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October 24, 2015 15:57
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#include <bits/stdc++.h> | |
#define REP(i,n) for(int i=0;i<(int)(n);i++) | |
#define ALL(x) (x).begin(),(x).end() | |
using namespace std; | |
typedef long double ld; | |
typedef complex<ld> P; | |
const ld eps = 1e-8, pi = acos(-1.0); | |
ld dot (P a, P b) { return real(conj(a) * b); } | |
ld cross (P a, P b) { return imag(conj(a) * b); } | |
struct C { P p; ld r, val; }; | |
bool operator<(const C &lhs, const C &rhs) { | |
return norm(lhs.p) - lhs.r * lhs.r < norm(rhs.p) - rhs.r * rhs.r; | |
} | |
struct Range { | |
ld angle, width; | |
Range operator*(const Range &rhs) { | |
ld l1 = angle, w1 = width; | |
ld l2 = rhs.angle, w2 = rhs.width; | |
if (l1 > l2) { swap(l1, l2); swap(w1, w2); } | |
if (l2 - l1 < pi) { | |
ld d = w1 + l1 - l2; | |
if (d < eps) return (Range){0, 0}; | |
return (Range){l2, min(w2, d)}; | |
} | |
else { | |
ld d = w2 + l2 - l1 - 2*pi; | |
if (d < eps) return (Range){0, 0}; | |
return (Range){l1, min(w1, d)}; | |
} | |
} | |
Range operator+(const Range &rhs) { | |
if (rhs.width < eps) return *this; | |
ld l1 = angle, w1 = width; | |
ld l2 = rhs.angle, w2 = rhs.width; | |
if (l1 > l2) { swap(l1, l2); swap(w1, w2); } | |
if (l2 - l1 < pi) return (Range){l1, max(w1, w2 + l2 - l1)}; | |
else return (Range){l2, max(w2, w1 + l1 - l2 + 2*pi)}; | |
} | |
}; | |
Range circle_range(const C &c1, const C &c2) { | |
ld w = asin((c1.r + c2.r) / abs(c1.p - c2.p)); | |
ld a = arg(c2.p - c1.p) - w; | |
if (a < -pi) a += 2 * pi; | |
return (Range){a, w * 2}; | |
} | |
int main() { | |
int N; | |
cin >> N; | |
vector<Range> dp(N); | |
vector<C> circle(N); | |
REP(i,N) { | |
ld x, y, r, w; | |
cin >> x >> y >> r >> w; | |
circle[i] = (C){P(x, y), r, w}; | |
} | |
sort(ALL(circle)); | |
REP(i,N) dp[i] = circle_range((C){P(0, 0), 0, 0}, circle[i]); | |
REP(i,N) REP(j,N) { | |
if (i == j) continue; | |
Range range = circle_range(circle[i], circle[j]); | |
dp[j] = dp[j] + range * dp[i]; | |
} | |
ld res = 0; | |
REP(i,N) res += circle[i].val * dp[i].width / 2 / pi; | |
cout << setprecision(9) << fixed; | |
cout << res << endl; | |
return 0; | |
} |
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