結果

問題 No.1720 Division Permutation
ユーザー 👑 hitonanodehitonanode
提出日時 2021-10-24 11:39:34
言語 C++23(draft)
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 168 ms / 4,000 ms
コード長 12,539 bytes
コンパイル時間 3,117 ms
コンパイル使用メモリ 239,876 KB
実行使用メモリ 26,532 KB
最終ジャッジ日時 2024-04-09 22:16:21
合計ジャッジ時間 10,654 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
このコードへのチャレンジ（β）

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 1 ms
6,812 KB
testcase_01 AC 2 ms
6,944 KB
testcase_02 AC 2 ms
6,940 KB
testcase_03 AC 2 ms
6,944 KB
testcase_04 AC 2 ms
6,940 KB
testcase_05 AC 2 ms
6,944 KB
testcase_06 AC 2 ms
6,944 KB
testcase_07 AC 2 ms
6,944 KB
testcase_08 AC 2 ms
6,944 KB
testcase_09 AC 2 ms
6,944 KB
testcase_10 AC 2 ms
6,940 KB
testcase_11 AC 2 ms
6,944 KB
testcase_12 AC 2 ms
6,944 KB
testcase_13 AC 163 ms
25,472 KB
testcase_14 AC 164 ms
24,960 KB
testcase_15 AC 98 ms
16,328 KB
testcase_16 AC 154 ms
25,012 KB
testcase_17 AC 123 ms
21,792 KB
testcase_18 AC 105 ms
25,776 KB
testcase_19 AC 158 ms
25,608 KB
testcase_20 AC 155 ms
25,900 KB
testcase_21 AC 158 ms
25,344 KB
testcase_22 AC 153 ms
25,996 KB
testcase_23 AC 153 ms
26,304 KB
testcase_24 AC 154 ms
25,432 KB
testcase_25 AC 156 ms
26,060 KB
testcase_26 AC 154 ms
25,124 KB
testcase_27 AC 157 ms
24,948 KB
testcase_28 AC 155 ms
26,268 KB
testcase_29 AC 158 ms
26,532 KB
testcase_30 AC 157 ms
25,680 KB
testcase_31 AC 156 ms
26,328 KB
testcase_32 AC 1 ms
6,944 KB
testcase_33 AC 2 ms
6,944 KB
testcase_34 AC 2 ms
6,940 KB
testcase_35 AC 1 ms
6,940 KB
testcase_36 AC 2 ms
6,944 KB
testcase_37 AC 1 ms
6,944 KB
testcase_38 AC 1 ms
6,940 KB
testcase_39 AC 1 ms
6,940 KB
testcase_40 AC 2 ms
6,940 KB
testcase_41 AC 1 ms
6,944 KB
testcase_42 AC 2 ms
6,944 KB
testcase_43 AC 147 ms
23,992 KB
testcase_44 AC 127 ms
22,448 KB
testcase_45 AC 116 ms
22,800 KB
testcase_46 AC 83 ms
15,220 KB
testcase_47 AC 119 ms
22,880 KB
testcase_48 AC 90 ms
15,996 KB
testcase_49 AC 144 ms
24,184 KB
testcase_50 AC 114 ms
22,092 KB
testcase_51 AC 92 ms
16,032 KB
testcase_52 AC 129 ms
22,092 KB
testcase_53 AC 167 ms
26,264 KB
testcase_54 AC 168 ms
24,428 KB
testcase_55 AC 159 ms
25,560 KB
testcase_56 AC 158 ms
25,192 KB
testcase_57 AC 162 ms
24,964 KB
testcase_58 AC 157 ms
25,944 KB
testcase_59 AC 158 ms
25,488 KB
testcase_60 AC 160 ms
26,264 KB
testcase_61 AC 159 ms
25,364 KB
testcase_62 AC 159 ms
26,000 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr)
#else
#define dbg(x) (x)
#define dbgif(cond, x) 0
#endif

