几何算法专题

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UVA 10652 Board Wrapping
UVA 11168 Airport
UVA 10256 The Great Divide
UVA 1453 Squares
UVA 1396 Most Distant Point from the Sea
UVA 1298 Triathlon
UVA 1475 Jungle Outpost

UVA 10652 Board Wrapping

#include<bits/stdc++.h>using namespace std;#define For(i,n) for(int i=1;i<=n;i++)#define Fork(i,k,n) for(int i=k;i<=n;i++)#define Rep(i,n) for(int i=0;i<n;i++)#define ForD(i,n) for(int i=n;i;i--)#define ForkD(i,k,n) for(int i=n;i>=k;i--)#define RepD(i,n) for(int i=n;i>=0;i--)#define Forp(x) for(int p=Pre[x];p;p=Next[p])#define Forpiter(x) for(int &p=iter[x];p;p=Next[p])  #define Lson (o<<1)#define Rson ((o<<1)+1)#define MEM(a) memset(a,0,sizeof(a));#define MEMI(a) memset(a,127,sizeof(a));#define MEMi(a) memset(a,128,sizeof(a));#define INF (2139062143)#define F (100000007)#define pb push_back#define mp make_pair #define fi first#define se second#define vi vector<int> #define pi pair<int,int>#define SI(a) ((a).size())typedef long long ll;typedef long double ld;typedef unsigned long long ull;ll mul(ll a,ll b){return (a*b)%F;}ll add(ll a,ll b){return (a+b)%F;}ll sub(ll a,ll b){return (a-b+llabs(a-b)/F*F+F)%F;}void upd(ll &a,ll b){a=(a%F+b%F)%F;}int read(){    int x=0,f=1; char ch=getchar();    while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}    while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}    return x*f;} ll sqr(ll a){return a*a;}ld sqr(ld a){return a*a;}double sqr(double a){return a*a;}ld PI = 3.141592653589793238462643383;class P{public:    double x,y;    P(double x=0,double y=0):x(x),y(y){}    friend long double dis2(P A,P B){return sqr(A.x-B.x)+sqr(A.y-B.y);  }    friend long double Dot(P A,P B) {return A.x*B.x+A.y*B.y; }    friend long double Length(P A) {return sqrt(Dot(A,A)); }    friend long double Angle(P A,P B) {return acos(Dot(A,B) / Length(A) / Length(B) ); }    friend P operator- (P A,P B) { return P(A.x-B.x,A.y-B.y); }    friend P operator+ (P A,P B) { return P(A.x+B.x,A.y+B.y); }    friend P operator* (P A,double p) { return P(A.x*p,A.y*p); }    friend P operator/ (P A,double p) { return P(A.x/p,A.y/p); }    friend bool operator< (const P& a,const P& b) {return a.x<b.x||(a.x==b.x&& a.y<b.y);}}; const double eps=1e-10;int dcmp(double x) {    if (fabs(x)<eps) return 0; else return x<0 ? -1 : 1; }bool operator==(const P& a,const P& b) {    return dcmp(a.x-b.x)==0 && dcmp(a.y-b.y) == 0;} typedef P V;double Cross(V A,V B) {return A.x*B.y - A.y*B.x;}double Area2(P A,P B,P C) {return Cross(B-A,C-A);}//rad 是弧度 逆时针旋转 V Rotate(V A,double rad) {    return V(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));} // A 不是 0向量 V Normal(V A) {     double L = Length(A);    return V(-A.y/L , A.x/L); }namespace complex_G{    typedef complex<double> Point;    //real(p):实部 imag(p):虚部 conj(p):共轭     typedef Point Vector;    double Dot(Vector A,Vector B) {return real(conj(A)*B); }    double Cross(Vector A,Vector B) {return imag(conj(A)*B); }    Vector Rotate(Vector A,double rad) {return A*exp(Point(0,rad)); }}//Cross(v,w)==0(平行)时,不能调这个函数 P GetLineIntersection(P p,V v,P Q,V w){    V u = p-Q;    double t = Cross(w,u)/Cross(v,w);    return p+v*t;}P GetLineIntersectionB(P p,V v,P Q,V w){    return GetLineIntersection(p,v-p,Q,w-Q);}double DistanceToLine(P p,P A,P B) {    V v1 = B-A, v2 = p-A;    return fabs(Cross(v1,v2))/Length(v1);}double DistanceToSegment(P p,P A,P B) {    if (A==B) return Length(p-A);    V v1 = B-A, v2 = p-A, v3 = p - B;    if (dcmp(Dot(v1,v2))<0) return Length(v2);    else if (dcmp(Dot(v1,v3))>0 ) return Length(v3);    else return fabs(Cross(v1,v2) ) / Length(v1);}P GetLineProjection(P p,P A,P B) {    V v=B-A;    return A+v*(Dot(v,p-A)/Dot(v,v));}//规范相交-线段相交且交点不在端点 bool SegmentProperIntersection(P a1,P a2,P b1,P b2) {     double  c1 = Cross(a2-a1,b1-a1) , c2 = Cross(a2-a1,b2-a1),            c3 = Cross(b2-b1,a1-b1) , c4 = Cross(b2-b1,a2-b1);    return dcmp(c1)*dcmp(c2)<0 && dcmp(c3)*dcmp(c4)<0;}//点在线段上（不包含端点） bool OnSegment(P p,P a1,P a2) {    return dcmp(Cross(a1-p,a2-p)) == 0 && dcmp(Dot(a1-p,a2-p))<0;}double PolygonArea(P *p,int n) {    double area=0;    For(i,n-2) area+=Cross(p[i]-p[0],p[i+1]-p[0]);    return area/2;} /*欧拉公式： V+F-E=2 V-点数 F面数 E边数 */P read_point() {    P a;    scanf("%lf%lf",&a.x,&a.y);    return a;   } struct C{    P c;    double r,x,y;    C(P c,double r):c(c),r(r),x(c.x),y(c.y){}    P point(double a) {        return P(c.x+cos(a)*r,c.y+sin(a)*r);    }};struct Line{    P p;    V v;    double ang;    Line(){}    Line(P p,V v):p(p),v(v) {ang=atan2(v.y,v.x); }    bool operator<(const Line & L) const {        return ang<L.ang;    }    P point(double a) {        return p+v*a;    }};int getLineCircleIntersection(Line L,C cir,double &t1,double &t2,vector<P> & sol) {    if (dcmp(DistanceToLine(cir.c,L.p,L.p+L.v)-cir.r)==0) {        sol.pb(GetLineProjection(cir.c,L.p,L.p+L.v));        return 1;    }    double a = L.v.x, b = L.p.x - cir.c.x, c = L.v.y, d= L.p.y - cir.c.y;    double e = a*a+c*c, f = 2*(a*b + c*d), g = b*b+d*d-cir.r*cir.r;    double delta = f*f - 4*e*g;    if (dcmp(delta)<0) return 0;    else if (dcmp(delta)==0) {        t1 = t2 = -f / (2*e); sol.pb(L.point(t1));        return 1;    }     t1 = (-f - sqrt(delta)) / (2*e); sol.pb(L.point(t1));    t2 = (-f + sqrt(delta)) / (2*e); sol.pb(L.point(t2));    return 2;}double angle(V v) {return atan2(v.y,v.x);}int getCircleCircleIntersection(C C1,C C2,vector<P>& sol) {    double d = Length(C1.c-C2.c);    if (dcmp(d)==0) {        if (dcmp(C1.r - C2.r)==0) return -1; //2圆重合         return 0;    }    if (dcmp(C1.r+C2.r-d)<0) return 0;    if (dcmp(fabs(C1.r-C2.r)-d)>0) return 0;    double a = angle(C2.c-C1.c);    double da = acos((C1.r*C1.r+d*d - C2.r*C2.r)/ (2*C1.r*d));    P p1 = C1.point(a-da), p2 = C1.point(a+da);    sol.pb(p1);    if (p1==p2) return 1;    sol.pb(p2);    return 2; }// Tangents-切线 int getTangents(P p,C c,V* v) {    V u= c.c-p;    double dist = Length(u);    if (dist<c.r) return 0;    else if (dcmp(dist-c.r)==0) {        v[0]=Rotate(u,PI/2);        return 1;    } else {        double ang = asin(c.r / dist);        v[0]=Rotate(u,-ang);        v[1]=Rotate(u,ang);        return 2;    }       }//这个函数假设整数坐标和整数半径//double时要把int改成double int getTangents(C A,C B,P* a,P* b) {    int cnt=0;    if (A.r<B.r) {swap(A,B),swap(a,b);}    int d2 = (A.c.x-B.c.x)*(A.c.x-B.c.x) + (A.c.y-B.c.y)*(A.c.y-B.c.y);    int rdiff = A.r-B.r;    int rsum = A.r+B.r;    if (d2<rdiff*rdiff) return 0;    double base = atan2(B.y-A.y,B.x-A.x);    if (d2==0 && A.r == B.r) return -1;    if (d2 == rdiff*rdiff) {        a[cnt] = A.point(base); b[cnt] = B.point(base); ++cnt;        return 1;    }    double ang = acos((A.r-B.r)/sqrt(d2));    a[cnt] = A.point(base+ang); b[cnt] = B.point(base+ang); ++cnt;    a[cnt] = A.point(base-ang); b[cnt] = B.point(base-ang); ++cnt;    if (d2==rsum*rsum) {        a[cnt] = A.point(base); b[cnt] = B.point(PI+base); ++cnt;    }    else if (d2>rsum*rsum) {        double ang = acos((A.r+B.r)/sqrt(d2));        a[cnt] = A.point(base+ang); b[cnt] = B.point(PI+base+ang); ++cnt;        a[cnt] = A.point(base-ang); b[cnt] = B.point(PI+base-ang); ++cnt;    }    return cnt; }//Circumscribed-外接 C CircumscribedCircle(P p1,P p2,P p3) {    double Bx = p2.x-p1.x, By= p2.y-p1.y;    double Cx = p3.x-p1.x, Cy= p3.y-p1.y;    double D = 2*(Bx*Cy-By*Cx);    double cx = (Cy*(Bx*Bx+By*By)-By*(Cx*Cx+Cy*Cy))/D + p1.x;    double cy = (Bx*(Cx*Cx+Cy*Cy)-Cx*(Bx*Bx+By*By))/D + p1.y;    P p =P(cx,cy);    return C(p,Length(p1-p));}//Inscribed-内接 C InscribedCircle(P p1,P p2,P p3) {    double a = Length(p2-p3);    double b = Length(p3-p1);    double c = Length(p1-p2);    P p = (p1*a+p2*b+p3*c)/(a+b+c);    return C(p,DistanceToLine(p,p1,p2));}double torad(double deg) {    return deg/180*acos(-1);}//把 角度+-pi 转换到 [0,pi) 上 double radToPositive(double rad) {    if (dcmp(rad)<0) rad=ceil(-rad/PI)*PI+rad;    if (dcmp(rad-PI)>=0) rad-=floor(rad/PI)*PI;     return rad;} double todeg(double rad) {    return rad*180/acos(-1);}//(R,lat,lng)->(x,y,z)void get_coord(double R,double lat,double lng,double &x,double &y,double &z) {    lat=torad(lat);    lng=torad(lng);    x=R*cos(lat)*cos(lng);    y=R*cos(lat)*sin(lng);    z=R*sin(lat);}void print(double a) {    printf("%.6lf",a); }void print(P p) {    printf("(%.6lf,%.6lf)",p.x,p.y);}template<class T>void print(vector<T> v) {    sort(v.begin(),v.end());    putchar('[');    int n=v.size();    Rep(i,n) {        print(v[i]);        if (i<n-1) putchar(',');     }    puts("]");}// 把直线沿v平移// Translation-平移 Line LineTranslation(Line l,V v) {    l.p=l.p+v;    return l;}void CircleThroughAPointAndTangentToALineWithRadius(P p,Line l,double r,vector<P>& sol) {    V e=Normal(l.v);    Line l1=LineTranslation(l,e*r),l2=LineTranslation(l,e*(-r));    double t1,t2;    getLineCircleIntersection(l1,C(p,r),t1,t2,sol);    getLineCircleIntersection(l2,C(p,r),t1,t2,sol);}void CircleTangentToTwoLinesWithRadius(Line l1,Line l2,double r,vector<P>& sol) {    V e1=Normal(l1.v),e2=Normal(l2.v);    Line L1[2]={LineTranslation(l1,e1*r),LineTranslation(l1,e1*(-r))},         L2[2]={LineTranslation(l2,e2*r),LineTranslation(l2,e2*(-r))};    Rep(i,2) Rep(j,2) sol.pb(GetLineIntersection(L1[i].p,L1[i].v,L2[j].p,L2[j].v));}void CircleTangentToTwoDisjointCirclesWithRadius(C c1,C c2,double r,vector<P>& sol) {    c1.r+=r; c2.r+=r;    getCircleCircleIntersection(c1,c2,sol);}//确定4个点能否组成凸多边形，并按顺序（不一定是逆时针）返回 bool ConvexPolygon(P &A,P &B,P &C,P &D) {    if (SegmentProperIntersection(A,C,B,D)) return 1;    swap(B,C);    if (SegmentProperIntersection(A,C,B,D)) return 1;    swap(D,C);    if (SegmentProperIntersection(A,C,B,D)) return 1;    return 0;}bool IsParallel(P A,P B,P C,P D) {    return dcmp(Cross(B-A,D-C))==0;}bool IsPerpendicular(V A,V B) {    return dcmp(Dot(A,B))==0;}//先调用ConvexPolygon 求凸包并确认是否是四边形// Trapezium-梯形 Rhombus-菱形  bool IsTrapezium(P A,P B,P C,P D){    return IsParallel(A,B,C,D)^IsParallel(B,C,A,D);}bool IsParallelogram(P A,P B,P C,P D) {    return IsParallel(A,B,C,D)&&IsParallel(B,C,A,D);}bool IsRhombus(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&dcmp(Length(B-A)-Length(C-B))==0;}bool IsRectangle(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&IsPerpendicular(B-A,D-A);}bool IsSquare(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&IsPerpendicular(B-A,D-A)&&dcmp(Length(B-A)-Length(C-B))==0;}//chord-弦 arc-弧 double ArcDis(double chord,double r) {    return 2*asin(chord/2/r)*r;} typedef vector<P> Polygon ;int isPointInPolygon(P p,Polygon poly) {    int wn=0;    int n=poly.size();    Rep(i,n) {        if (OnSegment(p,poly[i],poly[(i+1)%n])) return -1;        int k=dcmp(Cross(poly[(i+1)%n]-poly[i],p-poly[i]));        int d1 = dcmp(poly[i].y-p.y);        int d2 = dcmp(poly[(i+1)%n].y-p.y);        if ( k > 0 && d1 <= 0 && d2 > 0 ) wn++;        if ( k < 0 && d2 <= 0 && d1 > 0 ) wn--;    }    if (wn!=0) return 1;    return 0;}int ConvexHull(P *p,int n,P *ch) {    sort(p,p+n);    int m=0;    Rep(i,n) {        while(m>1 && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;        ch[m++]=p[i];    }    int k=m;    RepD(i,n-2) {        while(m>k && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;        ch[m++]=p[i];    }    if ( n > 1 ) m--;    return m;}#define MAXN (2500)P p[MAXN],ch[MAXN];int main(){//  freopen("uva10652.in","r",stdin);//  freopen(".out","w",stdout);    int T=read();    while(T--) {        int n=read(),pc=0;        double area1=0;        Rep(i,n) {            double x,y,w,h,j;            cin>>x>>y>>w>>h>>j;            j=-torad(j);            P o(x,y);            area1+=w*h;            p[pc++]= o + Rotate(V(w/2,h/2),j);            p[pc++]= o + Rotate(V(-w/2,h/2),j);            p[pc++]= o + Rotate(V(w/2,-h/2),j);            p[pc++]= o + Rotate(V(-w/2,-h/2),j);        }        int m=ConvexHull(p,pc,ch);        double area2 = PolygonArea(ch,m);        printf("%.1lf %%\n",area1*100/area2);     }    return 0;}

UVA 11168 Airport

#include<bits/stdc++.h>using namespace std;#define For(i,n) for(int i=1;i<=n;i++)#define Fork(i,k,n) for(int i=k;i<=n;i++)#define Rep(i,n) for(int i=0;i<n;i++)#define ForD(i,n) for(int i=n;i;i--)#define ForkD(i,k,n) for(int i=n;i>=k;i--)#define RepD(i,n) for(int i=n;i>=0;i--)#define Forp(x) for(int p=Pre[x];p;p=Next[p])#define Forpiter(x) for(int &p=iter[x];p;p=Next[p])  #define Lson (o<<1)#define Rson ((o<<1)+1)#define MEM(a) memset(a,0,sizeof(a));#define MEMI(a) memset(a,127,sizeof(a));#define MEMi(a) memset(a,128,sizeof(a));#define INF (2139062143)#define F (100000007)#define pb push_back#define mp make_pair #define fi first#define se second#define vi vector<int> #define pi pair<int,int>#define SI(a) ((a).size())typedef long long ll;typedef long double ld;typedef unsigned long long ull;ll mul(ll a,ll b){return (a*b)%F;}ll add(ll a,ll b){return (a+b)%F;}ll sub(ll a,ll b){return (a-b+llabs(a-b)/F*F+F)%F;}void upd(ll &a,ll b){a=(a%F+b%F)%F;}int read(){    int x=0,f=1; char ch=getchar();    while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}    while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}    return x*f;} ll sqr(ll a){return a*a;}ld sqr(ld a){return a*a;}double sqr(double a){return a*a;}ld PI = 3.141592653589793238462643383;class P{public:    double x,y;    P(double x=0,double y=0):x(x),y(y){}    friend long double dis2(P A,P B){return sqr(A.x-B.x)+sqr(A.y-B.y);  }    friend long double Dot(P A,P B) {return A.x*B.x+A.y*B.y; }    friend long double Length(P A) {return sqrt(Dot(A,A)); }    friend long double Angle(P A,P B) {return acos(Dot(A,B) / Length(A) / Length(B) ); }    friend P operator- (P A,P B) { return P(A.x-B.x,A.y-B.y); }    friend P operator+ (P A,P B) { return P(A.x+B.x,A.y+B.y); }    friend P operator* (P A,double p) { return P(A.x*p,A.y*p); }    friend P operator/ (P A,double p) { return P(A.x/p,A.y/p); }    friend bool operator< (const P& a,const P& b) {return a.x<b.x||(a.x==b.x&& a.y<b.y);}}; const double eps=1e-10;int dcmp(double x) {    if (fabs(x)<eps) return 0; else return x<0 ? -1 : 1; }bool operator==(const P& a,const P& b) {    return dcmp(a.x-b.x)==0 && dcmp(a.y-b.y) == 0;} typedef P V;double Cross(V A,V B) {return A.x*B.y - A.y*B.x;}double Area2(P A,P B,P C) {return Cross(B-A,C-A);}//rad 是弧度 逆时针旋转 V Rotate(V A,double rad) {    return V(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));} // A 不是 0向量 V Normal(V A) {     double L = Length(A);    return V(-A.y/L , A.x/L); }namespace complex_G{    typedef complex<double> Point;    //real(p):实部 imag(p):虚部 conj(p):共轭     typedef Point Vector;    double Dot(Vector A,Vector B) {return real(conj(A)*B); }    double Cross(Vector A,Vector B) {return imag(conj(A)*B); }    Vector Rotate(Vector A,double rad) {return A*exp(Point(0,rad)); }}//Cross(v,w)==0(平行)时,不能调这个函数 P GetLineIntersection(P p,V v,P Q,V w){    V u = p-Q;    double t = Cross(w,u)/Cross(v,w);    return p+v*t;}P GetLineIntersectionB(P p,V v,P Q,V w){    return GetLineIntersection(p,v-p,Q,w-Q);}double DistanceToLine(P p,P A,P B) {    V v1 = B-A, v2 = p-A;    return fabs(Cross(v1,v2))/Length(v1);}double DistanceToSegment(P p,P A,P B) {    if (A==B) return Length(p-A);    V v1 = B-A, v2 = p-A, v3 = p - B;    if (dcmp(Dot(v1,v2))<0) return Length(v2);    else if (dcmp(Dot(v1,v3))>0 ) return Length(v3);    else return fabs(Cross(v1,v2) ) / Length(v1);}P GetLineProjection(P p,P A,P B) {    V v=B-A;    return A+v*(Dot(v,p-A)/Dot(v,v));}//规范相交-线段相交且交点不在端点 bool SegmentProperIntersection(P a1,P a2,P b1,P b2) {     double  c1 = Cross(a2-a1,b1-a1) , c2 = Cross(a2-a1,b2-a1),            c3 = Cross(b2-b1,a1-b1) , c4 = Cross(b2-b1,a2-b1);    return dcmp(c1)*dcmp(c2)<0 && dcmp(c3)*dcmp(c4)<0;}//点在线段上（不包含端点） bool OnSegment(P p,P a1,P a2) {    return dcmp(Cross(a1-p,a2-p)) == 0 && dcmp(Dot(a1-p,a2-p))<0;}double PolygonArea(P *p,int n) {    double area=0;    For(i,n-2) area+=Cross(p[i]-p[0],p[i+1]-p[0]);    return area/2;} /*欧拉公式： V+F-E=2 V-点数 F面数 E边数 */P read_point() {    P a;    scanf("%lf%lf",&a.x,&a.y);    return a;   } struct C{    P c;    double r,x,y;    C(P c,double r):c(c),r(r),x(c.x),y(c.y){}    P point(double a) {        return P(c.x+cos(a)*r,c.y+sin(a)*r);    }};struct Line{    P p;    V v;    double ang;    Line(){}    Line(P p,V v):p(p),v(v) {ang=atan2(v.y,v.x); }    bool operator<(const Line & L) const {        return ang<L.ang;    }    P point(double a) {        return p+v*a;    }};int getLineCircleIntersection(Line L,C cir,double &t1,double &t2,vector<P> & sol) {    if (dcmp(DistanceToLine(cir.c,L.p,L.p+L.v)-cir.r)==0) {        sol.pb(GetLineProjection(cir.c,L.p,L.p+L.v));        return 1;    }    double a = L.v.x, b = L.p.x - cir.c.x, c = L.v.y, d= L.p.y - cir.c.y;    double e = a*a+c*c, f = 2*(a*b + c*d), g = b*b+d*d-cir.r*cir.r;    double delta = f*f - 4*e*g;    if (dcmp(delta)<0) return 0;    else if (dcmp(delta)==0) {        t1 = t2 = -f / (2*e); sol.pb(L.point(t1));        return 1;    }     t1 = (-f - sqrt(delta)) / (2*e); sol.pb(L.point(t1));    t2 = (-f + sqrt(delta)) / (2*e); sol.pb(L.point(t2));    return 2;}double angle(V v) {return atan2(v.y,v.x);}int getCircleCircleIntersection(C C1,C C2,vector<P>& sol) {    double d = Length(C1.c-C2.c);    if (dcmp(d)==0) {        if (dcmp(C1.r - C2.r)==0) return -1; //2圆重合         return 0;    }    if (dcmp(C1.r+C2.r-d)<0) return 0;    if (dcmp(fabs(C1.r-C2.r)-d)>0) return 0;    double a = angle(C2.c-C1.c);    double da = acos((C1.r*C1.r+d*d - C2.r*C2.r)/ (2*C1.r*d));    P p1 = C1.point(a-da), p2 = C1.point(a+da);    sol.pb(p1);    if (p1==p2) return 1;    sol.pb(p2);    return 2; }// Tangents-切线 int getTangents(P p,C c,V* v) {    V u= c.c-p;    double dist = Length(u);    if (dist<c.r) return 0;    else if (dcmp(dist-c.r)==0) {        v[0]=Rotate(u,PI/2);        return 1;    } else {        double ang = asin(c.r / dist);        v[0]=Rotate(u,-ang);        v[1]=Rotate(u,ang);        return 2;    }       }//这个函数假设整数坐标和整数半径//double时要把int改成double int getTangents(C A,C B,P* a,P* b) {    int cnt=0;    if (A.r<B.r) {swap(A,B),swap(a,b);}    int d2 = (A.c.x-B.c.x)*(A.c.x-B.c.x) + (A.c.y-B.c.y)*(A.c.y-B.c.y);    int rdiff = A.r-B.r;    int rsum = A.r+B.r;    if (d2<rdiff*rdiff) return 0;    double base = atan2(B.y-A.y,B.x-A.x);    if (d2==0 && A.r == B.r) return -1;    if (d2 == rdiff*rdiff) {        a[cnt] = A.point(base); b[cnt] = B.point(base); ++cnt;        return 1;    }    double ang = acos((A.r-B.r)/sqrt(d2));    a[cnt] = A.point(base+ang); b[cnt] = B.point(base+ang); ++cnt;    a[cnt] = A.point(base-ang); b[cnt] = B.point(base-ang); ++cnt;    if (d2==rsum*rsum) {        a[cnt] = A.point(base); b[cnt] = B.point(PI+base); ++cnt;    }    else if (d2>rsum*rsum) {        double ang = acos((A.r+B.r)/sqrt(d2));        a[cnt] = A.point(base+ang); b[cnt] = B.point(PI+base+ang); ++cnt;        a[cnt] = A.point(base-ang); b[cnt] = B.point(PI+base-ang); ++cnt;    }    return cnt; }//Circumscribed-外接 C CircumscribedCircle(P p1,P p2,P p3) {    double Bx = p2.x-p1.x, By= p2.y-p1.y;    double Cx = p3.x-p1.x, Cy= p3.y-p1.y;    double D = 2*(Bx*Cy-By*Cx);    double cx = (Cy*(Bx*Bx+By*By)-By*(Cx*Cx+Cy*Cy))/D + p1.x;    double cy = (Bx*(Cx*Cx+Cy*Cy)-Cx*(Bx*Bx+By*By))/D + p1.y;    P p =P(cx,cy);    return C(p,Length(p1-p));}//Inscribed-内接 C InscribedCircle(P p1,P p2,P p3) {    double a = Length(p2-p3);    double b = Length(p3-p1);    double c = Length(p1-p2);    P p = (p1*a+p2*b+p3*c)/(a+b+c);    return C(p,DistanceToLine(p,p1,p2));}double torad(double deg) {    return deg/180*acos(-1);}//把 角度+-pi 转换到 [0,pi) 上 double radToPositive(double rad) {    if (dcmp(rad)<0) rad=ceil(-rad/PI)*PI+rad;    if (dcmp(rad-PI)>=0) rad-=floor(rad/PI)*PI;     return rad;} double todeg(double rad) {    return rad*180/acos(-1);}//(R,lat,lng)->(x,y,z)void get_coord(double R,double lat,double lng,double &x,double &y,double &z) {    lat=torad(lat);    lng=torad(lng);    x=R*cos(lat)*cos(lng);    y=R*cos(lat)*sin(lng);    z=R*sin(lat);}void print(double a) {    printf("%.6lf",a); }void print(P p) {    printf("(%.6lf,%.6lf)",p.x,p.y);}template<class T>void print(vector<T> v) {    sort(v.begin(),v.end());    putchar('[');    int n=v.size();    Rep(i,n) {        print(v[i]);        if (i<n-1) putchar(',');     }    puts("]");}// 把直线沿v平移// Translation-平移 Line LineTranslation(Line l,V v) {    l.p=l.p+v;    return l;}void CircleThroughAPointAndTangentToALineWithRadius(P p,Line l,double r,vector<P>& sol) {    V e=Normal(l.v);    Line l1=LineTranslation(l,e*r),l2=LineTranslation(l,e*(-r));    double t1,t2;    getLineCircleIntersection(l1,C(p,r),t1,t2,sol);    getLineCircleIntersection(l2,C(p,r),t1,t2,sol);}void CircleTangentToTwoLinesWithRadius(Line l1,Line l2,double r,vector<P>& sol) {    V e1=Normal(l1.v),e2=Normal(l2.v);    Line L1[2]={LineTranslation(l1,e1*r),LineTranslation(l1,e1*(-r))},         L2[2]={LineTranslation(l2,e2*r),LineTranslation(l2,e2*(-r))};    Rep(i,2) Rep(j,2) sol.pb(GetLineIntersection(L1[i].p,L1[i].v,L2[j].p,L2[j].v));}void CircleTangentToTwoDisjointCirclesWithRadius(C c1,C c2,double r,vector<P>& sol) {    c1.r+=r; c2.r+=r;    getCircleCircleIntersection(c1,c2,sol);}//确定4个点能否组成凸多边形，并按顺序（不一定是逆时针）返回 bool ConvexPolygon(P &A,P &B,P &C,P &D) {    if (SegmentProperIntersection(A,C,B,D)) return 1;    swap(B,C);    if (SegmentProperIntersection(A,C,B,D)) return 1;    swap(D,C);    if (SegmentProperIntersection(A,C,B,D)) return 1;    return 0;}bool IsParallel(P A,P B,P C,P D) {    return dcmp(Cross(B-A,D-C))==0;}bool IsPerpendicular(V A,V B) {    return dcmp(Dot(A,B))==0;}//先调用ConvexPolygon 求凸包并确认是否是四边形// Trapezium-梯形 Rhombus-菱形  bool IsTrapezium(P A,P B,P C,P D){    return IsParallel(A,B,C,D)^IsParallel(B,C,A,D);}bool IsParallelogram(P A,P B,P C,P D) {    return IsParallel(A,B,C,D)&&IsParallel(B,C,A,D);}bool IsRhombus(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&dcmp(Length(B-A)-Length(C-B))==0;}bool IsRectangle(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&IsPerpendicular(B-A,D-A);}bool IsSquare(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&IsPerpendicular(B-A,D-A)&&dcmp(Length(B-A)-Length(C-B))==0;}//chord-弦 arc-弧 double ArcDis(double chord,double r) {    return 2*asin(chord/2/r)*r;} typedef vector<P> Polygon ;int isPointInPolygon(P p,Polygon poly) {    int wn=0;    int n=poly.size();    Rep(i,n) {        if (OnSegment(p,poly[i],poly[(i+1)%n])) return -1;        int k=dcmp(Cross(poly[(i+1)%n]-poly[i],p-poly[i]));        int d1 = dcmp(poly[i].y-p.y);        int d2 = dcmp(poly[(i+1)%n].y-p.y);        if ( k > 0 && d1 <= 0 && d2 > 0 ) wn++;        if ( k < 0 && d2 <= 0 && d1 > 0 ) wn--;    }    if (wn!=0) return 1;    return 0;}int ConvexHull(P *p,int n,P *ch) {    sort(p,p+n);    int m=0;    Rep(i,n) {        while(m>1 && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;        ch[m++]=p[i];    }    int k=m;    RepD(i,n-2) {        while(m>k && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;        ch[m++]=p[i];    }    if ( n > 1 ) m--;    return m;}#define MAXN (10000+10)P p[MAXN],ch[MAXN];void calc(P A,P B,double &a,double &b,double &c){    a = A.y - B.y;    b = B.x - A.x;    c = Cross(A,B);}int main(){//  freopen("uva11168.in","r",stdin);//  freopen(".out","w",stdout);    int T=read();    For(kcase,T) {        int n=read();        double sx=0,sy=0;        Rep(i,n) {            p[i]=read_point();            sx+=p[i].x; sy+=p[i].y;        }        int m=ConvexHull(p,n,ch);        double ans=0;        Rep(i,m) {            double a,b,c;            calc(ch[i],ch[(i+1)%m],a,b,c);            double d = fabs(a*sx+b*sy+c*n) / sqrt(a*a + b*b);            if (!i) ans=d;            ans=min(ans,d);         }        if (n<=2) ans=0;          printf("Case #%d: %.3lf\n",kcase,ans/n);    }    return 0;}

UVA 10256 The Great Divide

#include<bits/stdc++.h>using namespace std;#define For(i,n) for(int i=1;i<=n;i++)#define Fork(i,k,n) for(int i=k;i<=n;i++)#define Rep(i,n) for(int i=0;i<n;i++)#define ForD(i,n) for(int i=n;i;i--)#define ForkD(i,k,n) for(int i=n;i>=k;i--)#define RepD(i,n) for(int i=n;i>=0;i--)#define Forp(x) for(int p=Pre[x];p;p=Next[p])#define Forpiter(x) for(int &p=iter[x];p;p=Next[p])  #define Lson (o<<1)#define Rson ((o<<1)+1)#define MEM(a) memset(a,0,sizeof(a));#define MEMI(a) memset(a,127,sizeof(a));#define MEMi(a) memset(a,128,sizeof(a));#define INF (2139062143)#define F (100000007)#define pb push_back#define mp make_pair #define fi first#define se second#define vi vector<int> #define pi pair<int,int>#define SI(a) ((a).size())typedef long long ll;typedef long double ld;typedef unsigned long long ull;ll mul(ll a,ll b){return (a*b)%F;}ll add(ll a,ll b){return (a+b)%F;}ll sub(ll a,ll b){return (a-b+llabs(a-b)/F*F+F)%F;}void upd(ll &a,ll b){a=(a%F+b%F)%F;}int read(){    int x=0,f=1; char ch=getchar();    while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}    while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}    return x*f;} ll sqr(ll a){return a*a;}ld sqr(ld a){return a*a;}double sqr(double a){return a*a;}ld PI = 3.141592653589793238462643383;class P{public:    double x,y;    P(double x=0,double y=0):x(x),y(y){}    friend long double dis2(P A,P B){return sqr(A.x-B.x)+sqr(A.y-B.y);  }    friend long double Dot(P A,P B) {return A.x*B.x+A.y*B.y; }    friend long double Length(P A) {return sqrt(Dot(A,A)); }    friend long double Angle(P A,P B) {return acos(Dot(A,B) / Length(A) / Length(B) ); }    friend P operator- (P A,P B) { return P(A.x-B.x,A.y-B.y); }    friend P operator+ (P A,P B) { return P(A.x+B.x,A.y+B.y); }    friend P operator* (P A,double p) { return P(A.x*p,A.y*p); }    friend P operator/ (P A,double p) { return P(A.x/p,A.y/p); }    friend bool operator< (const P& a,const P& b) {return a.x<b.x||(a.x==b.x&& a.y<b.y);}}; const double eps=1e-10;int dcmp(double x) {    if (fabs(x)<eps) return 0; else return x<0 ? -1 : 1; }bool operator==(const P& a,const P& b) {    return dcmp(a.x-b.x)==0 && dcmp(a.y-b.y) == 0;} typedef P V;double Cross(V A,V B) {return A.x*B.y - A.y*B.x;}double Area2(P A,P B,P C) {return Cross(B-A,C-A);}V Rotate(V A,double rad) {    return V(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));} // A ²»ÊÇ 0ÏòÁ¿ V Normal(V A) {     double L = Length(A);    return V(-A.y/L , A.x/L); }namespace complex_G{    typedef complex<double> Point;    //real(p):Êµ²¿ imag(p):Ðé²¿ conj(p):¹²éî     typedef Point Vector;    double Dot(Vector A,Vector B) {return real(conj(A)*B); }    double Cross(Vector A,Vector B) {return imag(conj(A)*B); }    Vector Rotate(Vector A,double rad) {return A*exp(Point(0,rad)); }}//Cross(v,w)==0(Æ½ÐÐ)Ê±,²»ÄÜµ÷Õâ¸öº¯Êý P GetLineIntersection(P p,V v,P Q,V w){    V u = p-Q;    double t = Cross(w,u)/Cross(v,w);    return p+v*t;}P GetLineIntersectionB(P p,V v,P Q,V w){    return GetLineIntersection(p,v-p,Q,w-Q);}double DistanceToLine(P p,P A,P B) {    V v1 = B-A, v2 = p-A;    return fabs(Cross(v1,v2))/Length(v1);}double DistanceToSegment(P p,P A,P B) {    if (A==B) return Length(p-A);    V v1 = B-A, v2 = p-A, v3 = p - B;    if (dcmp(Dot(v1,v2))<0) return Length(v2);    else if (dcmp(Dot(v1,v3))>0 ) return Length(v3);    else return fabs(Cross(v1,v2) ) / Length(v1);}P GetLineProjection(P p,P A,P B) {    V v=B-A;    return A+v*(Dot(v,p-A)/Dot(v,v));}//¹æ·¶Ïà½»-Ïß¶ÎÏà½»ÇÒ½»µã²»ÔÚ¶Ëµã bool SegmentProperIntersection(P a1,P a2,P b1,P b2) {     double  c1 = Cross(a2-a1,b1-a1) , c2 = Cross(a2-a1,b2-a1),            c3 = Cross(b2-b1,a1-b1) , c4 = Cross(b2-b1,a2-b1);    return dcmp(c1)*dcmp(c2)<0 && dcmp(c3)*dcmp(c4)<0;}//µãÔÚÏß¶ÎÉÏ£¨²»°üº¬¶Ëµã£© bool OnSegment(P p,P a1,P a2) {    return dcmp(Cross(a1-p,a2-p)) == 0 && dcmp(Dot(a1-p,a2-p))<0;}double PolygonArea(P *p,int n) {    double area=0;    For(i,n-2) area+=Cross(p[i]-p[0],p[i+1]-p[0]);    return area/2;} /*Å·À¹«Ê½£º V+F-E=2 V-µãÊý FÃæÊý E±ßÊý */P read_point() {    P a;    scanf("%lf%lf",&a.x,&a.y);    return a;   } struct C{    P c;    double r,x,y;    C(P c,double r):c(c),r(r),x(c.x),y(c.y){}    P point(double a) {        return P(c.x+cos(a)*r,c.y+sin(a)*r);    }};struct Line{    P p;    V v;    double ang;    Line(){}    Line(P p,V v):p(p),v(v) {ang=atan2(v.y,v.x); }    bool operator<(const Line & L) const {        return ang<L.ang;    }    P point(double a) {        return p+v*a;    }};int getLineCircleIntersection(Line L,C cir,double &t1,double &t2,vector<P> & sol) {    if (dcmp(DistanceToLine(cir.c,L.p,L.p+L.v)-cir.r)==0) {        sol.pb(GetLineProjection(cir.c,L.p,L.p+L.v));        return 1;    }    double a = L.v.x, b = L.p.x - cir.c.x, c = L.v.y, d= L.p.y - cir.c.y;    double e = a*a+c*c, f = 2*(a*b + c*d), g = b*b+d*d-cir.r*cir.r;    double delta = f*f - 4*e*g;    if (dcmp(delta)<0) return 0;    else if (dcmp(delta)==0) {        t1 = t2 = -f / (2*e); sol.pb(L.point(t1));        return 1;    }     t1 = (-f - sqrt(delta)) / (2*e); sol.pb(L.point(t1));    t2 = (-f + sqrt(delta)) / (2*e); sol.pb(L.point(t2));    return 2;}double angle(V v) {return atan2(v.y,v.x);}int getCircleCircleIntersection(C C1,C C2,vector<P>& sol) {    double d = Length(C1.c-C2.c);    if (dcmp(d)==0) {        if (dcmp(C1.r - C2.r)==0) return -1; //2Ô²ÖØºÏ         return 0;    }    if (dcmp(C1.r+C2.r-d)<0) return 0;    if (dcmp(fabs(C1.r-C2.r)-d)>0) return 0;    double a = angle(C2.c-C1.c);    double da = acos((C1.r*C1.r+d*d - C2.r*C2.r)/ (2*C1.r*d));    P p1 = C1.point(a-da), p2 = C1.point(a+da);    sol.pb(p1);    if (p1==p2) return 1;    sol.pb(p2);    return 2; }// Tangents-ÇÐÏß int getTangents(P p,C c,V* v) {    V u= c.c-p;    double dist = Length(u);    if (dist<c.r) return 0;    else if (dcmp(dist-c.r)==0) {        v[0]=Rotate(u,PI/2);        return 1;    } else {        double ang = asin(c.r / dist);        v[0]=Rotate(u,-ang);        v[1]=Rotate(u,ang);        return 2;    }       }//Õâ¸öº¯Êý¼ÙÉèÕûÊý×ø±êºÍÕûÊý°ë¾¶//doubleÊ±Òª°Ñint¸Ä³Édouble int getTangents(C A,C B,P* a,P* b) {    int cnt=0;    if (A.r<B.r) {swap(A,B),swap(a,b);}    int d2 = (A.c.x-B.c.x)*(A.c.x-B.c.x) + (A.c.y-B.c.y)*(A.c.y-B.c.y);    int rdiff = A.r-B.r;    int rsum = A.r+B.r;    if (d2<rdiff*rdiff) return 0;    double base = atan2(B.y-A.y,B.x-A.x);    if (d2==0 && A.r == B.r) return -1;    if (d2 == rdiff*rdiff) {        a[cnt] = A.point(base); b[cnt] = B.point(base); ++cnt;        return 1;    }    double ang = acos((A.r-B.r)/sqrt(d2));    a[cnt] = A.point(base+ang); b[cnt] = B.point(base+ang); ++cnt;    a[cnt] = A.point(base-ang); b[cnt] = B.point(base-ang); ++cnt;    