結果

問題 No.2829 GCD Divination
ユーザー noya2noya2
提出日時 2024-08-02 22:53:54
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 301 ms / 2,000 ms
コード長 7,534 bytes
コンパイル時間 3,412 ms
コンパイル使用メモリ 265,656 KB
実行使用メモリ 179,872 KB
最終ジャッジ日時 2024-08-02 22:54:09
合計ジャッジ時間 14,194 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
（要ログイン）

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 269 ms
179,048 KB
testcase_01 AC 269 ms
178,112 KB
testcase_02 AC 269 ms
178,744 KB
testcase_03 AC 268 ms
178,764 KB
testcase_04 AC 267 ms
179,156 KB
testcase_05 AC 273 ms
179,056 KB
testcase_06 AC 275 ms
178,812 KB
testcase_07 AC 277 ms
179,392 KB
testcase_08 AC 275 ms
179,072 KB
testcase_09 AC 276 ms
178,640 KB
testcase_10 AC 269 ms
178,212 KB
testcase_11 AC 301 ms
178,212 KB
testcase_12 AC 270 ms
178,048 KB
testcase_13 AC 270 ms
178,088 KB
testcase_14 AC 272 ms
179,036 KB
testcase_15 AC 292 ms
179,872 KB
testcase_16 AC 270 ms
178,824 KB
testcase_17 AC 272 ms
178,200 KB
testcase_18 AC 268 ms
179,228 KB
testcase_19 AC 274 ms
178,140 KB
testcase_20 AC 273 ms
178,252 KB
testcase_21 AC 269 ms
178,408 KB
testcase_22 AC 266 ms
178,380 KB
testcase_23 AC 272 ms
179,080 KB
testcase_24 AC 297 ms
179,064 KB
testcase_25 AC 267 ms
179,512 KB
testcase_26 AC 270 ms
179,440 KB
testcase_27 AC 266 ms
178,456 KB
testcase_28 AC 297 ms
178,340 KB
testcase_29 AC 267 ms
178,284 KB
testcase_30 AC 267 ms
177,996 KB
testcase_31 AC 266 ms
178,956 KB
testcase_32 AC 264 ms
179,620 KB
testcase_33 AC 265 ms
178,988 KB
testcase_34 AC 270 ms
179,728 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 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
    is >> p.first >> p.second;
    return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "c.cpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/math/sieve.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/math/sieve.hpp"

namespace noya2{

struct Sieve {
    vector<int> primes, factor, mu;
    Sieve (int N = 1024){
        build(N);
    }
    void request(int N){
        int len = n_max();
        if (len >= N) return ;
        while (len < N) len <<= 1;
        build(len);
    }
    int n_max(){ return factor.size()-1; }
  private:
    void build (int N){
        primes.clear();
        factor.resize(N+1); fill(factor.begin(),factor.end(),0);
        mu.resize(N+1); fill(mu.begin(),mu.end(),1);

        for(int n = 2; n <= N; n++) {
            if (factor[n] == 0){
                primes.push_back(n);
                factor[n] = n;
                mu[n] = -1;
            }
            for (int p : primes){
                if(n * p > N || p > factor[n]) break;
                factor[n * p] = p;
                mu[n * p] = p == factor[n] ? 0 : -mu[n];
            }
        }
    }
} sieve;

int mobius_sieve(int n){
    assert(1 <= n && n <= sieve.n_max());
    return sieve.mu[n];
}
bool is_prime_sieve(int n){
    if (n <= 2) return n == 2;
    assert(n <= sieve.n_max());
    return sieve.factor[n] == n;
}

vector<pair<int,int>> prime_factorization_sieve(int n){
    assert(1 <= n && n <= sieve.n_max());
    vector<int> facts;
    while (n > 1){
        int p = sieve.factor[n];
        facts.push_back(p);
        n /= p;
    }
    vector<pair<int,int>> pes;
    int siz = facts.size();
    for (int l = 0, r = 0; l < siz; l = r){
        while (r < siz && facts[r] == facts[l]) r++;
        pes.emplace_back(facts[l],r-l);
    }
    return pes;
}

vector<int> divisor_enumeration_sieve(int n){
    auto pes = prime_factorization_sieve(n);
    vector<int> divs = {1};
    for (auto [p, e] : pes){
        vector<int> nxt; nxt.reserve(divs.size() * (e+1));
        for (auto x : divs){
            for (int tt = 0; tt <= e; tt++){
                nxt.push_back(x);
                x *= p;
            }
        }
        swap(divs,nxt);
    }
    return divs;
}

} // namespace noya2
#line 4 "c.cpp"

const int mx = 10010010;

void solve(){
    int n; in(n);
    vector<pii> pes = prime_factorization_sieve(n);
    vector<int> ds = divisor_enumeration_sieve(n);
    sort(all(ds));
    int sz = ds.size();
    vector<vector<int>> cnt(sz,vector<int>(sz));
    vector<int> buf(mx,0);
    rep(i,sz){
        rep(j,i+1){
            if (ds[i] % ds[j] != 0) continue;
            buf[ds[j]] = ds[i] / ds[j];
        }
        for (auto [p, e] : pes){
            rep(j,i+1){
                if (ds[i] % ds[j] != 0) continue;
                if ((ds[i] / ds[j]) % p != 0) continue;
                buf[ds[j]] -= buf[ds[j]*p];
            }
        }
        rep(j,i+1){
            if (ds[i] % ds[j] != 0) continue;
            cnt[i][j] = buf[ds[j]];
        }
    }
    vector<ld> dp(sz,0);
    repp(i,1,sz){
        ld add = ld(ds[i]) / ld(ds[i]-1);
        ld mul = ld(1) / ld(ds[i]-1);
        rep(j,i){
            dp[i] += (dp[j] + add) * cnt[i][j] * mul;
        }
    }
    out(dp[sz-1]);
    // out(cnt);
}

int main(){
    sieve.request(mx);
    int t = 1; //in(t);
    while (t--) { solve(); }
}
0