QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#16467 | #3008. Rocket Powered Hovercraft | Qingyu | AC ✓ | 3ms | 4392kb | C++20 | 1.7kb | 2021-12-19 23:53:05 | 2022-05-04 08:57:09 |
Judging History
answer
// Problem : Rocket Ship (NAIPC 2019)
// Author : Darcy Best
// Expected Result : AC
// Complexity : O(log(PRECISION))
// Once you know how long both rockets are activated, the other two are
// determinable
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <cstdlib>
using namespace std;
const double PI = acos(-1.0);
const double EPS = 1e-12;
double naive_answer; // Rotate first, then move
double x,y,w,v; // Input
double r,R; // Radii of the circles
double phi;
double sgn(double x){ return x < 0 ? -1 : 1; }
double g(double theta){
double X = r * cos(theta - PI/2);
double Y = r * sin(theta - PI/2) + r;
if(hypot(X,Y) > R) return naive_answer; // bad!
double a = abs(Y - r), b = abs(X);
if(atan2(Y-r,X) > 0) a = -a;
if(X < 0) b = -b;
double tA = a*a*(R*R-Y*Y) + 2*a*b*X*Y + b*b*(R*R-X*X);
double tB = a * X + b * Y;
double tC = a*a + b*b;
double t = max((-sqrt(tA) - tB) / tC,(sqrt(tA) - tB) / tC);
double Xp = X + a*t, Yp = Y + b*t;
double phi_p = atan2(Yp,Xp);
if(phi_p < 0) phi_p += 2*PI;
if(phi_p - phi > EPS) return naive_answer;
return (phi - phi_p) / w + (hypot(Xp-X,Yp-Y) + r * theta) / v;
}
double f(double lo, double hi){
double q1 = (2*lo + hi)/3, q2 = (lo + 2*hi)/3;
double a = g(q1), b = g(q2);
if(fabs(lo-hi) < EPS && fabs(a-b) < EPS) return (a+b)/2;
return a > b ? f(q1,hi) : f(lo,q2);
}
int main(){
cin >> x >> y >> v >> w;
y = abs(y);
r = v / w;
R = hypot(x,y);
phi = atan2(y,x);
naive_answer = g(0);
cout << fixed << setprecision(10) << min(f(0,PI/2),f(PI/2,PI)) << endl;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 3ms
memory: 4248kb
input:
45 179 0.94 3.34
output:
196.4571416878
result:
ok found '196.45714', expected '196.45714', error '0.00000'
Test #2:
score: 0
Accepted
time: 1ms
memory: 4356kb
input:
365 243 1.55 0.15
output:
283.1207010009
result:
ok found '283.12070', expected '283.12070', error '0.00000'
Test #3:
score: 0
Accepted
time: 3ms
memory: 4388kb
input:
356 -176 0.18 0.71
output:
2206.2986086528
result:
ok found '2206.29861', expected '2206.29861', error '0.00000'
Test #4:
score: 0
Accepted
time: 3ms
memory: 4392kb
input:
326 -350 0.14 2.01
output:
3416.5110771656
result:
ok found '3416.51108', expected '3416.51108', error '0.00000'
Test #5:
score: 0
Accepted
time: 3ms
memory: 4324kb
input:
-360 -428 0.65 0.28
output:
864.9603835189
result:
ok found '864.96038', expected '864.96038', error '0.00000'
Test #6:
score: 0
Accepted
time: 3ms
memory: 4392kb
input:
-419 233 0.20 0.74
output:
2399.3423143047
result:
ok found '2399.34231', expected '2399.34231', error '0.00000'
Test #7:
score: 0
Accepted
time: 3ms
memory: 4236kb
input:
365 288 0.91 1.47
output:
510.9559101916
result:
ok found '510.95591', expected '510.95591', error '0.00000'
Test #8:
score: 0
Accepted
time: 3ms
memory: 4348kb
input:
-39 245 0.93 0.29
output:
269.2925950071
result:
ok found '269.29260', expected '269.29260', error '0.00000'
Test #9:
score: 0
Accepted
time: 3ms
memory: 4252kb
input:
66 461 2.17 0.32
output:
215.9964563815
result:
ok found '215.99646', expected '215.99646', error '0.00000'
Test #10:
score: 0
Accepted
time: 0ms
memory: 4184kb
input:
476 380 0.40 0.26
output:
1522.8868326091
result:
ok found '1522.88683', expected '1522.88683', error '0.00000'
Test #11:
score: 0
Accepted
time: 3ms
memory: 4232kb
input:
-459 -314 0.13 0.51
output:
4280.9215740274
result:
ok found '4280.92157', expected '4280.92157', error '0.00000'
Test #12:
score: 0
Accepted
time: 3ms
memory: 4388kb
input:
-38 -31 0.30 0.02
output:
244.0422809796
result:
ok found '244.04228', expected '244.04228', error '0.00000'
