#718280 (C++17) No.1753 Don't cheat.

• 問題: No.1753 Don't cheat.
• ユーザー: sapphire__15
• 提出日時: 2021-11-20 00:22:45
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 185 ms / 3,000 ms
• コード長: 7,669 bytes
• コンパイル時間: 1,214 ms
• コンパイル使用メモリ: 141,708 KB
• 最終ジャッジ日時: 2025-01-25 21:06:18
• ジャッジサーバーID （参考情報）: judge3 / judge3

ファイルパターン	結果
sample	AC * 2
other	AC * 30

ソースコード

#include <algorithm>
#include <cassert>
#include <climits>
#include <cmath>
#include <iostream>
#include <iterator>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#include <random>
#include <complex>
#include <bitset>
#include <iomanip>
#include <memory>
#include <chrono>
#include <functional>

#define rep(i, n, s) for(int i = (s); i < int(n); i++)
#define per(i, n, s) for(int i = (n - 1); i >= int(s); i--)
#define MM << " " <<
#define all(x) x.begin(), x.end()
#define rall(x) rbegin(x), rend(x)

template <class T>
using MinHeap = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <class T>
using MaxHeap = std::priority_queue<T>;

using ll = long long;
using Pii = std::pair<int, int>;
using Pll = std::pair<ll, ll>;
using Pdd = std::pair<double, double>;

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

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

template <class T>
void vdeb(const std::vector<T> &da) {
    auto n = da.size();
    for (size_t i = 0; i < n; i++) {
        if (i == n - 1)
            std::cout << da[i];
        else
            std::cout << da[i] << " ";
    }
    std::cout << std::endl;
}
template<class T>
void vdeb(const std::vector<std::vector<T>> &da) {
    auto n = da.size();
    for (size_t i = 0; i < n; i++) {
        std::cout << i << " : ";
        vdeb(da[i]);
    }
    std::cout << std::endl;
}

template <>
void vdeb(const std::vector<std::string> &da) {
    auto n = da.size();
    for (size_t i = 0; i < n; i++) { std::cout << da[i] << std::endl; }
}

struct modint {
    long long num;
    const static long long p = 998244353;
    constexpr static long long pow(long long n, long long k) {//n^k(mod p)
        long long ret = 1;
        while(k) {
            if(k&1) ret = ret * n % p;
            n = n * n % p;
            k >>= 1;
        }
        return ret;
    }
    // a*A + b*B = 1
    constexpr static void euclid(long long &a, long long &b) { // a>=b A*b+B*(a-a/b*b)=1
        if (a == 1) {
            a = 1;
        }
        else {
            long long A = b, B = a % b;
            euclid(A, B);
            b = (A - (p + a / b) % p * B % p + p) % p;
            a = B;
        }
    }
    constexpr static long long rev(const long long n) {// n*x-p*y=1
        //long long q = p;
        //euclid(p, n, p);
        //return n % q;
        return pow(n,p-2);
    }
    constexpr modint() : num(0) {}
    constexpr modint(long long x) : num(x%p < 0 ? x%p+p : x%p) {}
    constexpr modint inv() const {return rev(num);}
    modint operator-() const {return modint(p-num);}
    modint& operator+=(const modint &other){
        num = (num + other.num) % p;
        return *this;
    }
    modint& operator-=(const modint &other){
        num = (num - other.num + p) % p;
        return *this;
    }
    modint& operator*=(const modint &other){
        num = (num * other.num) % p;
        return *this;
    }
    modint& operator/=(const modint &other){
        (*this) *= other.inv();
        return *this;
    }
    modint& operator+=(const long long &other){
        num = (num + other) % p;
        return *this;
    }
    modint& operator-=(const long long &other){
        num = (num - other + p) % p;
        return *this;
    }
    modint& operator*=(const long long &other){
        num = (num * other) % p;
        return *this;
    }
    modint& operator/=(const long long &other){
        (*this) *= rev(other);
        return *this;
    }
    modint& operator++(){return *this += 1;}
    modint& operator--(){return *this -= 1;}
    modint& operator=(const long long &other){return (*this) = modint(other);}
    modint operator+(const modint &other) const{return modint(*this) += other;}
    modint operator-(const modint &other) const{return modint(*this) -= other;}
    modint operator*(const modint &other) const{return modint(*this) *= other;}
    modint operator/(const modint &other) const{return modint(*this) /= other;}
    modint operator+(const long long &other) const{return modint(*this) += other;}
    modint operator-(const long long &other) const{return modint(*this) -= other;}
    modint operator*(const long long &other) const{return modint(*this) *= other;}
    modint operator/(const long long &other) const{return modint(*this) /= other;}
    bool operator==(const modint &other) const{return num == other.num;}
};
std::istream& operator>>(std::istream &is, modint x) {
    is >> x.num;
    return is;
}
std::ostream& operator<<(std::ostream &os, const modint &x){
    os << x.num;
    return os;
}
/**
 * @brief fast-Walsh–Hadamard-transform
 * 
 * @tparam T element type of vector
 */
template<class T>
std::vector<T> fast_hadamard_transform(std::vector<T> vec) {
    using hadamard_size_type = typename std::vector<T>::size_type;

