結果

問題 No.1753 Don't cheat.
ユーザー 👑 hitonanodehitonanode
提出日時 2021-11-19 22:45:36
言語 C++23(draft)
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 267 ms / 3,000 ms
コード長 14,254 bytes
コンパイル時間 2,847 ms
コンパイル使用メモリ 179,176 KB
実行使用メモリ 31,992 KB
最終ジャッジ日時 2023-08-30 09:37:48
合計ジャッジ時間 11,006 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge12
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 137 ms
4,384 KB
testcase_01 AC 227 ms
10,228 KB
testcase_02 AC 211 ms
4,380 KB
testcase_03 AC 212 ms
4,380 KB
testcase_04 AC 210 ms
4,380 KB
testcase_05 AC 210 ms
4,380 KB
testcase_06 AC 210 ms
4,384 KB
testcase_07 AC 265 ms
31,852 KB
testcase_08 AC 265 ms
31,900 KB
testcase_09 AC 264 ms
31,724 KB
testcase_10 AC 265 ms
31,936 KB
testcase_11 AC 264 ms
31,992 KB
testcase_12 AC 264 ms
31,992 KB
testcase_13 AC 265 ms
31,736 KB
testcase_14 AC 264 ms
31,784 KB
testcase_15 AC 264 ms
31,740 KB
testcase_16 AC 267 ms
31,736 KB
testcase_17 AC 215 ms
4,888 KB
testcase_18 AC 219 ms
6,600 KB
testcase_19 AC 214 ms
4,848 KB
testcase_20 AC 240 ms
17,396 KB
testcase_21 AC 226 ms
10,240 KB
testcase_22 AC 220 ms
6,604 KB
testcase_23 AC 63 ms
4,376 KB
testcase_24 AC 214 ms
4,932 KB
testcase_25 AC 63 ms
4,380 KB
testcase_26 AC 218 ms
6,824 KB
testcase_27 AC 264 ms
31,944 KB
testcase_28 AC 264 ms
31,752 KB
testcase_29 AC 264 ms
31,852 KB
testcase_30 AC 264 ms
31,784 KB
testcase_31 AC 263 ms
31,828 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;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#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, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
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
constexpr int len = 8;
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
constexpr int len = 1024;
#define dbg(x) (x)
#define dbgif(cond, x) 0
#endif

template <int md> struct ModInt {
#if __cplusplus >= 201402L
#define MDCONST constexpr
#else
#define MDCONST
#endif
    using lint = long long;
    MDCONST static int mod() { return md; }
    static int get_primitive_root() {
        static int primitive_root = 0;
        if (!primitive_root) {
            primitive_root = [&]() {
                std::set<int> fac;
                int v = md - 1;
                for (lint i = 2; i * i <= v; i++)
                    while (v % i == 0) fac.insert(i), v /= i;
                if (v > 1) fac.insert(v);
                for (int g = 1; g < md; g++) {
                    bool ok = true;
                    for (auto i : fac)
                        if (ModInt(g).pow((md - 1) / i) == 1) {
                            ok = false;
                            break;
                        }
                    if (ok) return g;
                }
                return -1;
            }();
        }
        return primitive_root;
    }
    int val;
    MDCONST ModInt() : val(0) {}
    MDCONST ModInt &_setval(lint v) { return val = (v >= md ? v - md : v), *this; }
    MDCONST ModInt(lint v) { _setval(v % md + md); }
    MDCONST explicit operator bool() const { return val != 0; }
    MDCONST ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }
    MDCONST ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + md); }
    MDCONST ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % md); }
    MDCONST ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % md); }
    MDCONST ModInt operator-() const { return ModInt()._setval(md - val); }
    MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
    MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
    MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
    MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
    friend MDCONST ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % md + x.val); }
    friend MDCONST ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % md - x.val + md); }
    friend MDCONST ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.val % md); }
    friend MDCONST ModInt operator/(lint a, const ModInt &x) {
        return ModInt()._setval(a % md * x.inv() % md);
    }
    MDCONST bool operator==(const ModInt &x) const { return val == x.val; }
    MDCONST bool operator!=(const ModInt &x) const { return val != x.val; }
    MDCONST bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map<ModInt, T>
    friend std::istream &operator>>(std::istream &is, ModInt &x) {
        lint t;
        return is >> t, x = ModInt(t), is;
    }
    MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val; }
    MDCONST ModInt pow(lint n) const {
        ModInt ans = 1, tmp = *this;
        while (n) {
            if (n & 1) ans *= tmp;
            tmp *= tmp, n >>= 1;
        }
        return ans;
    }

    static std::vector<ModInt> facs, facinvs, invs;
    MDCONST static void _precalculation(int N) {
        int l0 = facs.size();
        if (N > md) N = md;
        if (N <= l0) return;
        facs.resize(N), facinvs.resize(N), invs.resize(N);
        for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;
        facinvs[N - 1] = facs.back().pow(md - 2);
        for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);
        for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];
    }
    MDCONST lint inv() const {
        if (this->val < std::min(md >> 1, 1 << 21)) {
            while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
            return invs[this->val].val;
        } else {
            return this->pow(md - 2).val;
        }
    }
    MDCONST ModInt fac() const {
        while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
        return facs[this->val];
    }
    MDCONST ModInt facinv() const {
        while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
        return facinvs[this->val];
    }
    MDCONST ModInt doublefac() const {
        lint k = (this->val + 1) / 2;
        return (this->val & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac())
                               : ModInt(k).fac() * ModInt(2).pow(k);
    }
    MDCONST ModInt nCr(const ModInt &r) const {
        return (this->val < r.val) ? 0 : this->fac() * (*this - r).facinv() * r.facinv();
    }
    MDCONST ModInt nPr(const ModInt &r) const {
        return (this->val < r.val) ? 0 : this->fac() * (*this - r).facinv();
    }