if (d2==rsum*rsum) {        a[cnt] = A.point(base); b[cnt] = B.point(PI+base); ++cnt;    }    else if (d2>rsum*rsum) {        double ang = acos((A.r+B.r)/sqrt(d2));        a[cnt] = A.point(base+ang); b[cnt] = B.point(PI+base+ang); ++cnt;        a[cnt] = A.point(base-ang); b[cnt] = B.point(PI+base-ang); ++cnt;    }    return cnt; }//Circumscribed-Íâ½Ó C CircumscribedCircle(P p1,P p2,P p3) {    double Bx = p2.x-p1.x, By= p2.y-p1.y;    double Cx = p3.x-p1.x, Cy= p3.y-p1.y;    double D = 2*(Bx*Cy-By*Cx);    double cx = (Cy*(Bx*Bx+By*By)-By*(Cx*Cx+Cy*Cy))/D + p1.x;    double cy = (Bx*(Cx*Cx+Cy*Cy)-Cx*(Bx*Bx+By*By))/D + p1.y;    P p =P(cx,cy);    return C(p,Length(p1-p));}//Inscribed-ÄÚ½Ó C InscribedCircle(P p1,P p2,P p3) {    double a = Length(p2-p3);    double b = Length(p3-p1);    double c = Length(p1-p2);    P p = (p1*a+p2*b+p3*c)/(a+b+c);    return C(p,DistanceToLine(p,p1,p2));}double torad(double deg) {    return deg/180*acos(-1);}//°Ñ ½Ç¶È+-pi ×ª»»µ½ [0,pi) ÉÏ double radToPositive(double rad) {    if (dcmp(rad)<0) rad=ceil(-rad/PI)*PI+rad;    if (dcmp(rad-PI)>=0) rad-=floor(rad/PI)*PI;     return rad;} double todeg(double rad) {    return rad*180/acos(-1);}//(R,lat,lng)->(x,y,z)void get_coord(double R,double lat,double lng,double &x,double &y,double &z) {    lat=torad(lat);    lng=torad(lng);    x=R*cos(lat)*cos(lng);    y=R*cos(lat)*sin(lng);    z=R*sin(lat);}void print(double a) {    printf("%.6lf",a); }void print(P p) {    printf("(%.6lf,%.6lf)",p.x,p.y);}template<class T>void print(vector<T> v) {    sort(v.begin(),v.end());    putchar('[');    int n=v.size();    Rep(i,n) {        print(v[i]);        if (i<n-1) putchar(',');     }    puts("]");}// °ÑÖ±ÏßÑØvÆ½ÒÆ// Translation-Æ½ÒÆ Line LineTranslation(Line l,V v) {    l.p=l.p+v;    return l;}void CircleThroughAPointAndTangentToALineWithRadius(P p,Line l,double r,vector<P>& sol) {    V e=Normal(l.v);    Line l1=LineTranslation(l,e*r),l2=LineTranslation(l,e*(-r));    double t1,t2;    getLineCircleIntersection(l1,C(p,r),t1,t2,sol);    getLineCircleIntersection(l2,C(p,r),t1,t2,sol);}void CircleTangentToTwoLinesWithRadius(Line l1,Line l2,double r,vector<P>& sol) {    V e1=Normal(l1.v),e2=Normal(l2.v);    Line L1[2]={LineTranslation(l1,e1*r),LineTranslation(l1,e1*(-r))},         L2[2]={LineTranslation(l2,e2*r),LineTranslation(l2,e2*(-r))};    Rep(i,2) Rep(j,2) sol.pb(GetLineIntersection(L1[i].p,L1[i].v,L2[j].p,L2[j].v));}void CircleTangentToTwoDisjointCirclesWithRadius(C c1,C c2,double r,vector<P>& sol) {    c1.r+=r; c2.r+=r;    getCircleCircleIntersection(c1,c2,sol);}//È·¶¨4¸öµãÄÜ·ñ×é³ÉÍ¹¶à±ßÐÎ£¬²¢°´Ë³Ðò£¨²»Ò»¶¨ÊÇÄæÊ±Õë£©·µ»Ø bool ConvexPolygon(P &A,P &B,P &C,P &D) {    if (SegmentProperIntersection(A,C,B,D)) return 1;    swap(B,C);    if (SegmentProperIntersection(A,C,B,D)) return 1;    swap(D,C);    if (SegmentProperIntersection(A,C,B,D)) return 1;    return 0;}bool IsParallel(P A,P B,P C,P D) {    return dcmp(Cross(B-A,D-C))==0;}bool IsPerpendicular(V A,V B) {    return dcmp(Dot(A,B))==0;}//ÏÈµ÷ÓÃConvexPolygon ÇóÍ¹°ü²¢È·ÈÏÊÇ·ñÊÇËÄ±ßÐÎ// Trapezium-ÌÝÐÎ Rhombus-ÁâÐÎ  bool IsTrapezium(P A,P B,P C,P D){    return IsParallel(A,B,C,D)^IsParallel(B,C,A,D);}bool IsParallelogram(P A,P B,P C,P D) {    return IsParallel(A,B,C,D)&&IsParallel(B,C,A,D);}bool IsRhombus(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&dcmp(Length(B-A)-Length(C-B))==0;}bool IsRectangle(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&IsPerpendicular(B-A,D-A);}bool IsSquare(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&IsPerpendicular(B-A,D-A)&&dcmp(Length(B-A)-Length(C-B))==0;}//chord-ÏÒ arc-»¡ double ArcDis(double chord,double r) {    return 2*asin(chord/2/r)*r;} typedef vector<P> Polygon ;int isPointInPolygon(P p,Polygon poly) {    int wn=0;    int n=poly.size();    Rep(i,n) {        if (OnSegment(p,poly[i],poly[(i+1)%n])) return -1;        int k=dcmp(Cross(poly[(i+1)%n]-poly[i],p-poly[i]));        int d1 = dcmp(poly[i].y-p.y);        int d2 = dcmp(poly[(i+1)%n].y-p.y);        if ( k > 0 && d1 <= 0 && d2 > 0 ) wn++;        if ( k < 0 && d2 <= 0 && d1 > 0 ) wn--;    }    if (wn!=0) return 1;    return 0;}int ConvexHull(P *p,int n,P *ch) {    sort(p,p+n);    int m=0;    Rep(i,n) {        while(m>1 && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;        ch[m++]=p[i];    }    int k=m;    RepD(i,n-2) {        while(m>k && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;        ch[m++]=p[i];    }    if ( n > 1 ) m--;    return m;}//°ÑÁ½µãÊ½×ªÎªÒ»°ãÊ½ ax+by+c=0 void Two_pointFormToGeneralForm(P A,P B,double &a,double &b,double &c){    a = A.y - B.y;    b = B.x - A.x;    c = Cross(A,B);}//ÓÐÏòÖ±ÏßA->B ÇÐ¸î¶à±ßÐÐpoly ¿ÉÄÜ·µ»Øµ¥µãÏß¶Î O(n)Polygon CutPolygon(Polygon poly,P A,P B){    Polygon newpoly;    int n=poly.size();    Rep(i,n) {        P C = poly[i];        P D = poly[(i+1)%n];        if (dcmp(Cross(B-A,C-A))>=0)  newpoly.pb(C);        if (dcmp(Cross(B-A,C-D))) {            P ip = GetLineIntersection(A,B-A,C,D-C);            if (OnSegment(ip,C,D)) newpoly.pb(ip);        }    }}//ÏßÉÏ²»Ëã bool OnLeft(Line L,P p) {    return Cross(L.v,p-L.p);} P GetIntersection(Line a,Line b) {    V u=a.p-b.p;    double t = Cross(b.v,u) / Cross(a.v, b.v);    return a.p + a.v*t;}int HalfplaneIntersection(Line *L, int n, P* poly) {    sort(L,L+n);    int fi,la;    P *p = new P[n];    Line *q = new Line[n];    q[fi=la=0 ] = L[0];    For(i,n-1) {        while (fi < la && !OnLeft(L[i],p[la-1])) la--;        while (fi < la && !OnLeft(L[i],p[fi])) fi++;        q[++la] = L[i];        if (fabs(Cross(q[la].v, q[la-1].v))<eps) {            la--;            if (OnLeft(q[la],L[i].p)) q[la] = L[i];        }        if (fi<la) p[la-1] = GetIntersection(q[la-1],q[la]);    }    while(fi < la && !OnLeft(q[fi],p[la-1])) la--;    if (la-fi<=1) return 0;     p[la] = GetIntersection(q[la],q[fi]);    int m=0;    Fork(i,fi,la) poly[m++]=p[i];    return m;} // hypot(double x,double y); return sqrt(x*x+y*y)#define MAXM (500+10)int n,m;P a[MAXM],b[MAXM];P polya[MAXM],polyb[MAXM];Polygon pl;bool check() {    Rep(i,n) Rep(j,m) {        if (SegmentProperIntersection(polya[i],polya[(i+1)%n],polyb[j],polyb[(j+1)%m]) ) return 0;    }    pl.clear();    Rep(i,m) pl.pb(polyb[i]);    Rep(i,n) if (isPointInPolygon(polya[i],pl )) return 0;    pl.clear();    Rep(i,n) pl.pb(polya[i]);    Rep(i,m) if (isPointInPolygon(polyb[i],pl )) return 0;    return 1;}int main(){//  freopen("uva10256.in","r",stdin);//  freopen(".out","w",stdout);    while(cin>>n>>m&&n&&m) {        Rep(i,n) a[i]=read_point();        Rep(i,m) b[i]=read_point();        n=ConvexHull(a,n,polya);        m=ConvexHull(b,m,polyb);        puts(check()?"Yes":"No");    }    return 0;}

UVA 1453 Squares

#include<bits/stdc++.h>using namespace std;#define For(i,n) for(int i=1;i<=n;i++)#define Fork(i,k,n) for(int i=k;i<=n;i++)#define Rep(i,n) for(int i=0;i<n;i++)#define ForD(i,n) for(int i=n;i;i--)#define ForkD(i,k,n) for(int i=n;i>=k;i--)#define RepD(i,n) for(int i=n;i>=0;i--)#define Forp(x) for(int p=Pre[x];p;p=Next[p])#define Forpiter(x) for(int &p=iter[x];p;p=Next[p])  #define Lson (o<<1)#define Rson ((o<<1)+1)#define MEM(a) memset(a,0,sizeof(a));#define MEMI(a) memset(a,127,sizeof(a));#define MEMi(a) memset(a,128,sizeof(a));#define INF (2139062143)#define F (100000007)#define pb push_back#define mp make_pair #define fi first#define se second#define vi vector<int> #define pi pair<int,int>#define SI(a) ((a).size())typedef long long ll;typedef long double ld;typedef unsigned long long ull;ll mul(ll a,ll b){return (a*b)%F;}ll add(ll a,ll b){return (a+b)%F;}ll sub(ll a,ll b){return (a-b+llabs(a-b)/F*F+F)%F;}void upd(ll &a,ll b){a=(a%F+b%F)%F;}int read(){    int x=0,f=1; char ch=getchar();    while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}    while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}    return x*f;} ll sqr(ll a){return a*a;}ld sqr(ld a){return a*a;}double sqr(double a){return a*a;}ld PI = 3.141592653589793238462643383;class P{public:    double x,y;    P(double x=0,double y=0):x(x),y(y){}    friend long double dis2(P A,P B){return sqr(A.x-B.x)+sqr(A.y-B.y);  }    friend long double Dot(P A,P B) {return A.x*B.x+A.y*B.y; }    friend long double Length(P A) {return sqrt(Dot(A,A)); }    friend long double Angle(P A,P B) {return acos(Dot(A,B) / Length(A) / Length(B) ); }    friend P operator- (P A,P B) { return P(A.x-B.x,A.y-B.y); }    friend P operator+ (P A,P B) { return P(A.x+B.x,A.y+B.y); }    friend P operator* (P A,double p) { return P(A.x*p,A.y*p); }    friend P operator/ (P A,double p) { return P(A.x/p,A.y/p); }    friend bool operator< (const P& a,const P& b) {return a.x<b.x||(a.x==b.x&& a.y<b.y);}}; const double eps=1e-10;int dcmp(double x) {    if (fabs(x)<eps) return 0; else return x<0 ? -1 : 1; }bool operator==(const P& a,const P& b) {    return dcmp(a.x-b.x)==0 && dcmp(a.y-b.y) == 0;} typedef P V;double Cross(V A,V B) {return A.x*B.y - A.y*B.x;}double Area2(P A,P B,P C) {return Cross(B-A,C-A);}V Rotate(V A,double rad) {    return V(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));} // A ²»ÊÇ 0ÏòÁ¿ V Normal(V A) {     double L = Length(A);    return V(-A.y/L , A.x/L); }namespace complex_G{    typedef complex<double> Point;    //real(p):Êµ²¿ imag(p):Ðé²¿ conj(p):¹²éî     typedef Point Vector;    double Dot(Vector A,Vector B) {return real(conj(A)*B); }    double Cross(Vector A,Vector B) {return imag(conj(A)*B); }    Vector Rotate(Vector A,double rad) {return A*exp(Point(0,rad)); }}//Cross(v,w)==0(Æ½ÐÐ)Ê±,²»ÄÜµ÷Õâ¸öº¯Êý P GetLineIntersection(P p,V v,P Q,V w){    V u = p-Q;    double t = Cross(w,u)/Cross(v,w);    return p+v*t;}P GetLineIntersectionB(P p,V v,P Q,V w){    return GetLineIntersection(p,v-p,Q,w-Q);}double DistanceToLine(P p,P A,P B) {    V v1 = B-A, v2 = p-A;    return fabs(Cross(v1,v2))/Length(v1);}double DistanceToSegment(P p,P A,P B) {    if (A==B) return Length(p-A);    V v1 = B-A, v2 = p-A, v3 = p - B;    if (dcmp(Dot(v1,v2))<0) return Length(v2);    else if (dcmp(Dot(v1,v3))>0 ) return Length(v3);    else return fabs(Cross(v1,v2) ) / Length(v1);}P GetLineProjection(P p,P A,P B) {    V v=B-A;    return A+v*(Dot(v,p-A)/Dot(v,v));}//¹æ·¶Ïà½»-Ïß¶ÎÏà½»ÇÒ½»µã²»ÔÚ¶Ëµã bool SegmentProperIntersection(P a1,P a2,P b1,P b2) {     double  c1 = Cross(a2-a1,b1-a1) , c2 = Cross(a2-a1,b2-a1),            c3 = Cross(b2-b1,a1-b1) , c4 = Cross(b2-b1,a2-b1);    return dcmp(c1)*dcmp(c2)<0 && dcmp(c3)*dcmp(c4)<0;}//µãÔÚÏß¶ÎÉÏ£¨²»°üº¬¶Ëµã£© bool OnSegment(P p,P a1,P a2) {    return dcmp(Cross(a1-p,a2-p)) == 0 && dcmp(Dot(a1-p,a2-p))<0;}double PolygonArea(P *p,int n) {    double area=0;    For(i,n-2) area+=Cross(p[i]-p[0],p[i+1]-p[0]);    return area/2;} /*Å·À¹«Ê½£º V+F-E=2 V-µãÊý FÃæÊý E±ßÊý */P read_point() {    P a;    scanf("%lf%lf",&a.x,&a.y);    return a;   } struct C{    P c;    double r,x,y;    C(P c,double r):c(c),r(r),x(c.x),y(c.y){}    P point(double a) {        return P(c.x+cos(a)*r,c.y+sin(a)*r);    }};struct Line{    P p;    V v;    double ang;    Line(){}    Line(P p,V v):p(p),v(v) {ang=atan2(v.y,v.x); }    bool operator<(const Line & L) const {        return ang<L.ang;    }    P point(double a) {        return p+v*a;    }};int getLineCircleIntersection(Line L,C cir,double &t1,double &t2,vector<P> & sol) {    if (dcmp(DistanceToLine(cir.c,L.p,L.p+L.v)-cir.r)==0) {        sol.pb(GetLineProjection(cir.c,L.p,L.p+L.v));        return 1;    }    double a = L.v.x, b = L.p.x - cir.c.x, c = L.v.y, d= L.p.y - cir.c.y;    double e = a*a+c*c, f = 2*(a*b + c*d), g = b*b+d*d-cir.r*cir.r;    double delta = f*f - 4*e*g;    if (dcmp(delta)<0) return 0;    else if (dcmp(delta)==0) {        t1 = t2 = -f / (2*e); sol.pb(L.point(t1));        return 1;    }     t1 = (-f - sqrt(delta)) / (2*e); sol.pb(L.point(t1));    t2 = (-f + sqrt(delta)) / (2*e); sol.pb(L.point(t2));    return 2;}double angle(V v) {return atan2(v.y,v.x);}int getCircleCircleIntersection(C C1,C C2,vector<P>& sol) {    double d = Length(C1.c-C2.c);    if (dcmp(d)==0) {        if (dcmp(C1.r - C2.r)==0) return -1; //2Ô²ÖØºÏ         return 0;    }    if (dcmp(C1.r+C2.r-d)<0) return 0;    if (dcmp(fabs(C1.r-C2.r)-d)>0) return 0;    double a = angle(C2.c-C1.c);    double da = acos((C1.r*C1.r+d*d - C2.r*C2.r)/ (2*C1.r*d));    P p1 = C1.point(a-da), p2 = C1.point(a+da);    sol.pb(p1);    if (p1==p2) return 1;    sol.pb(p2);    return 2; }// Tangents-ÇÐÏß int getTangents(P p,C c,V* v) {    V u= c.c-p;    double dist = Length(u);    if (dist<c.r) return 0;    else if (dcmp(dist-c.r)==0) {        v[0]=Rotate(u,PI/2);        return 1;    } else {        double ang = asin(c.r / dist);        v[0]=Rotate(u,-ang);        v[1]=Rotate(u,ang);        return 2;    }       }//Õâ¸öº¯Êý¼ÙÉèÕûÊý×ø±êºÍÕûÊý°ë¾¶//doubleÊ±Òª°Ñint¸Ä³Édouble int getTangents(C A,C B,P* a,P* b) {    int cnt=0;    if (A.r<B.r) {swap(A,B),swap(a,b);}    int d2 = (A.c.x-B.c.x)*(A.c.x-B.c.x) + (A.c.y-B.c.y)*(A.c.y-B.c.y);    int rdiff = A.r-B.r;    int rsum = A.r+B.r;    if (d2<rdiff*rdiff) return 0;    double base = atan2(B.y-A.y,B.x-A.x);    if (d2==0 && A.r == B.r) return -1;    if (d2 == rdiff*rdiff) {        a[cnt] = A.point(base); b[cnt] = B.point(base); ++cnt;        return 1;    }    double ang = acos((A.r-B.r)/sqrt(d2));    a[cnt] = A.point(base+ang); b[cnt] = B.point(base+ang); ++cnt;    a[cnt] = A.point(base-ang); b[cnt] = B.point(base-ang); ++cnt;    if (d2==rsum*rsum) {        a[cnt] = A.point(base); b[cnt] = B.point(PI+base); ++cnt;    }    else if (d2>rsum*rsum) {        double ang = acos((A.r+B.r)/sqrt(d2));        a[cnt] = A.point(base+ang); b[cnt] = B.point(PI+base+ang); ++cnt;        a[cnt] = A.point(base-ang); b[cnt] = B.point(PI+base-ang); ++cnt;    }    return cnt; }//Circumscribed-Íâ½Ó C CircumscribedCircle(P p1,P p2,P p3) {    double Bx = p2.x-p1.x, By= p2.y-p1.y;    double Cx = p3.x-p1.x, Cy= p3.y-p1.y;    double D = 2*(Bx*Cy-By*Cx);    double cx = (Cy*(Bx*Bx+By*By)-By*(Cx*Cx+Cy*Cy))/D + p1.x;    double cy = (Bx*(Cx*Cx+Cy*Cy)-Cx*(Bx*Bx+By*By))/D + p1.y;    P p =P(cx,cy);    return C(p,Length(p1-p));}//Inscribed-ÄÚ½Ó C InscribedCircle(P p1,P p2,P p3) {    double a = Length(p2-p3);    double b = Length(p3-p1);    double c = Length(p1-p2);    P p = (p1*a+p2*b+p3*c)/(a+b+c);    return C(p,DistanceToLine(p,p1,p2));}double torad(double deg) {    return deg/180*acos(-1);}//°Ñ ½Ç¶È+-pi ×ª»»µ½ [0,pi) ÉÏ double radToPositive(double rad) {    if (dcmp(rad)<0) rad=ceil(-rad/PI)*PI+rad;    if (dcmp(rad-PI)>=0) rad-=floor(rad/PI)*PI;     return rad;} double todeg(double rad) {    return rad*180/acos(-1);}//(R,lat,lng)->(x,y,z)void get_coord(double R,double lat,double lng,double &x,double &y,double &z) {    lat=torad(lat);    lng=torad(lng);    x=R*cos(lat)*cos(lng);    y=R*cos(lat)*sin(lng);    z=R*sin(lat);}void print(double a) {    printf("%.6lf",a); }void print(P p) {    printf("(%.6lf,%.6lf)",p.x,p.y);}template<class T>void print(vector<T> v) {    sort(v.begin(),v.end());    putchar('[');    int n=v.size();    Rep(i,n) {        print(v[i]);        if (i<n-1) putchar(',');     }    puts("]");}// °ÑÖ±ÏßÑØvÆ½ÒÆ// Translation-Æ½ÒÆ Line LineTranslation(Line l,V v) {    l.p=l.p+v;    return l;}void CircleThroughAPointAndTangentToALineWithRadius(P p,Line l,double r,vector<P>& sol) {    V e=Normal(l.v);    Line l1=LineTranslation(l,e*r),l2=LineTranslation(l,e*(-r));    double t1,t2;    getLineCircleIntersection(l1,C(p,r),t1,t2,sol);    getLineCircleIntersection(l2,C(p,r),t1,t2,sol);}void CircleTangentToTwoLinesWithRadius(Line l1,Line l2,double r,vector<P>& sol) {    V e1=Normal(l1.v),e2=Normal(l2.v);    Line L1[2]={LineTranslation(l1,e1*r),LineTranslation(l1,e1*(-r))},         L2[2]={LineTranslation(l2,e2*r),LineTranslation(l2,e2*(-r))};    Rep(i,2) Rep(j,2) sol.pb(GetLineIntersection(L1[i].p,L1[i].v,L2[j].p,L2[j].v));}void CircleTangentToTwoDisjointCirclesWithRadius(C c1,C c2,double r,vector<P>& sol) {    c1.r+=r; c2.r+=r;    getCircleCircleIntersection(c1,c2,sol);}//È·¶¨4¸öµãÄÜ·ñ×é³ÉÍ¹¶à±ßÐÎ£¬²¢°´Ë³Ðò£¨²»Ò»¶¨ÊÇÄæÊ±Õë£©·µ»Ø bool ConvexPolygon(P &A,P &B,P &C,P &D) {    if (SegmentProperIntersection(A,C,B,D)) return 1;    swap(B,C);    if (SegmentProperIntersection(A,C,B,D)) return 1;    swap(D,C);    if (SegmentProperIntersection(A,C,B,D)) return 1;    return 0;}bool IsParallel(P A,P B,P C,P D) {    return dcmp(Cross(B-A,D-C))==0;}bool IsPerpendicular(V A,V B) {    return dcmp(Dot(A,B))==0;}//ÏÈµ÷ÓÃConvexPolygon ÇóÍ¹°ü²¢È·ÈÏÊÇ·ñÊÇËÄ±ßÐÎ// Trapezium-ÌÝÐÎ Rhombus-ÁâÐÎ  bool IsTrapezium(P A,P B,P C,P D){    return IsParallel(A,B,C,D)^IsParallel(B,C,A,D);}bool IsParallelogram(P A,P B,P C,P D) {    return IsParallel(A,B,C,D)&&IsParallel(B,C,A,D);}bool IsRhombus(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&dcmp(Length(B-A)-Length(C-B))==0;}bool IsRectangle(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&IsPerpendicular(B-A,D-A);}bool IsSquare(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&IsPerpendicular(B-A,D-A)&&dcmp(Length(B-A)-Length(C-B))==0;}//chord-ÏÒ arc-»¡ double ArcDis(double chord,double r) {    return 2*asin(chord/2/r)*r;} typedef vector<P> Polygon ;int isPointInPolygon(P p,Polygon poly) {    int wn=0;    int n=poly.size();    Rep(i,n) {        if (OnSegment(p,poly[i],poly[(i+1)%n])) return -1;        int k=dcmp(Cross(poly[(i+1)%n]-poly[i],p-poly[i]));        int d1 = dcmp(poly[i].y-p.y);        int d2 = dcmp(poly[(i+1)%n].y-p.y);        if ( k > 0 && d1 <= 0 && d2 > 0 ) wn++;        if ( k < 0 && d2 <= 0 && d1 > 0 ) wn--;    }    if (wn!=0) return 1;    return 0;}int ConvexHull(P *p,int n,P *ch) {    sort(p,p+n);    int m=0;    Rep(i,n) {        while(m>1 && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;        ch[m++]=p[i];    }    int k=m;    RepD(i,n-2) {        while(m>k && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;        ch[m++]=p[i];    }    if ( n > 1 ) m--;    return m;}//°ÑÁ½µãÊ½×ªÎªÒ»°ãÊ½ ax+by+c=0 void Two_pointFormToGeneralForm(P A,P B,double &a,double &b,double &c){    a = A.y - B.y;    b = B.x - A.x;    c = Cross(A,B);}//ÓÐÏòÖ±ÏßA->B ÇÐ¸î¶à±ßÐÐpoly ¿ÉÄÜ·µ»Øµ¥µãÏß¶Î O(n)Polygon CutPolygon(Polygon poly,P A,P B){    Polygon newpoly;    int n=poly.size();    Rep(i,n) {        P C = poly[i];        P D = poly[(i+1)%n];        if (dcmp(Cross(B-A,C-A))>=0)  newpoly.pb(C);        if (dcmp(Cross(B-A,C-D))) {            P ip = GetLineIntersection(A,B-A,C,D-C);            if (OnSegment(ip,C,D)) newpoly.pb(ip);        }    }}//ÏßÉÏ²»Ëã bool OnLeft(Line L,P p) {    return Cross(L.v,p-L.p);} P GetIntersection(Line a,Line b) {    V u=a.p-b.p;    double t = Cross(b.v,u) / Cross(a.v, b.v);    return a.p + a.v*t;}int HalfplaneIntersection(Line *L, int n, P* poly) {    sort(L,L+n);    int fi,la;    P *p = new P[n];    Line *q = new Line[n];    q[fi=la=0 ] = L[0];    For(i,n-1) {        while (fi < la && !OnLeft(L[i],p[la-1])) la--;        while (fi < la && !OnLeft(L[i],p[fi])) fi++;        q[++la] = L[i];        if (fabs(Cross(q[la].v, q[la-1].v))<eps) {            la--;            if (OnLeft(q[la],L[i].p)) q[la] = L[i];        }        if (fi<la) p[la-1] = GetIntersection(q[la-1],q[la]);    }    while(fi < la && !OnLeft(q[fi],p[la-1])) la--;    if (la-fi<=1) return 0;     p[la] = GetIntersection(q[la],q[fi]);    int m=0;    Fork(i,fi,la) poly[m++]=p[i];    return m;} // hypot(double x,double y); return sqrt(x*x+y*y)double rotating_calipers(P *p,int n) {    int q=1;    double ans=0;    Rep(i,n) {        while(fabs(Area2(p[i],p[(i+1)%n],p[(q+1)%n]))> fabs(Area2(p[i],p[(i+1)%n],p[q] )) )             q=(q+1)%n;        ans = max( ans, (double)max(Length(p[i]- p[q]), Length(p[(i+1)%n] -p[q] ) ) );              }    return ans;}#define MAXN (400000+10)int n,cn;P a[MAXN],poly[MAXN];int main(){//  freopen("uva1453.in","r",stdin);//  freopen(".out","w",stdout);    int T=read();    while(cin>>n) {        cn=0;        Rep(i,n) {            P p=read_point();            double r=read();            a[cn++]=p;            a[cn++]=p+V(r,0);            a[cn++]=p+V(0,r);            a[cn++]=p+V(r,r);        }        cn=ConvexHull(a,cn,poly);        double ans = rotating_calipers(poly,cn);        printf("%.0lf\n",sqr(ans));    }    return 0;}

