結果

問題 No.2633 Subsequence Combination Score
ユーザー ebi_flyebi_fly
提出日時 2024-02-11 23:23:31
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 107 ms / 2,000 ms
コード長 8,676 bytes
コンパイル時間 4,110 ms
コンパイル使用メモリ 303,076 KB
実行使用メモリ 8,816 KB
最終ジャッジ日時 2024-09-28 19:38:59
合計ジャッジ時間 9,289 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
このコードへのチャレンジ
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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 90 ms
8,312 KB
testcase_01 AC 90 ms
8,312 KB
testcase_02 AC 89 ms
8,316 KB
testcase_03 AC 91 ms
8,336 KB
testcase_04 AC 90 ms
8,332 KB
testcase_05 AC 90 ms
8,456 KB
testcase_06 AC 92 ms
8,340 KB
testcase_07 AC 91 ms
8,460 KB
testcase_08 AC 99 ms
8,584 KB
testcase_09 AC 100 ms
8,712 KB
testcase_10 AC 101 ms
8,816 KB
testcase_11 AC 102 ms
8,652 KB
testcase_12 AC 102 ms
8,552 KB
testcase_13 AC 99 ms
8,676 KB
testcase_14 AC 100 ms
8,628 KB
testcase_15 AC 101 ms
8,712 KB
testcase_16 AC 102 ms
8,684 KB
testcase_17 AC 103 ms
8,676 KB
testcase_18 AC 98 ms
8,680 KB
testcase_19 AC 100 ms
8,608 KB
testcase_20 AC 97 ms
8,716 KB
testcase_21 AC 99 ms
8,712 KB
testcase_22 AC 103 ms
8,712 KB
testcase_23 AC 101 ms
8,584 KB
testcase_24 AC 100 ms
8,712 KB
testcase_25 AC 101 ms
8,580 KB
testcase_26 AC 101 ms
8,708 KB
testcase_27 AC 100 ms
8,584 KB
testcase_28 AC 99 ms
8,708 KB
testcase_29 AC 90 ms
8,316 KB
testcase_30 AC 92 ms
8,188 KB
testcase_31 AC 94 ms
8,184 KB
testcase_32 AC 91 ms
8,312 KB
testcase_33 AC 99 ms
8,712 KB
testcase_34 AC 98 ms
8,584 KB
testcase_35 AC 107 ms
8,712 KB
testcase_36 AC 104 ms
8,712 KB
testcase_37 AC 100 ms
8,584 KB
testcase_38 AC 101 ms
8,700 KB
testcase_39 AC 101 ms
8,696 KB
testcase_40 AC 102 ms
8,676 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 # 

#line 1 "template/template.hpp"
#include <bits/stdc++.h>

#define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++)
#define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--)
#define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++)
#define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()

#line 2 "template/debug_template.hpp"

#line 4 "template/debug_template.hpp"

namespace ebi {

#ifdef LOCAL
#define debug(...)                                                      \
    std::cerr << "LINE: " << __LINE__ << "  [" << #__VA_ARGS__ << "]:", \
        debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif

void debug_out() {
    std::cerr << std::endl;
}

template <typename Head, typename... Tail> void debug_out(Head h, Tail... t) {
    std::cerr << " " << h;
    if (sizeof...(t) > 0) std::cerr << " :";
    debug_out(t...);
}

}  // namespace ebi
#line 2 "template/int_alias.hpp"

#line 4 "template/int_alias.hpp"

namespace ebi {

using ld = long double;
using std::size_t;
using i8 = std::int8_t;
using u8 = std::uint8_t;
using i16 = std::int16_t;
using u16 = std::uint16_t;
using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;

}  // namespace ebi
#line 2 "template/io.hpp"

#line 5 "template/io.hpp"
#include <optional>
#line 7 "template/io.hpp"

namespace ebi {

template <typename T1, typename T2>
std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &pa) {
    return os << pa.first << " " << pa.second;
}

template <typename T1, typename T2>
std::istream &operator>>(std::istream &os, std::pair<T1, T2> &pa) {
    return os >> pa.first >> pa.second;
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &vec) {
    for (std::size_t i = 0; i < vec.size(); i++)
        os << vec[i] << (i + 1 == vec.size() ? "" : " ");
    return os;
}

template <typename T>
std::istream &operator>>(std::istream &os, std::vector<T> &vec) {
    for (T &e : vec) std::cin >> e;
    return os;
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::optional<T> &opt) {
    if (opt) {
        os << opt.value();
    } else {
        os << "invalid value";
    }
    return os;
}

void fast_io() {
    std::cout << std::fixed << std::setprecision(15);
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);
}

}  // namespace ebi
#line 2 "template/utility.hpp"

#line 5 "template/utility.hpp"

#line 7 "template/utility.hpp"

namespace ebi {

template <class T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template <class T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template <class T> T safe_ceil(T a, T b) {
    if (a % b == 0)
        return a / b;
    else if (a >= 0)
        return (a / b) + 1;
    else
        return -((-a) / b);
}

template <class T> T safe_floor(T a, T b) {
    if (a % b == 0)
        return a / b;
    else if (a >= 0)
        return a / b;
    else
        return -((-a) / b) - 1;
}

constexpr i64 LNF = std::numeric_limits<i64>::max() / 4;

constexpr int INF = std::numeric_limits<int>::max() / 2;

const std::vector<int> dy = {1, 0, -1, 0, 1, 1, -1, -1};
const std::vector<int> dx = {0, 1, 0, -1, 1, -1, 1, -1};

}  // namespace ebi
#line 2 "a.cpp"

#include <atcoder/modint>
#include <atcoder/convolution>

#line 2 "modint/base.hpp"

#include <concepts>
#line 6 "modint/base.hpp"

namespace ebi {

template <class T>
concept Modint = requires(T a, T b) {
    a + b;
    a - b;
    a * b;
    a / b;
    a.inv();
    a.val();
    a.pow(std::declval<long long>());
    T::mod();
};

template <Modint mint> std::istream &operator>>(std::istream &os, mint &a) {
    long long x;
    os >> x;
    a = x;
    return os;
}

template <Modint mint>
std::ostream &operator<<(std::ostream &os, const mint &a) {
    return os << a.val();
}

}  // namespace ebi
#line 2 "convolution/online_convolution.hpp"

#line 5 "convolution/online_convolution.hpp"
#include <bit>
#line 7 "convolution/online_convolution.hpp"

#line 9 "convolution/online_convolution.hpp"

namespace ebi {

struct online_convolution {
  private:
    using mint = atcoder::modint998244353;

  public:
    online_convolution() = default;

    mint add(int idx, mint ai, mint bi) {
        assert(p == idx);
        a.emplace_back(ai);
        b.emplace_back(bi);
        int z = std::countr_zero(u32(p + 2)), w = 1 << z;
        if (p + 2 == w) {
            auto a0 = a;
            a0.resize(2 * w);
            atcoder::internal::butterfly(a0);
            fa.emplace_back(a0.begin(), a0.begin() + w);
            auto b0 = b;
            b0.resize(2 * w);
            atcoder::internal::butterfly(b0);
            fb.emplace_back(b0.begin(), b0.begin() + w);
            for (int i = 0; i < 2 * w; i++) a0[i] *= b0[i];
            atcoder::internal::butterfly_inv(a0);
            mint inv_len = mint(2 * w).inv();
            c.resize(2 * p + 2);
            for (int i = 0; i < p + 1; i++) c[p + i] += a0[p + i] * inv_len;
        } else {
            std::vector<mint> a0 = {a.end() - w, a.end()};
            a0.resize(2 * w);
            atcoder::internal::butterfly(a0);
            std::vector<mint> b0 = {b.end() - w, b.end()};
            b0.resize(2 * w);
            atcoder::internal::butterfly(b0);
            for (int i = 0; i < 2 * w; i++) {
                a0[i] = a0[i] * fb[z][i] + fa[z][i] * b0[i];
            }
            atcoder::internal::butterfly_inv(a0);
            mint inv_len = mint(2 * w).inv();
            for (int i = 0; i < w; i++) c[p + i] += a0[w - 1 + i] * inv_len;
        }
        return c[p++];
    }

    mint operator[](int i) const {
        assert(0 <= i && i < p);
        return c[i];
    }

  private:
    int p = 0;
    std::vector<mint> a, b, c;
    std::vector<std::vector<mint>> fa, fb;
};

}  // namespace ebi
#line 2 "math/binomial.hpp"

#line 6 "math/binomial.hpp"
#include <ranges>
#line 8 "math/binomial.hpp"

#line 10 "math/binomial.hpp"

namespace ebi {

template <Modint mint> struct Binomial {
  private:
    static void extend(int len = -1) {
        int sz = (int)fact.size();
        if (len < 0)
            len = 2 * sz;
        else
            len = std::max(2 * sz, (int)std::bit_ceil(std::uint32_t(len)));
        len = std::min(len, mint::mod());
        assert(sz <= len);
        fact.resize(len);
        inv_fact.resize(len);
        for (int i : std::views::iota(sz, len)) {
            fact[i] = fact[i - 1] * i;
        }
        inv_fact[len - 1] = fact[len - 1].inv();
        for (int i : std::views::iota(sz, len) | std::views::reverse) {
            inv_fact[i - 1] = inv_fact[i] * i;
        }
    }

  public:
    Binomial() = default;

    Binomial(int n) {
        extend(n + 1);
    }

    static mint f(int n) {
        if (n >= (int)fact.size()) [[unlikely]] {
            extend(n + 1);
        }
        return fact[n];
    }

    static mint inv_f(int n) {
        if (n >= (int)fact.size()) [[unlikely]] {
            extend(n + 1);
        }
        return inv_fact[n];
    }

    static mint c(int n, int r) {
        if (r < 0 || n < r) return 0;
        return f(n) * inv_f(r) * inv_f(n - r);
    }

    static mint p(int n, int r) {
        if (r < 0 || n < r) return 0;
        return f(n) * inv_f(n - r);
    }

    static mint inv(int n) {
        return inv_f(n) * f(n - 1);
    }

    static void reserve(int n) {
        extend(n + 1);
    }

  private:
    static std::vector<mint> fact, inv_fact;
};

template <Modint mint>
std::vector<mint> Binomial<mint>::fact = std::vector<mint>(2, 1);

template <Modint mint>
std::vector<mint> Binomial<mint>::inv_fact = std::vector<mint>(2, 1);

}  // namespace ebi
#line 9 "a.cpp"

namespace ebi {

using mint = atcoder::modint998244353;

void main_() {
    const int max = 100'010;
    Binomial<mint> binom(max);
    int n;
    std::cin >> n;
    std::vector<int> a(n);
    std::cin >> a;
    std::vector<int> table(max, 0);
    rep(i,0,n) table[a[i]]++;
    online_convolution oc;
    mint ans = 0;
    rep(i,0,max) {
        mint ret = binom.inv_f(i);
        if(i > 0) ret += oc[i-1];
        ret *= mint(2).pow(table[i]) - 1;
        ans += ret * binom.f(i);
        oc.add(i, binom.inv_f(i+1), ret);
    }
    std::cout << ans << '\n';
}

}  // namespace ebi

int main() {
    ebi::fast_io();
    int t = 1;
    // std::cin >> t;
    while (t--) {
        ebi::main_();
    }
    return 0;
}
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