Test #13:
score: 0
Accepted
time: 3ms
memory: 4236kb
input:
-282 -57 0.50 0.01
output:
778.3327435529
result:
ok found '778.33274', expected '778.33274', error '0.00000'
Test #14:
score: 0
Accepted
time: 3ms
memory: 4252kb
input:
-261 -155 0.20 0.02
output:
1598.8862728257
result:
ok found '1598.88627', expected '1598.88627', error '0.00000'
Test #15:
score: 0
Accepted
time: 0ms
memory: 4244kb
input:
-135 47 0.68 0.01
output:
415.1412675016
result:
ok found '415.14127', expected '415.14127', error '0.00000'
Test #16:
score: 0
Accepted
time: 3ms
memory: 4184kb
input:
262 0 0.03 0.28
output:
8733.3333333333
result:
ok found '8733.33333', expected '8733.33333', error '0.00000'
Test #17:
score: 0
Accepted
time: 0ms
memory: 4284kb
input:
-10 10 1.00 0.10
output:
31.4159265359
result:
ok found '31.41593', expected '31.41593', error '0.00000'
Test #18:
score: 0
Accepted
time: 2ms
memory: 4184kb
input:
-20 0 1.00 0.10
output:
43.9724223676
result:
ok found '43.97242', expected '43.97242', error '0.00000'
Test #19:
score: 0
Accepted
time: 0ms
memory: 4312kb
input:
-18 112 1.00 0.10
output:
121.1797455767
result:
ok found '121.17975', expected '121.17975', error '0.00000'
Test #20:
score: 0
Accepted
time: 3ms
memory: 4392kb
input:
-18 112 0.10 10.00
output:
1134.4450922035
result:
ok found '1134.44509', expected '1134.44509', error '0.00000'
Test #21:
score: 0
Accepted
time: 3ms
memory: 4264kb
input:
-999 112 0.01 10.00
output:
100526.0703125447
result:
ok found '100526.07031', expected '100526.07031', error '0.00000'
Test #22:
score: 0
Accepted
time: 3ms
memory: 4356kb
input:
-999 112 10.00 0.01
output:
355.6584289993
result:
ok found '355.65843', expected '355.65843', error '0.00000'
Test #23:
score: 0
Accepted
time: 3ms
memory: 4280kb
input:
-1000 0 0.01 0.01
output:
100214.2092653631
result:
ok found '100214.20927', expected '100214.20927', error '0.00000'
Test #24:
score: 0
Accepted
time: 3ms
memory: 4340kb
input:
-1000 0 10.00 10.00
output:
100.2142092654
result:
ok found '100.21421', expected '100.21421', error '0.00000'
Test #25:
score: 0
Accepted
time: 1ms
memory: 4264kb
input:
-1 0 10.00 10.00
output:
0.3665191429
result:
ok found '0.36652', expected '0.36652', error '0.00000'
Test #26:
score: 0
Accepted
time: 3ms
memory: 4288kb
input:
-1 0 0.01 10.00
output:
100.2142092654
result:
ok found '100.21421', expected '100.21421', error '0.00000'
Test #27:
score: 0
Accepted
time: 3ms
memory: 4292kb
input:
-1 0 10.00 0.01
output:
314.2092653611
result:
ok found '314.20927', expected '314.20927', error '0.00000'
Test #28:
score: 0
Accepted
time: 3ms
memory: 4292kb
input:
1000 -1 10.00 0.01
output:
100.0000500166
result:
ok found '100.00005', expected '100.00005', error '0.00000'
Test #29:
score: 0
Accepted
time: 0ms
memory: 4272kb
input:
1000 -1 0.01 10.00
output:
100000.0499999875
result:
ok found '100000.05000', expected '100000.05000', error '0.00000'
Test #30:
score: 0
Accepted
time: 3ms
memory: 4280kb
input:
-862 -92 9.24 0.02
output:
209.2528658706
result:
ok found '209.25287', expected '209.25287', error '0.00000'
Test #31:
score: 0
Accepted
time: 0ms
memory: 4252kb
input:
-22 -8 0.24 0.02
output:
200.3014034502
result:
ok found '200.30140', expected '200.30140', error '0.00000'
Test #32:
score: 0
Accepted
time: 3ms
memory: 4248kb
input:
-574 -49 3.21 0.01
output:
413.7694710348
result:
ok found '413.76947', expected '413.76947', error '0.00000'
Test #33:
score: 0
Accepted
time: 3ms
memory: 4324kb
input:
-693 -228 7.62 0.02
output:
200.3083419730
result:
ok found '200.30834', expected '200.30834', error '0.00000'
Test #34:
score: 0
Accepted
time: 3ms
memory: 4184kb
input:
315 282 9.67 0.02
output:
59.1338985576
result:
ok found '59.13390', expected '59.13390', error '0.00000'