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

 /**************************************************************
     Problem: 3695
     User: rausen
     Language: C++
     Result: Accepted
     Time:24 ms
     Memory:820 kb
 ****************************************************************/

 #include <cstdio>
 #include <cmath>
 #include <algorithm>

 using namespace std;
 typedef double lf;
 const lf pi = acos(-1.0);
 const lf eps = 1e-;
 const int N = ;

 lf ans;
 int n, x;
 int h[N], v[N];

 inline lf calc(lf now) {
     lf res = , tmp = ;
     int i;
     for (i = ; i <= n; ++i) {
         res += (lf) h[i] / tan(now);
         tmp += (lf) h[i] / sin(now) / v[i];
         now = pi /  - asin(sin(pi /  - now) * v[i + ] / v[i]);
     }
     ans = tmp;
     return res;
 }

 int main() {
     int i;
     scanf("%d%d", &n, &x);
     for (i = ; i <= n; ++i) scanf("%d", h + i);
     for (i = ; i <= n; ++i) scanf("%d", v + i);
     lf l = , r = pi / , mid;
     while (l + eps < r) {
         mid = (l + r) / ;
         if (calc(mid) <= x) r = mid;
         else l = mid;
     }
     printf("%.3lf\n", ans);
     return ;
 }