UVA 1396 Most Distant Point from the Sea

#include<bits/stdc++.h>using namespace std;#define For(i,n) for(int i=1;i<=n;i++)#define Fork(i,k,n) for(int i=k;i<=n;i++)#define Rep(i,n) for(int i=0;i<n;i++)#define ForD(i,n) for(int i=n;i;i--)#define ForkD(i,k,n) for(int i=n;i>=k;i--)#define RepD(i,n) for(int i=n;i>=0;i--)#define Forp(x) for(int p=Pre[x];p;p=Next[p])#define Forpiter(x) for(int &p=iter[x];p;p=Next[p])  #define Lson (o<<1)#define Rson ((o<<1)+1)#define MEM(a) memset(a,0,sizeof(a));#define MEMI(a) memset(a,127,sizeof(a));#define MEMi(a) memset(a,128,sizeof(a));#define INF (2139062143)#define F (100000007)#define pb push_back#define mp make_pair #define fi first#define se second#define vi vector<int> #define pi pair<int,int>#define SI(a) ((a).size())typedef long long ll;typedef long double ld;typedef unsigned long long ull;ll mul(ll a,ll b){return (a*b)%F;}ll add(ll a,ll b){return (a+b)%F;}ll sub(ll a,ll b){return (a-b+llabs(a-b)/F*F+F)%F;}void upd(ll &a,ll b){a=(a%F+b%F)%F;}int read(){    int x=0,f=1; char ch=getchar();    while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}    while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}    return x*f;} ll sqr(ll a){return a*a;}ld sqr(ld a){return a*a;}double sqr(double a){return a*a;}ld PI = 3.141592653589793238462643383;class P{public:    double x,y;    P(double x=0,double y=0):x(x),y(y){}    friend long double dis2(P A,P B){return sqr(A.x-B.x)+sqr(A.y-B.y);  }    friend long double Dot(P A,P B) {return A.x*B.x+A.y*B.y; }    friend long double Length(P A) {return sqrt(Dot(A,A)); }    friend long double Angle(P A,P B) {return acos(Dot(A,B) / Length(A) / Length(B) ); }    friend P operator- (P A,P B) { return P(A.x-B.x,A.y-B.y); }    friend P operator+ (P A,P B) { return P(A.x+B.x,A.y+B.y); }    friend P operator* (P A,double p) { return P(A.x*p,A.y*p); }    friend P operator/ (P A,double p) { return P(A.x/p,A.y/p); }    friend bool operator< (const P& a,const P& b) {return a.x<b.x||(a.x==b.x&& a.y<b.y);}}; const double eps=1e-10;int dcmp(double x) {    if (fabs(x)<eps) return 0; else return x<0 ? -1 : 1; }bool operator==(const P& a,const P& b) {    return dcmp(a.x-b.x)==0 && dcmp(a.y-b.y) == 0;} typedef P V;double Cross(V A,V B) {return A.x*B.y - A.y*B.x;}double Area2(P A,P B,P C) {return Cross(B-A,C-A);}V Rotate(V A,double rad) {    return V(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));} // A 不是 0向量 V Normal(V A) {     double L = Length(A);    return V(-A.y/L , A.x/L); }namespace complex_G{    typedef complex<double> Point;    //real(p):实部 imag(p):虚部 conj(p):共轭     typedef Point Vector;    double Dot(Vector A,Vector B) {return real(conj(A)*B); }    double Cross(Vector A,Vector B) {return imag(conj(A)*B); }    Vector Rotate(Vector A,double rad) {return A*exp(Point(0,rad)); }}//Cross(v,w)==0(平行)时,不能调这个函数 P GetLineIntersection(P p,V v,P Q,V w){    V u = p-Q;    double t = Cross(w,u)/Cross(v,w);    return p+v*t;}P GetLineIntersectionB(P p,V v,P Q,V w){    return GetLineIntersection(p,v-p,Q,w-Q);}double DistanceToLine(P p,P A,P B) {    V v1 = B-A, v2 = p-A;    return fabs(Cross(v1,v2))/Length(v1);}double DistanceToSegment(P p,P A,P B) {    if (A==B) return Length(p-A);    V v1 = B-A, v2 = p-A, v3 = p - B;    if (dcmp(Dot(v1,v2))<0) return Length(v2);    else if (dcmp(Dot(v1,v3))>0 ) return Length(v3);    else return fabs(Cross(v1,v2) ) / Length(v1);}P GetLineProjection(P p,P A,P B) {    V v=B-A;    return A+v*(Dot(v,p-A)/Dot(v,v));}//规范相交-线段相交且交点不在端点 bool SegmentProperIntersection(P a1,P a2,P b1,P b2) {     double  c1 = Cross(a2-a1,b1-a1) , c2 = Cross(a2-a1,b2-a1),            c3 = Cross(b2-b1,a1-b1) , c4 = Cross(b2-b1,a2-b1);    return dcmp(c1)*dcmp(c2)<0 && dcmp(c3)*dcmp(c4)<0;}//点在线段上（不包含端点） bool OnSegment(P p,P a1,P a2) {    return dcmp(Cross(a1-p,a2-p)) == 0 && dcmp(Dot(a1-p,a2-p))<0;}double PolygonArea(P *p,int n) {    double area=0;    For(i,n-2) area+=Cross(p[i]-p[0],p[i+1]-p[0]);    return area/2;} /*欧拉公式： V+F-E=2 V-点数 F面数 E边数 */P read_point() {    P a;    scanf("%lf%lf",&a.x,&a.y);    return a;   } struct C{    P c;    double r,x,y;    C(P c,double r):c(c),r(r),x(c.x),y(c.y){}    P point(double a) {        return P(c.x+cos(a)*r,c.y+sin(a)*r);    }};struct Line{    P p;    V v;    double ang;    Line(){}    Line(P p,V v):p(p),v(v) {ang=atan2(v.y,v.x); }    bool operator<(const Line & L) const {        return ang<L.ang;    }    P point(double a) {        return p+v*a;    }};int getLineCircleIntersection(Line L,C cir,double &t1,double &t2,vector<P> & sol) {    if (dcmp(DistanceToLine(cir.c,L.p,L.p+L.v)-cir.r)==0) {        sol.pb(GetLineProjection(cir.c,L.p,L.p+L.v));        return 1;    }    double a = L.v.x, b = L.p.x - cir.c.x, c = L.v.y, d= L.p.y - cir.c.y;    double e = a*a+c*c, f = 2*(a*b + c*d), g = b*b+d*d-cir.r*cir.r;    double delta = f*f - 4*e*g;    if (dcmp(delta)<0) return 0;    else if (dcmp(delta)==0) {        t1 = t2 = -f / (2*e); sol.pb(L.point(t1));        return 1;    }     t1 = (-f - sqrt(delta)) / (2*e); sol.pb(L.point(t1));    t2 = (-f + sqrt(delta)) / (2*e); sol.pb(L.point(t2));    return 2;}double angle(V v) {return atan2(v.y,v.x);}int getCircleCircleIntersection(C C1,C C2,vector<P>& sol) {    double d = Length(C1.c-C2.c);    if (dcmp(d)==0) {        if (dcmp(C1.r - C2.r)==0) return -1; //2圆重合         return 0;    }    if (dcmp(C1.r+C2.r-d)<0) return 0;    if (dcmp(fabs(C1.r-C2.r)-d)>0) return 0;    double a = angle(C2.c-C1.c);    double da = acos((C1.r*C1.r+d*d - C2.r*C2.r)/ (2*C1.r*d));    P p1 = C1.point(a-da), p2 = C1.point(a+da);    sol.pb(p1);    if (p1==p2) return 1;    sol.pb(p2);    return 2; }// Tangents-切线 int getTangents(P p,C c,V* v) {    V u= c.c-p;    double dist = Length(u);    if (dist<c.r) return 0;    else if (dcmp(dist-c.r)==0) {        v[0]=Rotate(u,PI/2);        return 1;    } else {        double ang = asin(c.r / dist);        v[0]=Rotate(u,-ang);        v[1]=Rotate(u,ang);        return 2;    }       }//这个函数假设整数坐标和整数半径//double时要把int改成double int getTangents(C A,C B,P* a,P* b) {    int cnt=0;    if (A.r<B.r) {swap(A,B),swap(a,b);}    int d2 = (A.c.x-B.c.x)*(A.c.x-B.c.x) + (A.c.y-B.c.y)*(A.c.y-B.c.y);    int rdiff = A.r-B.r;    int rsum = A.r+B.r;    if (d2<rdiff*rdiff) return 0;    double base = atan2(B.y-A.y,B.x-A.x);    if (d2==0 && A.r == B.r) return -1;    if (d2 == rdiff*rdiff) {        a[cnt] = A.point(base); b[cnt] = B.point(base); ++cnt;        return 1;    }    double ang = acos((A.r-B.r)/sqrt(d2));    a[cnt] = A.point(base+ang); b[cnt] = B.point(base+ang); ++cnt;    a[cnt] = A.point(base-ang); b[cnt] = B.point(base-ang); ++cnt;    if (d2==rsum*rsum) {        a[cnt] = A.point(base); b[cnt] = B.point(PI+base); ++cnt;    }    else if (d2>rsum*rsum) {        double ang = acos((A.r+B.r)/sqrt(d2));        a[cnt] = A.point(base+ang); b[cnt] = B.point(PI+base+ang); ++cnt;        a[cnt] = A.point(base-ang); b[cnt] = B.point(PI+base-ang); ++cnt;    }    return cnt; }//Circumscribed-外接 C CircumscribedCircle(P p1,P p2,P p3) {    double Bx = p2.x-p1.x, By= p2.y-p1.y;    double Cx = p3.x-p1.x, Cy= p3.y-p1.y;    double D = 2*(Bx*Cy-By*Cx);    double cx = (Cy*(Bx*Bx+By*By)-By*(Cx*Cx+Cy*Cy))/D + p1.x;    double cy = (Bx*(Cx*Cx+Cy*Cy)-Cx*(Bx*Bx+By*By))/D + p1.y;    P p =P(cx,cy);    return C(p,Length(p1-p));}//Inscribed-内接 C InscribedCircle(P p1,P p2,P p3) {    double a = Length(p2-p3);    double b = Length(p3-p1);    double c = Length(p1-p2);    P p = (p1*a+p2*b+p3*c)/(a+b+c);    return C(p,DistanceToLine(p,p1,p2));}double torad(double deg) {    return deg/180*acos(-1);}//把 角度+-pi 转换到 [0,pi) 上 double radToPositive(double rad) {    if (dcmp(rad)<0) rad=ceil(-rad/PI)*PI+rad;    if (dcmp(rad-PI)>=0) rad-=floor(rad/PI)*PI;     return rad;} double todeg(double rad) {    return rad*180/acos(-1);}//(R,lat,lng)->(x,y,z)void get_coord(double R,double lat,double lng,double &x,double &y,double &z) {    lat=torad(lat);    lng=torad(lng);    x=R*cos(lat)*cos(lng);    y=R*cos(lat)*sin(lng);    z=R*sin(lat);}void print(double a) {    printf("%.6lf",a); }void print(P p) {    printf("(%.6lf,%.6lf)",p.x,p.y);}template<class T>void print(vector<T> v) {    sort(v.begin(),v.end());    putchar('[');    int n=v.size();    Rep(i,n) {        print(v[i]);        if (i<n-1) putchar(',');     }    puts("]");}// 把直线沿v平移// Translation-平移 Line LineTranslation(Line l,V v) {    l.p=l.p+v;    return l;}void CircleThroughAPointAndTangentToALineWithRadius(P p,Line l,double r,vector<P>& sol) {    V e=Normal(l.v);    Line l1=LineTranslation(l,e*r),l2=LineTranslation(l,e*(-r));    double t1,t2;    getLineCircleIntersection(l1,C(p,r),t1,t2,sol);    getLineCircleIntersection(l2,C(p,r),t1,t2,sol);}void CircleTangentToTwoLinesWithRadius(Line l1,Line l2,double r,vector<P>& sol) {    V e1=Normal(l1.v),e2=Normal(l2.v);    Line L1[2]={LineTranslation(l1,e1*r),LineTranslation(l1,e1*(-r))},         L2[2]={LineTranslation(l2,e2*r),LineTranslation(l2,e2*(-r))};    Rep(i,2) Rep(j,2) sol.pb(GetLineIntersection(L1[i].p,L1[i].v,L2[j].p,L2[j].v));}void CircleTangentToTwoDisjointCirclesWithRadius(C c1,C c2,double r,vector<P>& sol) {    c1.r+=r; c2.r+=r;    getCircleCircleIntersection(c1,c2,sol);}//确定4个点能否组成凸多边形，并按顺序（不一定是逆时针）返回 bool ConvexPolygon(P &A,P &B,P &C,P &D) {    if (SegmentProperIntersection(A,C,B,D)) return 1;    swap(B,C);    if (SegmentProperIntersection(A,C,B,D)) return 1;    swap(D,C);    if (SegmentProperIntersection(A,C,B,D)) return 1;    return 0;}bool IsParallel(P A,P B,P C,P D) {    return dcmp(Cross(B-A,D-C))==0;}bool IsPerpendicular(V A,V B) {    return dcmp(Dot(A,B))==0;}//先调用ConvexPolygon 求凸包并确认是否是四边形// Trapezium-梯形 Rhombus-菱形  bool IsTrapezium(P A,P B,P C,P D){    return IsParallel(A,B,C,D)^IsParallel(B,C,A,D);}bool IsParallelogram(P A,P B,P C,P D) {    return IsParallel(A,B,C,D)&&IsParallel(B,C,A,D);}bool IsRhombus(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&dcmp(Length(B-A)-Length(C-B))==0;}bool IsRectangle(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&IsPerpendicular(B-A,D-A);}bool IsSquare(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&IsPerpendicular(B-A,D-A)&&dcmp(Length(B-A)-Length(C-B))==0;}//chord-弦 arc-弧 double ArcDis(double chord,double r) {    return 2*asin(chord/2/r)*r;} typedef vector<P> Polygon ;int isPointInPolygon(P p,Polygon poly) {    int wn=0;    int n=poly.size();    Rep(i,n) {        if (OnSegment(p,poly[i],poly[(i+1)%n])) return -1;        int k=dcmp(Cross(poly[(i+1)%n]-poly[i],p-poly[i]));        int d1 = dcmp(poly[i].y-p.y);        int d2 = dcmp(poly[(i+1)%n].y-p.y);        if ( k > 0 && d1 <= 0 && d2 > 0 ) wn++;        if ( k < 0 && d2 <= 0 && d1 > 0 ) wn--;    }    if (wn!=0) return 1;    return 0;}int ConvexHull(P *p,int n,P *ch) {    sort(p,p+n);    int m=0;    Rep(i,n) {        while(m>1 && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;        ch[m++]=p[i];    }    int k=m;    RepD(i,n-2) {        while(m>k && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;        ch[m++]=p[i];    }    if ( n > 1 ) m--;    return m;}//把两点式转为一般式 ax+by+c=0 void Two_pointFormToGeneralForm(P A,P B,double &a,double &b,double &c){    a = A.y - B.y;    b = B.x - A.x;    c = Cross(A,B);}//有向直线A->B 切割多边行poly 可能返回单点线段 O(n)Polygon CutPolygon(Polygon poly,P A,P B){    Polygon newpoly;    int n=poly.size();    Rep(i,n) {        P C = poly[i];        P D = poly[(i+1)%n];        if (dcmp(Cross(B-A,C-A))>=0)  newpoly.pb(C);        if (dcmp(Cross(B-A,C-D))) {            P ip = GetLineIntersection(A,B-A,C,D-C);            if (OnSegment(ip,C,D)) newpoly.pb(ip);        }    }}//线上不算 bool OnLeft(Line L,P p) {    return Cross(L.v,p-L.p) > 0;} P GetIntersection(Line a,Line b) {    V u=a.p-b.p;    double t = Cross(b.v,u) / Cross(a.v, b.v);    return a.p + a.v*t;}int HalfplaneIntersection(Line *L, int n, P* poly) {    sort(L,L+n);    int fi,la;    P *p = new P[n];    Line *q = new Line[n];    q[fi=la=0 ] = L[0];    For(i,n-1) {        while (fi < la && !OnLeft(L[i],p[la-1])) la--;        while (fi < la && !OnLeft(L[i],p[fi])) fi++;        q[++la] = L[i];        if (fabs(Cross(q[la].v, q[la-1].v))<eps) {            la--;            if (OnLeft(q[la],L[i].p)) q[la] = L[i];        }        if (fi<la) p[la-1] = GetIntersection(q[la-1],q[la]);    }    while(fi < la && !OnLeft(q[fi],p[la-1])) la--;    if (la-fi<=1) return 0;     p[la] = GetIntersection(q[la],q[fi]);    int m=0;    Fork(i,fi,la) poly[m++]=p[i];    return m;} // hypot(double x,double y); return sqrt(x*x+y*y)P p[200],poly[200];Line L[200];V v[200],v2[200];int n;int main(){//  freopen("uva1396.in","r",stdin);//  freopen(".out","w",stdout);    while(cin>>n&&n) {        Rep(i,n) {            p[i]=read_point();        }        Rep(i,n) {            v[i] = p[(i+1)%n] - p[i];            v2[i] = Normal(v[i]);        }        double l=0,r=20000;        while(r-l>1e-7) {            double m=(r+l)/2;            Rep(i,n) L[i]=LineTranslation(Line(p[i],v[i]),v2[i]*m);            if (!HalfplaneIntersection(L,n,poly)) r=m; else l=m;         }        printf("%.6lf\n",l);    }    return 0;}

