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// 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);
} |