結果

問題 No.2120 場合の数の下８桁
ユーザー nagisa5101nagisa5101
提出日時 2023-03-30 02:28:28
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 781 ms / 2,000 ms
コード長 5,485 bytes
コンパイル時間 4,836 ms
コンパイル使用メモリ 276,988 KB
実行使用メモリ 210,944 KB
最終ジャッジ日時 2024-09-21 16:01:36
合計ジャッジ時間 9,948 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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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 1 ms
5,248 KB
testcase_01 AC 2 ms
5,376 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 2 ms
5,376 KB
testcase_06 AC 780 ms
210,816 KB
testcase_07 AC 1 ms
5,376 KB
testcase_08 AC 2 ms
5,376 KB
testcase_09 AC 7 ms
5,376 KB
testcase_10 AC 372 ms
105,216 KB
testcase_11 AC 775 ms
210,944 KB
testcase_12 AC 3 ms
5,376 KB
testcase_13 AC 7 ms
5,376 KB
testcase_14 AC 16 ms
7,552 KB
testcase_15 AC 362 ms
103,424 KB
testcase_16 AC 737 ms
200,320 KB
testcase_17 AC 772 ms
207,104 KB
testcase_18 AC 2 ms
5,376 KB
testcase_19 AC 781 ms
210,944 KB
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ソースコード

diff # 

#include <bits/stdc++.h>
#include <atcoder/all>

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

using namespace std;
using namespace atcoder;

#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repll(i, n) for (long long i = 0; i < (long long)(n); i++)
#define rep2(i, n, m) for (int i = n; i < (int)(m); i++)
#define repll2(i, n, m) for (long long i = n; i < (long long)(m); i++)
#define all(v) v.begin(),v.end()
using ll=long long;
using ld=long double;
using vi=vector<int>;
using vvi=vector<vi>;
using vvvi=vector<vvi>;
using vl=vector<ll>;
using vvl=vector<vl>;
using vvvl=vector<vvl>;
using vld=vector<ld>;
using vvld=vector<vld>;

int dx[8]={1,0,-1,0,1,1,-1,-1};
int dy[8]={0,1,0,-1,1,-1,1,-1};

const double PI = acos(-1);
//const ll MOD=1e9+7;
//const ll MOD=998244353;
const ll INF=(1LL<<60);
const int INF2=(1<<30);
//using mint=modint1000000007;
//using mint=modint998244353;

// referece: https://37zigen.com/linear-sieve/
class LinearSieve {
    public:
        LinearSieve(unsigned int n) : _n(n), min_prime_factor(std::vector<unsigned int>(n + 1)) {
            std::iota(min_prime_factor.begin(), min_prime_factor.end(), 0);
            prime_list.reserve(_n + 1);
            for (unsigned int d = 2; d <= _n; ++d) {
                if (min_prime_factor[d] == d) {
                    prime_list.push_back(d);
                }
                unsigned int prime_max = std::min(min_prime_factor[d], _n / d);
                for (unsigned int prime : prime_list) {
                    if (prime > prime_max) {
                        break;
                    }
                    min_prime_factor[prime * d] = prime;
                }
            }
        }
        unsigned int prime_num() const {
            return prime_list.size();
        }
        const std::vector<unsigned int>& get_prime_list() const {
            return prime_list;
        }
        const std::vector<unsigned int>& get_min_prime_factor() const {
            return min_prime_factor;
        }
    private:
        const unsigned int _n;
        std::vector<unsigned int> min_prime_factor;
        std::vector<unsigned int> prime_list;
};

template <typename mint>
class ArbitraryModBinomialCoefficients {
    public:
        ArbitraryModBinomialCoefficients(unsigned int N) :
            _N(N), _M(mint::mod()), _sieve(LinearSieve(N)), _binom(std::vector<mint>(N + 1)) {
            solve();
        }
        mint operator[](unsigned int k) const {
            return _binom[k];
        }
        const std::vector<mint>& get_coeffs() const {
            return _binom;
        }
        const LinearSieve& get_sieve() const {
            return _sieve;
        }
    private:
        const unsigned int _N, _M;
        const LinearSieve _sieve;
        std::vector<mint> _binom;

        void mod_invs(std::vector<mint>& invs) {
            auto &mpf = _sieve.get_min_prime_factor();
            if (_N >= 1) invs[1] = 1;
            for (unsigned int i = 2; i <= _N; ++i) {
                unsigned int pf = mpf[i];
                if (pf == i) {
                    if (_M % pf) invs[i] = mint(i).inv();
                } else {
                    invs[i] = invs[pf] * invs[i / pf];
                }
            }
        }

        void solve() {
            auto &primes = _sieve.get_prime_list();
            std::vector<unsigned int> d(_N + 1, 0);
            std::vector<unsigned int> p;
            for (unsigned int prime : primes) {
                if (_M % prime) continue;
                p.push_back(prime);
                unsigned int sz = p.size();
                for (unsigned int v = prime; v <= _N; v += prime) {
                    d[v] = sz;
                }
            }
            const unsigned int L = p.size();
            p.insert(p.begin(), 0);
            std::vector<mint> invs(_N + 1);
            mod_invs(invs);
            std::vector<std::vector<mint>> powers(L + 1);
            for (unsigned int i = 1; i <= L; ++i) {
                unsigned int max_index = _N / (p[i] - 1);
                powers[i].resize(max_index + 1);
                mint pi = p[i];
                powers[i][0] = 1;
                for (unsigned int j = 0; j < max_index; ++j) {
                    powers[i][j + 1] = powers[i][j] * pi;
                }
            }
            const unsigned int half = (_N + 1) / 2;
            mint S = 1;
            std::vector<unsigned int> T(L + 1, 0);
            _binom[0] = 1;
            for (unsigned int k = 1; k <= half; ++k) {
                unsigned int num = _N - k + 1, den = k;
                while (d[num]) ++T[d[num]], num /= p[d[num]];
                while (d[den]) --T[d[den]], den /= p[d[den]];
                S *= num * invs[den];
                _binom[k] = S;
                for (unsigned int i = 1; i <= L; ++i) {
                    _binom[k] *= powers[i][T[i]];
                }
            }
            for (unsigned int k = half + 1; k <= _N; ++k) {
                _binom[k] = _binom[_N - k];
            }
        }
};

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

    using mint=atcoder::modint;
    mint::set_mod(100000000);

    int m,n;cin>>m>>n;
    if(n>m){
        cout<<"00000000"<<endl;
        return 0;
    }
    ArbitraryModBinomialCoefficients<mint> AMBC(m);
    int v=AMBC[n].val();
    string ans=to_string(v);
    while(int(ans.size())<8)ans='0'+ans;
    cout<<ans<<endl;
    return 0;
}
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