    ModInt sqrt() const {
        if (val == 0) return 0;
        if (md == 2) return val;
        if (pow((md - 1) / 2) != 1) return 0;
        ModInt b = 1;
        while (b.pow((md - 1) / 2) == 1) b += 1;
        int e = 0, m = md - 1;
        while (m % 2 == 0) m >>= 1, e++;
        ModInt x = pow((m - 1) / 2), y = (*this) * x * x;
        x *= (*this);
        ModInt z = b.pow(m);
        while (y != 1) {
            int j = 0;
            ModInt t = y;
            while (t != 1) j++, t *= t;
            z = z.pow(1LL << (e - j - 1));
            x *= z, z *= z, y *= z;
            e = j;
        }
        return ModInt(std::min(x.val, md - x.val));
    }
};
template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};
using mint = ModInt<998244353>;

// Fast Walsh-Hadamard transform and its abstraction
// Tutorials: <https://codeforces.com/blog/entry/71899>
//            <https://csacademy.com/blog/fast-fourier-transform-and-variations-of-it>
template <typename T, typename F> void abstract_fwht(std::vector<T>& seq, F f) {
    const int n = seq.size();
    assert(__builtin_popcount(n) == 1);
    for (int w = 1; w < n; w *= 2) {
        for (int i = 0; i < n; i += w * 2) {
            for (int j = 0; j < w; j++) { f(seq[i + j], seq[i + j + w]); }
        }
    }
}

template <typename T, typename F1, typename F2> std::vector<T> bitwise_conv(std::vector<T> x, std::vector<T> y, F1 f, F2 finv) {
    const int n = x.size();
    assert(__builtin_popcount(n) == 1);
    assert(x.size() == y.size());
    if (x == y) {
        abstract_fwht(x, f), y = x;
    } else {
        abstract_fwht(x, f), abstract_fwht(y, f);
    }
    for (size_t i = 0; i < x.size(); i++) { x[i] *= y[i]; }
    abstract_fwht(x, finv);
    return x;
}

// bitwise xor convolution (FWHT-based)
// ret[i] = \sum_j x[j] * y[i ^ j]
// if T is integer, ||x||_1 * ||y||_1 * 2 < numeric_limits<T>::max()
template <typename T> std::vector<T> xorconv(std::vector<T> x, std::vector<T> y) {
    auto f = [](T& lo, T& hi) {
        T c = lo + hi;
        hi = lo - hi, lo = c;
    };
    auto finv = [](T& lo, T& hi) {
        T c = lo + hi;
        hi = (lo - hi) / 2, lo = c / 2; // Reconsider HEAVY complexity of division by 2 when T is ModInt
    };
    return bitwise_conv(x, y, f, finv);
}

// bitwise AND conolution
// ret[i] = \sum_{(j & k) == i} x[j] * y[k]
template <typename T> std::vector<T> andconv(std::vector<T> x, std::vector<T> y) {
    return bitwise_conv(
        x, y, [](T& lo, T& hi) { lo += hi; }, [](T& lo, T& hi) { lo -= hi; });
}

// bitwise OR convolution
// ret[i] = \sum_{(j | k) == i} x[j] * y[k]
template <typename T> std::vector<T> orconv(std::vector<T> x, std::vector<T> y) {
    return bitwise_conv(
        x, y, [](T& lo, T& hi) { hi += lo; }, [](T& lo, T& hi) { hi -= lo; });
}


int main() {
    int N;
    cin >> N;
    vector<mint> A(N + 1);
    // dp[0] = 1;
    cin >> A;
    mint sumainv = accumulate(A.begin(), A.end(), mint(0)).inv();
    for (auto &x : A) x *= sumainv;

    mint p0 = A[0];
    A[0] = 0;

    dbg(A);

    auto f = [](mint &lo, mint &hi) {
        mint c = lo + hi;
        hi = lo - hi, lo = c;
    };
    auto finv = [](mint &lo, mint &hi) {
        mint c = lo + hi;
        hi = (lo - hi) / 2, lo = c / 2; // Reconsider HEAVY complexity of division by 2 when T is ModInt
    };
    A.resize(len);

    mint ret = 0;
    {
        auto trans = A;
        vector<mint> dp(len, 1);
        abstract_fwht(trans, f);
        abstract_fwht(dp, f);
        for (auto &a : trans) a = (1 - a).inv();
        REP(i, dp.size()) dp[i] *= trans[i];
        abstract_fwht(dp, finv);
        dbg(dp);
        ret += dp[0] * p0;
    }

    FOR(i, 1, len) {
        auto trans = A;
        trans[i] = 0;
        vector<mint> dp(len);
        dp[i] = 1;
        abstract_fwht(trans, f);
        abstract_fwht(dp, f);
        for (auto &a : trans) a = (1 - a).inv();
        REP(i, dp.size()) dp[i] *= trans[i];
        abstract_fwht(dp, finv);
        ret -= dp[0] * p0;
    }
    cout << 1 - ret << '\n';
}
0