| #include <iostream> |
| #include <complex> |
| #include <vector> |
| #include <cmath> |
| #include <algorithm> |
| using namespace std; |
|
|
| typedef long double ld; |
| typedef complex<ld> point, vect; |
| typedef vector<point> polygon; |
| typedef polygon::iterator polIter; |
| const ld inf = 1e9; const ld eps = 1e-9; const ld pi = acos(-1.0); |
|
|
| ld area(polygon &p) { |
| ld result = 0.0; |
| for (int i = 0; i < p.size(); i++) |
| result += imag(conj(p[i])*p[(i+1)%p.size()]); |
| return abs(result) / 2.0; |
| } |
|
|
| double dist(point p1, point p2) { |
| return hypot(p1.real() - p2.real(), p1.imag() - p2.imag()); |
| } |
|
|
| double cross(vect a, vect b) { |
| return a.real() * b.imag() - a.imag() * b.real(); |
| } |
|
|
| vect toVec(point a, point b) { |
| return vect(b.real() - a.real(), b.imag() - a.imag()); |
| } |
|
|
| bool ccw(point p, point q, point r) { |
| return cross(toVec(p, q), toVec(p, r)) > 0; |
| } |
|
|
| bool collinear(point p, point q, point r) { |
| return fabs(cross(toVec(p, q), toVec(p, r))) < eps; |
| } |
|
|
| point pivot(0, 0); |
| bool angleCmp(point a, point b) { |
| if (collinear(pivot, a, b)) return dist(pivot, a) < dist(pivot, b); |
| double d1x = a.real() - pivot.real(), d1y = a.imag() - pivot.imag(); |
| double d2x = b.real() - pivot.real(), d2y = b.imag() - pivot.imag(); |
| return (atan2(d1y, d1x) - atan2(d2y, d2x)) < 0; |
| } |
|
|
| polygon CH(polygon P) { |
| int i, j, n = (int)P.size(); |
| if (n <= 3) { |
| if (!(P[0] == P[n-1])) P.push_back(P[0]); |
| return P; |
| } |
| int P0 = 0; |
| for (i = 1; i < n; i++) |
| if (P[i].imag() < P[P0].imag() || (P[i].imag() == P[P0].imag() && P[i].real() > P[P0].real())) |
| P0 = i; |
| point temp = P[0]; P[0] = P[P0]; P[P0] = temp; |
| pivot = P[0]; |
| sort(++P.begin(), P.end(), angleCmp); |
| polygon S; |
| S.push_back(P[n-1]); S.push_back(P[0]); S.push_back(P[1]); |
| i = 2; |
| while (i < n) { |
| j = (int)S.size()-1; |
| if (ccw(S[j-1], S[j], P[i])) S.push_back(P[i++]); |
| else S.pop_back(); |
| } |
| return S; |
| } |
|
|
| int main() { |
| int N, c = 1; |
| while (cin >> N && N != 0) { |
| polygon pol; |
| for (int i = 0; i < N; i++) { |
| double x, y; |
| cin >> x >> y; |
| pol.push_back(point(x, y)); |
| } |
| ld tArea = abs(area(pol)); |
| polygon chull = CH(pol); |
| ld hArea = abs(area(chull)); |
| printf("Tile #%d\n", c); |
| printf("Wasted Space = %.2Lf %%\n\n", ((hArea-tArea)*100)/hArea); |
| c++; |
| } |
| return 0; |
| } |
|
|
