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| #include <cmath>
#include <cstdio>
#include <vector>
#include <cstring>
#include <algorithm>
using std::vector;
inline int sign(const double x)
{
static const double EPS = 1e-8;
if (x > EPS) return 1;
return x < -EPS ? -1 : 0;
}
const double PI = std::acos(-1.0);
const int MAXN = 200;
const int HASHMOD = 65497;
const int SEED = 57123577;
int Testcase, n, cnt, hashid[65536], hashpos[MAXN*MAXN];
struct Point
{
double x, y;
Point() { }
Point(const double a, const double b): x(a), y(b) { }
};
const Point EMPTY(-10086, -12580);
Point O, hash[65536];
inline bool operator!=(const Point& lhs, const Point& rhs) { return sign(lhs.x-rhs.x) || sign(lhs.y-rhs.y); }
inline Point operator-(const Point& lhs, const Point& rhs) { return Point(lhs.x-rhs.x, lhs.y-rhs.y); }
inline bool operator<(const Point& lhs, const Point& rhs) { return sign(lhs.x-rhs.x) < 0 || (sign(lhs.x-rhs.x) == 0 && sign(lhs.y-rhs.y) < 0); }
inline double cross(const Point& A, const Point& B, const Point& C, const Point& D)
{
const double x1 = B.x-A.x, y1 = B.y-A.y;
const double x2 = D.x-C.x, y2 = D.y-C.y;
return x1*y2 - x2*y1;
}
int intersection(const Point& p1, const Point& p2, const Point& p3, const Point& p4, Point& p)
{
const double s1 = cross(p1, p3, p1, p4);
const double s2 = cross(p2, p3, p2, p4);
const double s3 = cross(p3, p1, p3, p2);
const double s4 = cross(p4, p1, p4, p2);
if (s1*s2 < 0 && s3*s4 < 0)
{
p.x = (s1*p2.x - s2*p1.x) / (s1 - s2);
p.y = (s1*p2.y - s2*p1.y) / (s1 - s2);
return 5;
}
return 0;
}
inline bool cmp(const Point& lhs, const Point& rhs) { return std::atan2(lhs.y, lhs.x) < std::atan2(rhs.y, rhs.x); }
inline int locate(const Point& p)
{
const long long x = static_cast<long long>(p.x * 1e8);
const long long y = static_cast<long long>(p.y * 1e8);
int h = ((x * SEED + y) % HASHMOD + HASHMOD) % HASHMOD;
while (hash[h] != EMPTY && hash[h] != p) ++h;
return h;
}
inline int getid(const Point& p)
{
const int h = locate(p);
if (hashid[h] != -1) return hashid[h];
hash[h] = p, hashpos[cnt] = h;
return hashid[h] = cnt++;
}
struct Segment
{
bool arc, vis;
int target;
//Segment() { }
Segment(const int v, const bool isarc): arc(isarc), vis(false), target(v) { }
};
vector<Segment> v[MAXN*MAXN];
void addedge(const Point& x, const Point& y, const bool isarc)
{
const int a = getid(x), b = getid(y);
v[a].push_back(Segment(b, isarc));
if (!isarc) v[b].push_back(Segment(a, isarc));
}
inline double arcarea(const Point& a, const Point& b)
{
double angle = - std::atan2(a.y, a.x) + std::atan2(b.y, b.x);
if (sign(angle) < 0) angle += 2.0*PI;
return 50.0 * (angle - std::sin(angle));
}
inline bool cmp2(const Segment& lhs, const Segment& rhs)
{
if (lhs.target == rhs.target) return (lhs.arc ? 1 : 0) > (rhs.arc ? 1 : 0);
return cmp(hash[hashpos[lhs.target]]-O, hash[hashpos[rhs.target]]-O);
}
double go(int st, vector<Segment>::iterator edge)
{
const int first = st;
vector<int> p;
double res = .0;
do
{
const int target = edge->target;
if (edge->arc)
res += arcarea(hash[hashpos[st]], hash[hashpos[target]]);
edge->vis = true;
p.push_back(st);
for (vector<Segment>::iterator e = v[target].begin(); e != v[target].end(); ++e)
if (edge->arc == e->arc && (edge->arc || e->target == st))
{
edge = e == v[target].begin() ? v[target].end() : e;
--edge;
break;
}
st = target;
}
while (st != first);
p.push_back(first);
for (vector<int>::size_type i = 1; i < p.size(); ++i)
res += cross(O, hash[hashpos[p[i-1]]], O, hash[hashpos[p[i]]]) / 2.0;
return res;
}
double solve()
{
static Point p[MAXN*MAXN], cut[MAXN][2], tmp;
memset(hashid, 0xFF, sizeof(hashid));
memset(hashpos, 0xFF, sizeof(hashpos));
std::fill(hash, hash+65536, EMPTY);
cnt = 0;
for (int i = 0; i < n; ++i)
{
double a, b;
scanf("%lf%lf", &a, &b);
cut[i][0].x = 10.0 * std::cos(a), cut[i][0].y = 10.0 * std::sin(a);
cut[i][1].x = 10.0 * std::cos(b), cut[i][1].y = 10.0 * std::sin(b);
p[2*i] = cut[i][0], p[2*i+1] = cut[i][1];
}
std::sort(p, p+2*n, cmp);
for (int i = 0; i < 2*n; ++i)
addedge(p[i], p[(i+1)%(2*n)], true);
for (int i = 0; i < n; ++i)
{
int tot = 0;
p[tot++] = cut[i][0], p[tot++] = cut[i][1];
for (int j = 0; j < n; ++j)
if (i != j && intersection(cut[i][0], cut[i][1], cut[j][0], cut[j][1], tmp))
p[tot++] = tmp;
std::sort(p, p+tot);
for (int i = 1; i < tot; ++i)
addedge(p[i-1], p[i], false);
}
for (int i = 0; i < cnt; ++i)
{
O = hash[hashpos[i]];
std::sort(v[i].begin(), v[i].end(), cmp2);
}
double ans = .0;
for (int i = 0; i < cnt; ++i)
for (vector<Segment>::iterator e = v[i].begin(); e != v[i].end(); ++e)
if (!e->vis)
{
const double s = go(i, e);
ans = std::max(ans, s);
}
for (int i = 0; i < cnt; ++i)
v[i].clear();
return ans;
}
int main()
{
for (scanf("%d", &Testcase); Testcase--; )
{
scanf("%d", &n);
printf("%.2f\n", solve());
}
}
|