UVA 1298 Triathlon

#include<bits/stdc++.h>using namespace std;#define For(i,n) for(int i=1;i<=n;i++)#define Fork(i,k,n) for(int i=k;i<=n;i++)#define Rep(i,n) for(int i=0;i<n;i++)#define ForD(i,n) for(int i=n;i;i--)#define ForkD(i,k,n) for(int i=n;i>=k;i--)#define RepD(i,n) for(int i=n;i>=0;i--)#define Forp(x) for(int p=Pre[x];p;p=Next[p])#define Forpiter(x) for(int &p=iter[x];p;p=Next[p])  #define Lson (o<<1)#define Rson ((o<<1)+1)#define MEM(a) memset(a,0,sizeof(a));#define MEMI(a) memset(a,127,sizeof(a));#define MEMi(a) memset(a,128,sizeof(a));#define INF (2139062143)#define F (100000007)#define pb push_back#define mp make_pair #define fi first#define se second#define vi vector<int> #define pi pair<int,int>#define SI(a) ((a).size())typedef long long ll;typedef long double ld;typedef unsigned long long ull;ll mul(ll a,ll b){return (a*b)%F;}ll add(ll a,ll b){return (a+b)%F;}ll sub(ll a,ll b){return (a-b+llabs(a-b)/F*F+F)%F;}void upd(ll &a,ll b){a=(a%F+b%F)%F;}int read(){    int x=0,f=1; char ch=getchar();    while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}    while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}    return x*f;} ll sqr(ll a){return a*a;}ld sqr(ld a){return a*a;}double sqr(double a){return a*a;}ld PI = 3.141592653589793238462643383;class P{public:    double x,y;    P(double x=0,double y=0):x(x),y(y){}    friend long double dis2(P A,P B){return sqr(A.x-B.x)+sqr(A.y-B.y);  }    friend long double Dot(P A,P B) {return A.x*B.x+A.y*B.y; }    friend long double Length(P A) {return sqrt(Dot(A,A)); }    friend long double Angle(P A,P B) {return acos(Dot(A,B) / Length(A) / Length(B) ); }    friend P operator- (P A,P B) { return P(A.x-B.x,A.y-B.y); }    friend P operator+ (P A,P B) { return P(A.x+B.x,A.y+B.y); }    friend P operator* (P A,double p) { return P(A.x*p,A.y*p); }    friend P operator/ (P A,double p) { return P(A.x/p,A.y/p); }    friend bool operator< (const P& a,const P& b) {return a.x<b.x||(a.x==b.x&& a.y<b.y);}}; const double eps=1e-10;int dcmp(double x) {    if (fabs(x)<eps) return 0; else return x<0 ? -1 : 1; }bool operator==(const P& a,const P& b) {    return dcmp(a.x-b.x)==0 && dcmp(a.y-b.y) == 0;} typedef P V;double Cross(V A,V B) {return A.x*B.y - A.y*B.x;}double Area2(P A,P B,P C) {return Cross(B-A,C-A);}V Rotate(V A,double rad) {    return V(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));} // A 不是 0向量 V Normal(V A) {     double L = Length(A);    return V(-A.y/L , A.x/L); }namespace complex_G{    typedef complex<double> Point;    //real(p):实部 imag(p):虚部 conj(p):共轭     typedef Point Vector;    double Dot(Vector A,Vector B) {return real(conj(A)*B); }    double Cross(Vector A,Vector B) {return imag(conj(A)*B); }    Vector Rotate(Vector A,double rad) {return A*exp(Point(0,rad)); }}//Cross(v,w)==0(平行)时,不能调这个函数 P GetLineIntersection(P p,V v,P Q,V w){    V u = p-Q;    double t = Cross(w,u)/Cross(v,w);    return p+v*t;}P GetLineIntersectionB(P p,V v,P Q,V w){    return GetLineIntersection(p,v-p,Q,w-Q);}double DistanceToLine(P p,P A,P B) {    V v1 = B-A, v2 = p-A;    return fabs(Cross(v1,v2))/Length(v1);}double DistanceToSegment(P p,P A,P B) {    if (A==B) return Length(p-A);    V v1 = B-A, v2 = p-A, v3 = p - B;    if (dcmp(Dot(v1,v2))<0) return Length(v2);    else if (dcmp(Dot(v1,v3))>0 ) return Length(v3);    else return fabs(Cross(v1,v2) ) / Length(v1);}P GetLineProjection(P p,P A,P B) {    V v=B-A;    return A+v*(Dot(v,p-A)/Dot(v,v));}//规范相交-线段相交且交点不在端点 bool SegmentProperIntersection(P a1,P a2,P b1,P b2) {     double  c1 = Cross(a2-a1,b1-a1) , c2 = Cross(a2-a1,b2-a1),            c3 = Cross(b2-b1,a1-b1) , c4 = Cross(b2-b1,a2-b1);    return dcmp(c1)*dcmp(c2)<0 && dcmp(c3)*dcmp(c4)<0;}//点在线段上（不包含端点） bool OnSegment(P p,P a1,P a2) {    return dcmp(Cross(a1-p,a2-p)) == 0 && dcmp(Dot(a1-p,a2-p))<0;}double PolygonArea(P *p,int n) {    double area=0;    For(i,n-2) area+=Cross(p[i]-p[0],p[i+1]-p[0]);    return area/2;} /*欧拉公式： V+F-E=2 V-点数 F面数 E边数 */P read_point() {    P a;    scanf("%lf%lf",&a.x,&a.y);    return a;   } struct C{    P c;    double r,x,y;    C(P c,double r):c(c),r(r),x(c.x),y(c.y){}    P point(double a) {        return P(c.x+cos(a)*r,c.y+sin(a)*r);    }};struct Line{    P p;    V v;    double ang;    Line(){}    Line(P p,V v):p(p),v(v) {ang=atan2(v.y,v.x); }    bool operator<(const Line & L) const {        return ang<L.ang;    }    P point(double a) {        return p+v*a;    }};int getLineCircleIntersection(Line L,C cir,double &t1,double &t2,vector<P> & sol) {    if (dcmp(DistanceToLine(cir.c,L.p,L.p+L.v)-cir.r)==0) {        sol.pb(GetLineProjection(cir.c,L.p,L.p+L.v));        return 1;    }    double a = L.v.x, b = L.p.x - cir.c.x, c = L.v.y, d= L.p.y - cir.c.y;    double e = a*a+c*c, f = 2*(a*b + c*d), g = b*b+d*d-cir.r*cir.r;    double delta = f*f - 4*e*g;    if (dcmp(delta)<0) return 0;    else if (dcmp(delta)==0) {        t1 = t2 = -f / (2*e); sol.pb(L.point(t1));        return 1;    }     t1 = (-f - sqrt(delta)) / (2*e); sol.pb(L.point(t1));    t2 = (-f + sqrt(delta)) / (2*e); sol.pb(L.point(t2));    return 2;}double angle(V v) {return atan2(v.y,v.x);}int getCircleCircleIntersection(C C1,C C2,vector<P>& sol) {    double d = Length(C1.c-C2.c);    if (dcmp(d)==0) {        if (dcmp(C1.r - C2.r)==0) return -1; //2圆重合         return 0;    }    if (dcmp(C1.r+C2.r-d)<0) return 0;    if (dcmp(fabs(C1.r-C2.r)-d)>0) return 0;    double a = angle(C2.c-C1.c);    double da = acos((C1.r*C1.r+d*d - C2.r*C2.r)/ (2*C1.r*d));    P p1 = C1.point(a-da), p2 = C1.point(a+da);    sol.pb(p1);    if (p1==p2) return 1;    sol.pb(p2);    return 2; }// Tangents-切线 int getTangents(P p,C c,V* v) {    V u= c.c-p;    double dist = Length(u);    if (dist<c.r) return 0;    else if (dcmp(dist-c.r)==0) {        v[0]=Rotate(u,PI/2);        return 1;    } else {        double ang = asin(c.r / dist);        v[0]=Rotate(u,-ang);        v[1]=Rotate(u,ang);        return 2;    }       }//这个函数假设整数坐标和整数半径//double时要把int改成double int getTangents(C A,C B,P* a,P* b) {    int cnt=0;    if (A.r<B.r) {swap(A,B),swap(a,b);}    int d2 = (A.c.x-B.c.x)*(A.c.x-B.c.x) + (A.c.y-B.c.y)*(A.c.y-B.c.y);    int rdiff = A.r-B.r;    int rsum = A.r+B.r;    if (d2<rdiff*rdiff) return 0;    double base = atan2(B.y-A.y,B.x-A.x);    if (d2==0 && A.r == B.r) return -1;    if (d2 == rdiff*rdiff) {        a[cnt] = A.point(base); b[cnt] = B.point(base); ++cnt;        return 1;    }    double ang = acos((A.r-B.r)/sqrt(d2));    a[cnt] = A.point(base+ang); b[cnt] = B.point(base+ang); ++cnt;    a[cnt] = A.point(base-ang); b[cnt] = B.point(base-ang); ++cnt;    if (d2==rsum*rsum) {        a[cnt] = A.point(base); b[cnt] = B.point(PI+base); ++cnt;    }    else if (d2>rsum*rsum) {        double ang = acos((A.r+B.r)/sqrt(d2));        a[cnt] = A.point(base+ang); b[cnt] = B.point(PI+base+ang); ++cnt;        a[cnt] = A.point(base-ang); b[cnt] = B.point(PI+base-ang); ++cnt;    }    return cnt; }//Circumscribed-外接 C CircumscribedCircle(P p1,P p2,P p3) {    double Bx = p2.x-p1.x, By= p2.y-p1.y;    double Cx = p3.x-p1.x, Cy= p3.y-p1.y;    double D = 2*(Bx*Cy-By*Cx);    double cx = (Cy*(Bx*Bx+By*By)-By*(Cx*Cx+Cy*Cy))/D + p1.x;    double cy = (Bx*(Cx*Cx+Cy*Cy)-Cx*(Bx*Bx+By*By))/D + p1.y;    P p =P(cx,cy);    return C(p,Length(p1-p));}//Inscribed-内接 C InscribedCircle(P p1,P p2,P p3) {    double a = Length(p2-p3);    double b = Length(p3-p1);    double c = Length(p1-p2);    P p = (p1*a+p2*b+p3*c)/(a+b+c);    return C(p,DistanceToLine(p,p1,p2));}double torad(double deg) {    return deg/180*acos(-1);}//把 角度+-pi 转换到 [0,pi) 上 double radToPositive(double rad) {    if (dcmp(rad)<0) rad=ceil(-rad/PI)*PI+rad;    if (dcmp(rad-PI)>=0) rad-=floor(rad/PI)*PI;     return rad;} double todeg(double rad) {    return rad*180/acos(-1);}//(R,lat,lng)->(x,y,z)void get_coord(double R,double lat,double lng,double &x,double &y,double &z) {    lat=torad(lat);    lng=torad(lng);    x=R*cos(lat)*cos(lng);    y=R*cos(lat)*sin(lng);    z=R*sin(lat);}void print(double a) {    printf("%.6lf",a); }void print(P p) {    printf("(%.6lf,%.6lf)",p.x,p.y);}template<class T>void print(vector<T> v) {    sort(v.begin(),v.end());    