BZOJ3695 滑行

转化模型就变成几层折射率不同的玻璃光要怎么走才能从(0, 0)到(x, y)

我们发现第一次光线射出去的角度确定，之后光的行程是确定的

而且角度和最后到达y时的x成正相关，于是可以二分！

然后物理学学好就可以了QAQ

 1 /**************************************************************
 2     Problem: 3695
 3     User: rausen
 4     Language: C++
 5     Result: Accepted
 6     Time:24 ms
 7     Memory:820 kb
 8 ****************************************************************/
 9
10 #include <cstdio>
11 #include <cmath>
12 #include <algorithm>
13
14 using namespace std;
15 typedef double lf;
16 const lf pi = acos(-1.0);
17 const lf eps = 1e-12;
18 const int N = 105;
19
20 lf ans;
21 int n, x;
22 int h[N], v[N];
23
24 inline lf calc(lf now) {
25     lf res = 0, tmp = 0;
26     int i;
27     for (i = 1; i <= n; ++i) {
28         res += (lf) h[i] / tan(now);
29         tmp += (lf) h[i] / sin(now) / v[i];
30         now = pi / 2 - asin(sin(pi / 2 - now) * v[i + 1] / v[i]);
31     }
32     ans = tmp;
33     return res;
34 }
35
36 int main() {
37     int i;
38     scanf("%d%d", &n, &x);
39     for (i = 1; i <= n; ++i) scanf("%d", h + i);
40     for (i = 1; i <= n; ++i) scanf("%d", v + i);
41     lf l = 0, r = pi / 2, mid;
42     while (l + eps < r) {
43         mid = (l + r) / 2;
44         if (calc(mid) <= x) r = mid;
45         else l = mid;
46     }
47     printf("%.3lf\n", ans);
48     return 0;
49 }