結果

問題 No.3318 客に卵をかける
コンテスト
ユーザー noya2
提出日時 2025-11-27 15:33:03
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 13 ms / 2,000 ms
コード長 6,199 bytes
コンパイル時間 3,387 ms
コンパイル使用メモリ 283,060 KB
実行使用メモリ 7,848 KB
最終ジャッジ日時 2025-11-27 15:33:08
合計ジャッジ時間 4,266 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 1
other AC * 3
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 #
raw source code 

#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"


void solve(){
    ll n, x, y, p, q, r; in(n,x,y,p,q,r);
    if (p == q){
        out(n*p);
        return ;
    }
    auto calc = [&](ll pr) -> ld {
        assert(0 <= pr && pr <= n);
        ll ix = x + y * pr;
        ll iscore = p * pr;
        ll rem = n - pr;
        if (rem == 0){
            return iscore;
        }
        if (ix <= r / q){
            ld ret = ix * q * (1 - powl(1 - ld(1) / ix, rem));
            ret += iscore;
            return ret;
        }
        if (ix == 1){
            assert(q > r);
            ld ret = (q - r / ld(ix)) * (rem - 1) + q;
            ret += iscore;
            return ret;
        }
        ld nlim = log1pl(-r / ld(ix * q)) / log1pl(-1 / ld(ix));
        if (nlim >= rem){
            ld ret = ix * q * (1 - powl(1 - ld(1) / ix, rem));
            ret += iscore;
            return ret;
        }
        ll md = floorl(nlim) + 1;
        ld ret = ix * q * (1 - powl(1 - ld(1) / ix, md));
        ret += (q - r / ld(ix)) * (rem - md);
        ret += iscore;
        return ret;
    };
    ll le = 0, ri = n;
    while (ri - le > 2){
        ll m1 = (le + le + ri) / 3;
        ll m2 = (le + ri + ri) / 3;
        ld v1 = calc(m1);
        ld v2 = calc(m2);
        if (v1 < v2){
            le = m1;
        }
        else {
            ri = m2;
        }
    }
    ld ans = 0;
    for (ll pr = le; pr <= ri; pr++){
        chmax(ans,calc(pr));
    }
    // vector<ld> a(n+1);
    // out("a");
    // for (ll pr = 0; pr <= n; pr++){
    //     a[pr] = calc(pr);
    //     out(a[pr]);
    // }
    // vector<ld> b(n);
    // out("b");
    // rep(i,n){
    //     b[i] = a[i+1] - a[i];
    //     out(b[i]);
    // }
    // out();
    // return ;
    // ld ans = 0;
    // for (ll pr = 0; pr <= n; pr++){
    //     chmax(ans,calc(pr));
    // }
    out(ans);
}

int main(){
    int t = 1; in(t);
    while (t--) { solve(); }
}
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