QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#162963#7110. Kuririn MIRACLEucup-team1196TL 118ms3660kbC++233.2kb2023-09-03 18:17:122023-09-03 18:17:13

Judging History

你现在查看的是最新测评结果

  • [2023-09-03 18:17:13]
  • 评测
  • 测评结果:TL
  • 用时:118ms
  • 内存:3660kb
  • [2023-09-03 18:17:12]
  • 提交

answer

/*
     _/_/_/              _/                     _/_/_/                                               
  _/           _/_/_/                        _/         _/    _/    _/_/_/   _/_/_/       _/_/_/   
 _/         _/    _/   _/                   _/  _/_/   _/    _/  _/    _/   _/    _/   _/    _/    
_/         _/    _/   _/                   _/    _/   _/    _/  _/    _/   _/    _/   _/    _/     
 _/_/_/     _/_/_/   _/                     _/_/_/     _/_/_/    _/_/_/   _/    _/     _/_/_/      
                            _/_/_/_/_/                                                    _/       
                                                                                     _/_/_/
*/
#include <bits/stdc++.h>

using namespace std;

constexpr long double pi = acos(-1.0l);
constexpr long double eps = 1e-9;
#define hps eps*0.5
long double a, b, v, r, d;

long double f(long double x) {
    return (long double)2.0l * r / v / (sqrtl(3.0l + sinl(x) * sinl(x)) - sinl(x));
}

long double simpson(long double l,long double r){
    return (r-l)*(f(l)+f(r)+4.0l*f((l+r)/2.0l))/6.0l;
}

long double jf(long double l,long double r,long double ans,long double step){
    long double mid=(1.0l*l+r)/2.0l;
    long double fl=simpson(l,mid),fr=simpson(mid,r);
    if(abs(fl+fr-ans)<15.0l*eps&&step<0.0l)  return ans;
    else return jf(l,mid,fl,step-1.0l)+jf(mid,r,fr,step-1.0l);
}

void solve()
{
srand(998244353);
    cin >> v >> r >> d;
    // cout << v << ' ' << r << ' ' << d << '\n';
    long double l = 1.0l*pi/2.0l, rr = pi;
    auto check = [&](long double mid) {
        long double t = jf((long double)0.0l, mid, simpson(0.0l, mid), 0.0l);
        long double dis = 2.0l * r + v * t;
        //cout<<mid<<'\n';
        //cout << dis << '\n';
        long double delta = d - dis;
        long double shengyu = pi - mid;
        //cout << delta << '\n';
        long double dd = sqrt(delta * delta + 4 * r * r - 4 * r * delta * cos(shengyu));
        long double s1 = 2 * r * sin(shengyu) / dd;
        long double s2 = (sqrtl(3.0l + sinl(mid) * sinl(mid)) - sinl(mid)) * cos(mid) / -2 ;
        //cout<<shengyu<<" "<<s2<<"\n";
        if(s2 < s1) {
            return false;
        } return true;
    };
    for(int i = 1; i <= 100; i++) {
        long double mid = (l + rr) / 2;
        if(check(mid)) {
            rr = mid;
        } else {
            l = mid;
        }
    }
    long double t = jf((long double)0.0l, rr, simpson(0, rr), 0);
    long double shengyu = pi - rr;
    long double dis = 2.0l * r + v * t;
    long double delta = d - dis;
    long double py = 2 *r*sin(shengyu);
    long double px = 2 *r*cos(shengyu);
    long double dd = sqrt(delta * delta + 4 * r * r - 4 * r * delta * cos(shengyu));
    // cout << t << '\n';
    long double t2 = d / v,he = (d - 4 * r ) / v;
    cout << fixed << setprecision(10) << '\n';
    if(t+dd /2 / v > he)
    cout << t2 << '\n';
    else
    cout << t + dd / 2 / v<< '\n';
}

signed main() {

     ios::sync_with_stdio(false);
     cin.tie(nullptr);
     cout.tie(nullptr);
     int t;
     cin >> t;
     while(t--) {
          solve();
     }
     return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 2ms
memory: 3648kb

input:

1
2.00 3 30.0

output:


8.3105799566

result:

ok found '8.3105800', expected '8.3105799', error '0.0000000'

Test #2:

score: 0
Accepted
time: 118ms
memory: 3660kb

input:

100
8.66 6.05 71.59
8.44 8.67 82.55
4.23 9.68 24.74
6.63 9.95 7.45
1.2 7.27 97.55
2.08 2.94 31.61
8.48 5.56 20.16
7.35 5.55 52.48
1.35 8.15 51.23
3.88 9.02 72.37
7.03 1.97 57.03
1.78 4.44 93.44
5.5 6.11 52.94
1.09 9.64 69.01
1.01 3.54 16.78
1.63 4.55 44.06
5.82 5.51 5.92
5.62 2.93 76.01
4.75 4.43 73...

output:


4.4578371330

5.4883608307

5.8486997636

1.1236802413

43.2664800858

8.3054901571

2.3773584906

4.0154860009

37.9481481481

18.6520618557

4.1551236497

27.1789630139

9.6254545455

63.3119266055

16.6138613861

15.0939945133

1.0171821306

6.9496235167

8.1504303414

8.8584474886

1.7697642164...

result:

ok 100 numbers

Test #3:

score: -100
Time Limit Exceeded

input:

1000
7.52 6.68 80.67
5.34 6.82 45.75
3.57 6.35 22.35
9.55 3.65 31.38
9.37 5.73 40.42
1.83 8.38 82.97
4.86 6.13 9.45
3.88 5.34 84.19
6.49 4.15 85.24
6.51 7.23 42.97
3.0 5.98 57.53
9.35 2.76 69.07
6.76 9.16 91.24
2.98 9.89 49.2
9.16 3.85 66.14
1.84 3.03 37.43
8.01 5.04 50.98
4.05 9.86 4.76
5.4 5.49 60...

output:


5.7708826606

8.5674157303

6.2605042017

3.2858638743

4.3137673426

25.1764842491

1.9444444444

11.4062996263

6.8071912335

6.6006144393

10.7277126092

3.8001978533

7.4844843240

16.5100671141

3.7756970302

10.9157110785

3.5175276608

1.1753086420

6.0952874502

14.4431818182

8.4168241292
...

result: