134 lines
3.3 KiB
C++
134 lines
3.3 KiB
C++
#include<cstdio>
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#include<cmath>
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#include<algorithm>
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#include<cassert>
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using namespace std;
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struct Point
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{
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double x,y;
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Point(double _x=0,double _y=0):x(_x),y(_y) { }
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inline bool operator<(const Point &b) { return x<b.x||(x==b.x&&y<b.y); }
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};
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typedef Point Vector;
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inline Vector operator+(const Vector &a,const Vector &b) { return Vector(a.x+b.x,a.y+b.y); }
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inline Vector operator-(const Vector &a,const Vector &b) { return Vector(a.x-b.x,a.y-b.y); }
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inline Vector operator*(const Vector &a,double b) { return Vector(a.x*b,a.y*b); }
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inline Vector operator/(const Vector &a,double b) { return Vector(a.x/b,a.y/b); }
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inline double Dot(const Vector &a,const Vector &b) { return a.x*b.x+a.y*b.y; }
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inline double Cross(const Vector &a,const Vector &b) { return a.x*b.y-a.y*b.x; }
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inline double Length(const Vector &a) { return sqrt(Dot(a,a)); }
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const double eps=1e-6;
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inline int dcmp(double x) { return fabs(x)<eps?0:(x>0?1:-1); }
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inline bool SIT(const Point &a1,const Point &a2,const Point &b1,const Point &b2)
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{
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double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1),
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c3=Cross(b2-b1,a1-b1),c4=Cross(b2-b1,a2-b1);
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return dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0;
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}
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inline Point LIT(const Point &P,const Vector &v,const Point &Q,const Vector &w)
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{
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Vector u=P-Q;
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double t=Cross(w,u)/Cross(v,w);
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return P+v*t;
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}
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const int maxn=105;
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int n,kase;
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double x[maxn*3+maxn*maxn];
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Point L[maxn][2][2];
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int main()
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{
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#ifdef local
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freopen("pro.in","r",stdin);
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#endif
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while(scanf("%d",&n)==1&&n)
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{
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int c=0; double res=0;
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for(int i=0;i<n;i++)
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{
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double X,H,B;
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scanf("%lf%lf%lf",&X,&H,&B);
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L[i][0][0]=Point(X-B*0.5,0);
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L[i][0][1]=L[i][1][0]=Point(X,H);
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L[i][1][1]=Point(X+B*0.5,0);
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x[c++]=X-B*0.5; x[c++]=X; x[c++]=X+B*0.5;
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}
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#ifdef debug
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printf("Points:\n");
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for(int i=0;i<n;i++)
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printf("(%g,%g)\n(%g,%g)\n(%g,%g)\n"
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,L[i][0][0].x,L[i][0][0].y
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,L[i][0][1].x,L[i][0][1].y
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,L[i][1][1].x,L[i][1][1].y);
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printf("\n");
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#endif
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for(int i=0;i<n;i++) for(int a=0;a<2;a++)
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for(int j=i+1;j<n;j++) for(int b=0;b<2;b++)
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{
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Point &P1=L[i][a][0],&P2=L[i][a][1],&P3=L[j][b][0],&P4=L[j][b][1];
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if(SIT(P1,P2,P3,P4))
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{
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x[c++]=LIT(P1,P2-P1,P3,P4-P3).x;
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double nowx=x[c-1];
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assert(P1.x<=P2.x);
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assert(P3.x<=P4.x);
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assert(P1.x<=nowx&&nowx<=P2.x);
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assert(P3.x<=nowx&&nowx<=P4.x);
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}
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}
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sort(x,x+c);
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c=unique(x,x+c)-x;
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Point l=Point(x[0],0);
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#ifdef debug
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printf("x:\n");
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for(int i=0;i<c;i++) printf("%.5lf\n",x[i]);
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printf("\n");
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#endif
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for(int i=1;i<c;i++)
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{
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Point r=Point(x[i],0);
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double lx=x[i-1],rx=x[i];
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for(int j=0;j<n;j++) for(int a=0;a<2;a++)
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{
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Point &P1=L[j][a][0],&P2=L[j][a][1];
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assert(P1.x<=P2.x);
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if(P1.x<=lx&&lx<=P2.x&&P1.x<=rx&&rx<=P2.x)
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{
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Vector v=P2-P1;
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Point tr=P1+v*(rx-P1.x)/(P2.x-P1.x);
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if(tr.y>=r.y) r=tr;
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}
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}
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l.y=max(l.y,0.0);
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if(dcmp(l.y)||dcmp(r.y))
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{
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res+=Length(r-l);
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#ifdef debug
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printf("i=%d res+=%.5lf l=(%.5lf,%.5lf) r=(%.5lf,%.5lf)\n"
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,i,Length(r-l)
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,l.x,l.y
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,r.x,r.y);
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assert(dcmp(r.x-x[i])==0);
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assert(dcmp(r.y+1));
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#endif
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}
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#ifdef debug
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printf("after i=%d res is %.5lf\n",i,res);
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printf("\n");
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#endif
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l=r;
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}
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printf("Case %d: %.0lf\n\n",++kase,res);
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}
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return 0;
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}
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/*
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1
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100 50 100
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3
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20 30 35
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37 24 29
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60 20 13
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0
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*/
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