// StarrySkyTree: segment tree for Range Minimum Query & Range Add Query
// Complexity: (N)$ (construction), (\log N)$ (add / get / prod)
// - RangeAddRangeMin(std::vector<Tp> data_init) : Initialize array x by data_init.
// - add(int begin, int end, Tp vadd) : Update x[i] <- x[i] + vadd for all begin <= i < end.
// - get(int pos) : Get x[pos].
// - prod(int begin, int end) : Get min(x[begin], ..., x[end - 1]).
template <typename Tp, Tp defaultT = std::numeric_limits<Tp>::max() / 2> struct RangeAddRangeMin {
    int N, head;
    std::vector<Tp> range_min, range_add;
    static inline Tp f(Tp x, Tp y) noexcept { return std::min(x, y); }

    inline void _merge(int pos) {
        range_min[pos] = f(range_min[pos * 2] + range_add[pos * 2], range_min[pos * 2 + 1] + range_add[pos * 2 + 1]);
    }
    void initialize(const std::vector<Tp> &data_init) {
        N = data_init.size(), head = 1;
        while (head < N) head <<= 1;
        range_min.assign(head * 2, defaultT);
        range_add.assign(head * 2, 0);
        std::copy(data_init.begin(), data_init.end(), range_min.begin() + head);
        for (int pos = head; --pos;) _merge(pos);
    }
    RangeAddRangeMin() = default;
    RangeAddRangeMin(const std::vector<Tp> &data_init) { initialize(data_init); }
    void _add(int begin, int end, int pos, int l, int r, Tp vadd) noexcept {
        if (r <= begin or end <= l) return;
        if (begin <= l and r <= end) {
            range_add[pos] += vadd;
            return;
        }
        _add(begin, end, pos * 2, l, (l + r) / 2, vadd);
        _add(begin, end, pos * 2 + 1, (l + r) / 2, r, vadd);
        _merge(pos);
    }
    // Add `vadd` to (x_begin, ..., x_{end - 1})
    void add(int begin, int end, Tp vadd) noexcept { return _add(begin, end, 1, 0, head, vadd); }
    Tp _get(int begin, int end, int pos, int l, int r) const noexcept {
        if (r <= begin or end <= l) return defaultT;
        if (begin <= l and r <= end) return range_min[pos] + range_add[pos];
        return f(_get(begin, end, pos * 2, l, (l + r) / 2), _get(begin, end, pos * 2 + 1, (l + r) / 2, r)) + range_add[pos];
    }
    // Return f(x_begin, ..., x_{end - 1})
    Tp get(int pos) const noexcept { return prod(pos, pos + 1); }
    Tp prod(int begin, int end) const noexcept { return _get(begin, end, 1, 0, head); }
};


struct permutation_tree {
    enum NodeType {
        JoinAsc,
        JoinDesc,
        Cut,
        Leaf,
        None,
    };
    struct node {
        NodeType tp;
        int L, R;  // i in [L, R)
        int mini, maxi;  // A[i] in [min, max]
        std::vector<int> child;
        int sz() const { return maxi - mini + 1; }
        template <class OStream> friend OStream &operator<<(OStream &os, const node &n) {
            os << "[[" << n.L << ',' << n.R << ")(ch:";
            for (auto i : n.child) os << i << ',';
            return os << ")(tp=" << n.tp << ")]";
        }
    };

    int root;
    std::vector<int> A;
    std::vector<node> nodes;

    bool is_adj(int lid, int rid) const { return nodes[lid].maxi + 1 == nodes[rid].mini; }
    void add_child(int parid, int chid) {
        nodes[parid].child.push_back(chid);
        nodes[parid].L = std::min(nodes[parid].L, nodes[chid].L);
        nodes[parid].R = std::max(nodes[parid].R, nodes[chid].R);
        nodes[parid].mini = std::min(nodes[parid].mini, nodes[chid].mini);
        nodes[parid].maxi = std::max(nodes[parid].maxi, nodes[chid].maxi);
    }
    NodeType findtype(int lid, int rid) const {
        const auto &l = nodes[lid].tp, &r = nodes[rid].tp;
        if (is_adj(lid, rid)) return NodeType::JoinAsc;
        if (is_adj(rid, lid)) return NodeType::JoinDesc;
        return NodeType::None;
    }

    permutation_tree(const std::vector<int> &A_) : root(-1), A(A_) { // A: 0-origin

        RangeAddRangeMin<int> segtree((std::vector<int>(A.size())));

        std::vector<std::pair<int, int>> hi{{A.size() + 1, -1}}, lo{{-1, -1}};
        std::vector<int> st;
        for (int i = 0; i < int(A.size()); ++i) {
            while (A[i] > hi.back().first) {
                segtree.add(hi[hi.size() - 2].second + 1, hi.back().second + 1, A[i] - hi.back().first);
                hi.pop_back();
            }
            hi.emplace_back(A[i], i);
            while (A[i] < lo.back().first) {
                segtree.add(lo[lo.size() - 2].second + 1, lo.back().second + 1, lo.back().first - A[i]);
                lo.pop_back();
            }
            lo.emplace_back(A[i], i);

