112 lines
2.4 KiB
C++
112 lines
2.4 KiB
C++
#include <iostream>
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#include <cstdio>
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#include <cstring>
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#include <cmath>
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#include <algorithm>
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#define PI acos(-1.0)
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using namespace std;
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struct Node
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{
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double h,x;
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};
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Node a[1005],b[1005],st[1005];
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double L;
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int n,T1,T2,top;
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inline int DB(double x)
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{
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if(x>1e-10) return 1;
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if(x<-1e-10) return -1;
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return 0;
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}
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double cal1(Node a,Node b)
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{
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double k=(a.h-b.h)/(a.x-b.x);
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double x=a.x-a.h/k;
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return x;
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}
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double cal2(double x1,double x2,double h,int t)
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{
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double a=sqrt(h*h+x2*x2)-sqrt(h*h+x1*x1);
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double b=(x2-x1)*cos(PI/12.0*t);
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double c=12.0/PI;
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return c*(a-b);
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}
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double cal(double x1,double x2,double h,int t)
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{
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double B1,B2,B3;
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if(DB(x1)==0) B1=PI/2;
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else B1=atan(fabs(h/x1));
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B2=atan(fabs(h/x2));
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B3=PI/12*t;
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if(DB(B3-B1)>=0) return cal2(x1,x2,h,t);
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if(DB(B2-B3)>=0) return 0;
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double k=-tan(B3);
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return cal2(-h/k,x2,h,t);
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}
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int OK(Node a,Node b,Node c)
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{
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double k1=(a.h-b.h)/(a.x-b.x);
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double k2=(b.h-c.h)/(b.x-c.x);
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if(DB(k1-k2)==-1) return 1;
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return 0;
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}
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double solve(int t,Node a[])
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{
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top=0;
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st[++top]=a[1];
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double ans=0;
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int i,j;
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double x1,x2;
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for(i=2;i<=n;i++)
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{
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x1=a[i-1].x;
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x2=a[i-1].x;
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for(j=top;j>=2;j--)
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{
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x2=cal1(st[j-1],st[j]);
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if(DB(x2-a[i].x)>=0) break;
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ans+=cal(x1-st[j].x,x2-st[j].x,st[j].h,t);
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x1=x2;
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}
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ans+=cal(x1-st[j].x,a[i].x-st[j].x,st[j].h,t);
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while(top>=2&&OK(st[top-1],st[top],a[i])||top>=1&&DB(a[i].h-st[top].h)>=0)
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top--;
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st[++top]=a[i];
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}
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return ans;
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}
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int cmp(Node a,Node b)
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{
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return a.x<b.x;
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}
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double deal(int t)
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{
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double ans=0;
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int i;
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for(i=1;i<=n;i++)
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{
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b[i]=a[n+1-i];
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b[i].x=L-b[i].x;
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}
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double xx,yy,zz;
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if(t<=6) ans=solve(t,a);
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else
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{
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ans=solve(6,a);
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ans+=solve(6,b)-solve(12-t,b);
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}
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return ans;
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}
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int main()
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{
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while(scanf("%lf%d",&L,&n),n||L)
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{
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scanf("%d%d",&T1,&T2);
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int i;
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for(i=1;i<=n;i++) scanf("%lf%lf",&a[i].x,&a[i].h);
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sort(a+1,a+n+1,cmp);
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printf("%.5lf\n",deal(T2-6)-deal(T1-6));
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}
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return 0;
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}
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