2017/finals/poles.cpp

// Hacker Cup 2017
// Final Round
// Fox Poles
// Jacob Plachta

#include <algorithm>
#include <functional>
#include <numeric>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <complex>
#include <cstdlib>
#include <ctime>
#include <cstring>
#include <cassert>
#include <string>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <sstream>
using namespace std;

#define LL long long
#define LD long double
#define PR pair<int,int>

#define Fox(i,n) for (i=0; i<n; i++)
#define Fox1(i,n) for (i=1; i<=n; i++)
#define FoxI(i,a,b) for (i=a; i<=b; i++)
#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
#define FoxR1(i,n) for (i=n; i>0; i--)
#define FoxRI(i,a,b) for (i=b; i>=a; i--)
#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
#define Min(a,b) a=min(a,b)
#define Max(a,b) a=max(a,b)
#define Sz(s) int((s).size())
#define All(s) (s).begin(),(s).end()
#define Fill(s,v) memset(s,v,sizeof(s))
#define pb push_back
#define mp make_pair
#define x first
#define y second

template<typename T> T Abs(T x) { return(x<0 ? -x : x); }
template<typename T> T Sqr(T x) { return(x*x); }

const int INF = (int)1e9;
const LD EPS = 1e-10;
const LD PI = acos(-1.0);

bool Read(int &x)
{
	char c,r=0,n=0;
	x=0;
		for(;;)
		{
			c=getchar();
				if ((c<0) && (!r))
					return(0);
				if ((c=='-') && (!r))
					n=1;
				else
				if ((c>='0') && (c<='9'))
					x=x*10+c-'0',r=1;
				else
				if (r)
					break;
		}
		if (n)
			x=-x;
	return(1);
}

#define LIM 800001

pair<int,LD> O[LIM],P[LIM];
LD mx[LIM];
vector<int> ch[LIM];
int ss,st[LIM];

LD Calc(LD h,LD a1,LD a2)
{
	return(-h*(log(cos(a2))-log(cos(a1))));
}

int main()
{
	// vars
	int T,t;
	int N;
	bool D[2];
	LD A[2];
	int i,j,c,p,w,z;
	double v;
	LD a,a1,a2,tot,ans[2];
	// testcase loop
	Read(T);
		Fox1(t,T)
		{
			// input
			Read(N);
				Fox(i,2)
				{
					Read(j);
					D[i]=int(j<0);
					A[i]=j*PI/180;
				}
				Fox(i,N)
				{
					scanf("%d%lf",&O[i].x,&v);
					O[i].y=v;
				}
			// consider each direction
				Fox(z,2)
				{
					// reverse poles horizontally if necessary
					memcpy(P,O,sizeof(P));
						if (D[z])
							Fox(i,N)
								P[i].x=-P[i].x;
					// sort poles left-to-right
					sort(P,P+N);
					// init
						Fox(i,N+1)
							ch[i].clear();
					// consider poles left-to-right, constructing convex hull of coverage
					ss=0;
						Fox(i,N)
						{
							// find this pole's parent, if any
								while (ss>0)
								{
									j=st[ss-1];
									a=atan2(P[i].x-P[j].x,P[j].y-P[i].y);
										if (a<mx[j]-EPS)
											break;
									ss--;
								}
								if (!ss)
								{
									mx[i]=Abs(A[z]);
									ch[N].pb(i);
								}
								else
								{
									mx[i]=a;
									ch[j].pb(i);
								}
							st[ss++]=i;
						}
					// augment tree
						Fox(j,Sz(ch[N])-1)
							ch[ch[N][j]].pb(ch[N][j+1]);
						Fox(i,N)
							Fox(j,Sz(ch[i])-1)
								ch[ch[i][j]].pb(ch[i][j+1]);
					// consider each left pole
					ans[z]=0;
						Fox(i,N)
						{
							a=0;
								Fox(c,Sz(ch[i]))
								{
									j=ch[i][c];
									a1=max(a,atan2(P[j].x-P[i].x,P[i].y));
									a2=atan2(P[j].x-P[i].x,P[i].y-P[j].y);
									// partial shadow until bottom
										if (a1>mx[i]-EPS)
											break;
									ans[z]+=Calc(P[i].y,a,a1);
									// full shadow until top
									w=P[j].x-P[i].x;
										if (a2>mx[i]-EPS)
										{
											ans[z]+=w*(mx[i]-a1);
											goto Done;
										}
									ans[z]+=w*(a2-a1);
									a=a2;
								}
							ans[z]+=Calc(P[i].y,a,mx[i]);
Done:;
						}
				}
			// compute answer
				if (D[0]==D[1])
					tot=Abs(ans[0]-ans[1]);
				else
					tot=ans[0]+ans[1];
			tot/=A[1]-A[0];
			// output
			printf("Case #%d: %.9lf\n",t,(double)tot);
		}
	return(0);
}