Created
September 22, 2016 05:59
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typedef long double ld; | |
const ld PI = acos(-1); | |
typedef complex<ld> P; | |
struct L { | |
P a, b, v; | |
L(){} | |
L(P _a, P _b) : a(_a), b(_b), v(b - a) {} | |
}; | |
P rot(P p, ld theta) { | |
ld x = p.real(), y = p.imag(); | |
return P(x * cos(theta) - y * sin(theta), x * sin(theta) + y * cos(theta)); | |
} | |
ld cross(P a, P b) { | |
return imag(conj(a) * b); | |
} | |
P crosspointSS(L l1, L l2) { | |
ld d1 = abs(cross(l2.v, l1.a - l2.a)); // <----???? | |
// ld d1 = abs(cross(l2.v, l1.a - l2.b)); // <----???? | |
// ld d1 = abs(cross(l2.v, l1.b - l2.a)); // <----???? | |
ld d2 = abs(cross(l2.v, l1.b - l2.a)); | |
ld t = d1 / (d1 + d2); | |
return l1.a + t * l1.v; | |
} | |
ld distanceLP(L l, P p) { | |
return abs(cross(l.v, p - l.a)) / abs(l.v); | |
} | |
ld area(P p0, P p1, P p2) { | |
p1 -= p0, p2 -= p0; | |
return abs(cross(p1, p2)) / 2; | |
} | |
signed main() { | |
std::ios::sync_with_stdio(false); | |
std::cin.tie(0); | |
ld N, K; | |
cin >> N >> K; | |
ld theta = 2 * PI / N; | |
P p0(1, 0); | |
P p1 = rot(p0, K * theta); | |
P q0 = rot(p0, theta); | |
P q1 = rot(q0, - K * theta); | |
L l(p0, p1); | |
L m(q0, q1); | |
P C = crosspointSS(l, m); | |
const P O(0, 0); | |
ld ans = N * (area(O, p0, q0) - area(C, p0, q0)); | |
cout << setprecision(10) << ans << endl; | |
} |
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