    auto vec_size = vec.size();

    assert(((vec_size - 1)&vec_size) == 0); // check vec_size is power of 2
    
    for(hadamard_size_type i = 1; i < vec_size; i = i << 1) {
        auto mask = ~i;
        for(auto j = i; j < vec_size; j = (j+1)|i) {
            T a = vec[j&mask];
            T &b = vec[j];
            vec[j&mask] += b;
            b = a - b;
        }
    }

    return vec;
}

/**
 * @brief invrese-fast-Walsh–Hadamard-transform
 * 
 * @tparam T std::vector<S>
 * @tparam S element type of T
 * @param inv_vec_size inverse of size of vec
 */
template<class T, class S>
auto inv_fast_hadamard_transform
    (T &&vec, S inv_vec_size) {
    auto &&ret = fast_hadamard_transform(std::forward<T>(vec));
    for(auto &i : ret) i *= inv_vec_size;
    return ret;
}

/**
 * @brief invrese-fast-Walsh–Hadamard-transform
 * 
 * @tparam T std::vector<>
 */
template<class T>
auto inv_fast_hadamard_transform (T &&vec) {
    auto vec_size = vec.size();
    auto &&ret = fast_hadamard_transform(std::forward<T>(vec));
    for(auto &i : ret) i /= vec_size;
    return ret;
}

/**
 * @brief bitwise xor convolution using fast-Walsh–Hadamard-transform.
 * 
 * @tparam T element type of vector
 */
template<class T>
std::vector<T> xor_convolution
    (const std::vector<T> &a, const std::vector<T> &b) {
    using xorconv_size_type = typename std::vector<T>::size_type;

    assert(a.size() == b.size());

    auto vec_size = a.size();
    std::vector<T> &&transa = fast_hadamard_transform(a),
                   &&transb = fast_hadamard_transform(b);
    
    for(xorconv_size_type i = 0; i < vec_size; i++) {
        transa[i] *= transb[i];
    }
    std::vector<T> &&ret = inv_fast_hadamard_transform(transa);
    return ret;
}
using namespace std;


using mint = modint;
const int M = 1<<10;
const mint INV = mint(1) / M;

int main() {
    int n; cin >> n;
    vector<int> da(n+1);
    rep(i,n+1,0) {
        cin >> da[i];
    }
    int su = accumulate(all(da), 0);
    vector<mint> base(M);
    rep(i,n+1,1) {
        base[i] += da[i];
        base[i] /= su;
    }
    vector<vector<mint>> li(n+1, base);
    base = fast_hadamard_transform(base);
    rep(i,M,0) base[i] = base[i] / (mint(1) - base[i]);
    base = inv_fast_hadamard_transform(base, INV);
    rep(i,n+1,1) {
        li[i][i] = 0;
        auto tmp = fast_hadamard_transform(li[i]);
        rep(i,M,0) tmp[i] = tmp[i] / (mint(1) - tmp[i]);
        li[i] = inv_fast_hadamard_transform(tmp, INV);
    }
    mint ans = (base[0] + 1) * da[0] / su;
    rep(i,n+1,1) {
        ans += (base[i] - li[i][i]) * da[0] / su;
    }
    cout << mint(1) - ans << endl;
}