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| #include <cmath>
#include <cstdio>
#include <algorithm>
const double EPS = 1e-6;
inline int sign(const double x) { return x < -EPS ? -1 : x > EPS; }
inline double sqr(const double x) { return x*x; }
int n;
double alpha, lef = 1e10, rig = -1e10, h[501], r[501], X1[501], Y1[501], X2[501], Y2[501];
inline double f(const double x)
{
double fun = .0, tmp;
for (int i = 0; i < n; ++i)
if (sign(tmp = sqr(r[i]) - sqr(x-h[i])) >= 0)
fun = std::max(fun, tmp);
fun = std::sqrt(fun);
for (int i = 0; i < n; ++i)
if (0 <= sign(x-X1[i]) && sign(x-X2[i]) <= 0)
fun = std::max(fun, Y1[i] + (Y2[i]-Y1[i])*(x-X1[i])/(X2[i]-X1[i]));
return fun;
}
inline double simpson(const double l, const double r, const double fl, const double fm, const double fr)
{ return (r-l) * (fl + 4.0*fm + fr) / 6.0; }
inline double autosimpson(const double l, const double r, const double fl, const double fm, const double fr)
{
static double sl, sr, whole;
const double m = (l+r)/2.0;
const double tmp1 = f((l+m)/2), tmp2 = f((m+r)/2);
sl = simpson(l, m, fl, tmp1, fm), sr = simpson(m, r, fm, tmp2, fr), whole = simpson(l, r, fl, fm, fr);
if (sign(sl+sr-whole) == 0) return whole;
return autosimpson(l, m, fl, tmp1, fm) + autosimpson(m, r, fm, tmp2, fr);
}
int main()
{
scanf("%d%lf", &n, &alpha);
alpha = 1 / std::tan(alpha);
for (int i = 0; i <= n; ++i)
{
scanf("%lf", h+i);
h[i] *= alpha;
if (i) h[i] += h[i-1];
}
for (int i = 0; i < n; ++i)
{
scanf("%lf", r+i);
lef = std::min(lef, h[i]-r[i]);
rig = std::max(rig, h[i]+r[i]);
}
rig = std::max(rig, h[n]);
for (int i = 0; i < n; ++i)
if (sign(h[i+1]-h[i]-std::fabs(r[i+1]-r[i])) > 0)
{
X1[i] = h[i] + r[i] * (r[i]-r[i+1]) / (h[i+1]-h[i]);
Y1[i] = std::sqrt(sqr(r[i])-sqr(X1[i]-h[i]));
X2[i] = h[i+1] + r[i+1] * (r[i]-r[i+1]) / (h[i+1]-h[i]);
Y2[i] = std::sqrt(sqr(r[i+1])-sqr(X2[i]-h[i+1]));
}
printf("%.2f", autosimpson(lef, rig, f(lef), f((lef+rig)/2), f(rig)) * 2.0);
}
|