            int h = nodes.size();
            nodes.push_back({NodeType::Leaf, i, i + 1, A[i], A[i], std::vector<int>{}});

            while (true) {
                NodeType join_tp;
                if (st.size() and (join_tp = findtype(st.back(), h)) != NodeType::None) {
                    const node &vtp = nodes[st.back()];
                    // Insert v as the child of the top node in the stack
                    if (join_tp == vtp.tp) {
                        // Append child to existing Join node
                        add_child(st.back(), h);
                        h = st.back();
                        st.pop_back();
                    } else {
                        // Make new join node (with exactly two children)
                        // TODO: Refactor here
                        nodes.push_back({join_tp, std::min(vtp.L, nodes[h].L), std::max(vtp.R, nodes[h].R), std::min(vtp.mini, nodes[h].mini), std::max(vtp.maxi, nodes[h].maxi), {st.back(), h}});
                        h = nodes.size() - 1;
                        st.pop_back();
                    }
                } else if (segtree.prod(0, i + 1 - nodes[h].sz()) == 0) {
                    // Make Cut node
                    // TODO: Refactor here
                    int sz = nodes[h].sz(), L = nodes[h].L, R = nodes[h].R, maxi = nodes[h].maxi, mini = nodes[h].mini;
                    int j;
                    std::vector<int> new_ch{h};
                    do {
                        int j = st.back();
                        st.pop_back();
                        new_ch.push_back(j);
                        node &n = nodes[j];
                        sz += n.sz(), L = n.L, maxi = std::max(maxi, n.maxi), mini = std::min(mini, n.mini);
                    } while (maxi - mini + 1 != sz);
                    std::reverse(new_ch.begin(), new_ch.end());
                    nodes.push_back({NodeType::Cut, L, R, mini, maxi, new_ch});
                    h = nodes.size() - 1;
                } else {
                    break;
                }
            }
            st.push_back(h);
            segtree.add(0, i + 1, -1);
        }
        assert(st.size() == 1);
        root = st[0];
    }
    void to_DOT(std::string filename = "") const {
        if (filename.empty()) filename = "permutation_tree_" + std::to_string(A.size()) + ".DOT";

        std::ofstream ss(filename);
        ss << "digraph{\n";
        int nleaf = 0;
        for (int i = 0; i < int(nodes.size()); i++) {
            ss << i << "[\n";
            std::string lbl;
            if (nodes[i].tp == NodeType::Leaf) {
                lbl = "A[" + std::to_string(nleaf) + "] = " + std::to_string(A[nleaf]), nleaf++;
            } else {
                lbl += std::string(nodes[i].tp == NodeType::Cut ? "Cut" : "Join") + "\\n";
                lbl += "[" + std::to_string(nodes[i].L) + ", " + std::to_string(nodes[i].R) + ")";
            }
            ss << "label = \"" << lbl << "\",\n";
            ss << "]\n";
            for (const auto &ch : nodes[i].child) {
                ss << i << " -> " << ch << ";\n";
            }
        }
        ss << "{rank = same;";
        for (int i = 0; i < int(nodes.size()); i++) {
            if (nodes[i].tp == NodeType::Leaf) ss << ' ' << i << ';';
        }
        ss << "}\n";
        ss << "}\n";
        ss.close();
        return;
    }
};
#include <atcoder/modint>
using mint = atcoder::modint998244353;


int main() {
    cin.tie(nullptr), ios::sync_with_stdio(false);

    int N, K;
    cin >> N >> K;
    vector<int> P(N);

    for (auto &x : P) cin >> x;
    for (auto &x : P) x--;

    permutation_tree tree(P);

    vector dp(K + 1, vector<mint>(N + 1));
    dp[0][0] = 1;

    auto rec = [&](auto &&self, int now) -> void {
        auto &v = tree.nodes[now];
        if (v.tp == permutation_tree::NodeType::Cut or v.tp == permutation_tree::NodeType::Leaf) {
            REP(k, K) dp[k + 1][v.R] += dp[k][v.L];
        }

        vector<mint> sum(K);
        for (auto ch : v.child) {
            self(self, ch);
            if (v.tp == permutation_tree::NodeType::JoinAsc or v.tp == permutation_tree::JoinDesc) {
                for (int k = 0; k < K; ++k) {
                    dp[k + 1][tree.nodes[ch].R] += sum[k];
                    sum[k] += dp[k][tree.nodes[ch].L];
                }
            }
        }
    };
    rec(rec, tree.root);

    for (int i = 1; i <= K; i++) cout << dp[i][N].val() << '\n';
}
0