好きなお姉ちゃん
コンテスト
ユーザー kimiyuki
提出日時 2020-07-15 05:14:53
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 142 ms / 3,500 ms
コード長 6,930 bytes
コンパイル時間 1,290 ms
コンパイル使用メモリ 84,812 KB
最終ジャッジ日時 2025-01-11 20:53:22
ジャッジサーバーID
（参考情報） 		judge2 / judge2
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ファイルパターン 結果
sample AC * 3
other AC * 53
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: In function ‘int main()’:
main.cpp:60:17: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
   60 | std::vector<std::vector<int> > adjacent_list_from_children(const std::vector<std::vector<int> > & children) {
      |            ~~~~~^~~~~~~~~~
main.cpp:63:14: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
   63 |     REP (x, n) {
      |         ~~~~~^~~

ソースコード

diff # 

#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;
}
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