putchar('[');    int n=v.size();    Rep(i,n) {        print(v[i]);        if (i<n-1) putchar(',');     }    puts("]");}// 把直线沿v平移// Translation-平移 Line LineTranslation(Line l,V v) {    l.p=l.p+v;    return l;}void CircleThroughAPointAndTangentToALineWithRadius(P p,Line l,double r,vector<P>& sol) {    V e=Normal(l.v);    Line l1=LineTranslation(l,e*r),l2=LineTranslation(l,e*(-r));    double t1,t2;    getLineCircleIntersection(l1,C(p,r),t1,t2,sol);    getLineCircleIntersection(l2,C(p,r),t1,t2,sol);}void CircleTangentToTwoLinesWithRadius(Line l1,Line l2,double r,vector<P>& sol) {    V e1=Normal(l1.v),e2=Normal(l2.v);    Line L1[2]={LineTranslation(l1,e1*r),LineTranslation(l1,e1*(-r))},         L2[2]={LineTranslation(l2,e2*r),LineTranslation(l2,e2*(-r))};    Rep(i,2) Rep(j,2) sol.pb(GetLineIntersection(L1[i].p,L1[i].v,L2[j].p,L2[j].v));}void CircleTangentToTwoDisjointCirclesWithRadius(C c1,C c2,double r,vector<P>& sol) {    c1.r+=r; c2.r+=r;    getCircleCircleIntersection(c1,c2,sol);}//确定4个点能否组成凸多边形，并按顺序（不一定是逆时针）返回 bool ConvexPolygon(P &A,P &B,P &C,P &D) {    if (SegmentProperIntersection(A,C,B,D)) return 1;    swap(B,C);    if (SegmentProperIntersection(A,C,B,D)) return 1;    swap(D,C);    if (SegmentProperIntersection(A,C,B,D)) return 1;    return 0;}bool IsParallel(P A,P B,P C,P D) {    return dcmp(Cross(B-A,D-C))==0;}bool IsPerpendicular(V A,V B) {    return dcmp(Dot(A,B))==0;}//先调用ConvexPolygon 求凸包并确认是否是四边形// Trapezium-梯形 Rhombus-菱形  bool IsTrapezium(P A,P B,P C,P D){    return IsParallel(A,B,C,D)^IsParallel(B,C,A,D);}bool IsParallelogram(P A,P B,P C,P D) {    return IsParallel(A,B,C,D)&&IsParallel(B,C,A,D);}bool IsRhombus(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&dcmp(Length(B-A)-Length(C-B))==0;}bool IsRectangle(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&IsPerpendicular(B-A,D-A);}bool IsSquare(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&IsPerpendicular(B-A,D-A)&&dcmp(Length(B-A)-Length(C-B))==0;}//chord-弦 arc-弧 double ArcDis(double chord,double r) {    return 2*asin(chord/2/r)*r;} typedef vector<P> Polygon ;int isPointInPolygon(P p,Polygon poly) {    int wn=0;    int n=poly.size();    Rep(i,n) {        if (OnSegment(p,poly[i],poly[(i+1)%n])) return -1;        int k=dcmp(Cross(poly[(i+1)%n]-poly[i],p-poly[i]));        int d1 = dcmp(poly[i].y-p.y);        int d2 = dcmp(poly[(i+1)%n].y-p.y);        if ( k > 0 && d1 <= 0 && d2 > 0 ) wn++;        if ( k < 0 && d2 <= 0 && d1 > 0 ) wn--;    }    if (wn!=0) return 1;    return 0;}int ConvexHull(P *p,int n,P *ch) {    sort(p,p+n);    int m=0;    Rep(i,n) {        while(m>1 && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;        ch[m++]=p[i];    }    int k=m;    RepD(i,n-2) {        while(m>k && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;        ch[m++]=p[i];    }    if ( n > 1 ) m--;    return m;}//把两点式转为一般式 ax+by+c=0 void Two_pointFormToGeneralForm(P A,P B,double &a,double &b,double &c){    a = A.y - B.y;    b = B.x - A.x;    c = Cross(A,B);}//ax+by+c>0 的 P,V有向线段 void GeneralFormToPointVectorForm(P &p,V &v,double a,double b,double c){    v=V(b,-a);    if (fabs(a)>fabs(b)) p=P(-c/a,0);    else p=P(0,-c/b);}//有向直线A->B 切割多边行poly 可能返回单点线段 O(n)Polygon CutPolygon(Polygon poly,P A,P B){    Polygon newpoly;    int n=poly.size();    Rep(i,n) {        P C = poly[i];        P D = poly[(i+1)%n];        if (dcmp(Cross(B-A,C-A))>=0)  newpoly.pb(C);        if (dcmp(Cross(B-A,C-D))) {            P ip = GetLineIntersection(A,B-A,C,D-C);            if (OnSegment(ip,C,D)) newpoly.pb(ip);        }    }}//线上不算 bool OnLeft(Line L,P p) {    return Cross(L.v,p-L.p) > 0;} P GetIntersection(Line a,Line b) {    V u=a.p-b.p;    double t = Cross(b.v,u) / Cross(a.v, b.v);    return a.p + a.v*t;}int HalfplaneIntersection(Line *L, int n, P* poly) {    sort(L,L+n);    int fi,la;    P *p = new P[n];    Line *q = new Line[n];    q[fi=la=0 ] = L[0];    For(i,n-1) {        while (fi < la && !OnLeft(L[i],p[la-1])) la--;        while (fi < la && !OnLeft(L[i],p[fi])) fi++;        q[++la] = L[i];        if (fabs(Cross(q[la].v, q[la-1].v))<eps) {            la--;            if (OnLeft(q[la],L[i].p)) q[la] = L[i];        }        if (fi<la) p[la-1] = GetIntersection(q[la-1],q[la]);    }    while(fi < la && !OnLeft(q[fi],p[la-1])) la--;    if (la-fi<=1) return 0;     p[la] = GetIntersection(q[la],q[fi]);    int m=0;    Fork(i,fi,la) poly[m++]=p[i];    return m;} // hypot(double x,double y); return sqrt(x*x+y*y)int v[200],u[200],w[200];P p[200],poly[200];Line L[200];int n;int main(){    freopen("uva1298.in","r",stdin);//  freopen(".out","w",stdout);    while(cin>>n&&n) {        Rep(i,n) {            cin>>v[i]>>u[i]>>w[i];        }        Rep(i,n) {            bool flag=0;            double k=10000;            int lc=0;            Rep(j,n) if (i^j) {                if(v[i]<=v[j]&&u[i]<=u[j]&&w[i]<=w[j]) {                    flag=1; break;                }                if (v[i]>=v[j]&&u[i]>=u[j]&&w[i]>=w[j]) continue;                double a=k/v[j]-k/w[j]-(k/v[i]-k/w[i]);                double b=k/u[j]-k/w[j]-(k/u[i]-k/w[i]);                double c=k/w[j]-k/w[i];                P p1,v1;                GeneralFormToPointVectorForm(p1,v1,a,b,c);                L[lc++] = Line(p1,v1);            }            if (!flag) {                L[lc++] = Line(P(0,0),V(1,0));                L[lc++] = Line(P(0,0),V(0,-1));                L[lc++] = Line(P(0,1),V(-1,1));                if (!HalfplaneIntersection(L,lc,poly)) flag=1;            }            if (!flag) puts("Yes"); else puts("No");         }    }    return 0;}

UVA 1475 Jungle Outpost

#include<bits/stdc++.h>using namespace std;#define For(i,n) for(int i=1;i<=n;i++)#define Fork(i,k,n) for(int i=k;i<=n;i++)#define Rep(i,n) for(int i=0;i<n;i++)#define ForD(i,n) for(int i=n;i;i--)#define ForkD(i,k,n) for(int i=n;i>=k;i--)#define RepD(i,n) for(int i=n;i>=0;i--)#define Forp(x) for(int p=Pre[x];p;p=Next[p])#define Forpiter(x) for(int &p=iter[x];p;p=Next[p])  #define Lson (o<<1)#define Rson ((o<<1)+1)#define MEM(a) memset(a,0,sizeof(a));#define MEMI(a) memset(a,127,sizeof(a));#define MEMi(a) memset(a,128,sizeof(a));#define INF (2139062143)#define F (100000007)#define pb push_back#define mp make_pair #define fi first#define se second#define vi vector<int> #define pi pair<int,int>#define SI(a) ((a).size())typedef long long ll;typedef long double ld;typedef unsigned long long ull;ll mul(ll a,ll b){return (a*b)%F;}ll add(ll a,ll b){return (a+b)%F;}ll sub(ll a,ll b){return (a-b+llabs(a-b)/F*F+F)%F;}void upd(ll &a,ll b){a=(a%F+b%F)%F;}int read(){    int x=0,f=1; char ch=getchar();    while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}    while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}    return x*f;} ll sqr(ll a){return a*a;}ld sqr(ld a){return a*a;}double sqr(double a){return a*a;}ld PI = 3.141592653589793238462643383;class P{public:    double x,y;    P(double x=0,double y=0):x(x),y(y){}    friend long double dis2(P A,P B){return sqr(A.x-B.x)+sqr(A.y-B.y);  }    friend long double Dot(P A,P B) {return A.x*B.x+A.y*B.y; }    friend long double Length(P A) {return sqrt(Dot(A,A)); }    friend long double Angle(P A,P B) {return acos(Dot(A,B) / Length(A) / Length(B) ); }    friend P operator- (P A,P B) { return P(A.x-B.x,A.y-B.y); }    friend P operator+ (P A,P B) { return P(A.x+B.x,A.y+B.y); }    friend P operator* (P A,double p) { return P(A.x*p,A.y*p); }    friend P operator/ (P A,double p) { return P(A.x/p,A.y/p); }    friend bool operator< (const P& a,const P& b) {return a.x<b.x||(a.x==b.x&& a.y<b.y);}}; const double eps=1e-10;int dcmp(double x) {    if (fabs(x)<eps) return 0; else return x<0 ? -1 : 1; }bool operator==(const P& a,const P& b) {    return dcmp(a.x-b.x)==0 && dcmp(a.y-b.y) == 0;} typedef P V;double Cross(V A,V B) {return A.x*B.y - A.y*B.x;}double Area2(P A,P B,P C) {return Cross(B-A,C-A);}V Rotate(V A,double rad) {    return V(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));} // A 不是 0向量 V Normal(V A) {     double L = Length(A);    return V(-A.y/L , A.x/L); }namespace complex_G{    typedef complex<double> Point;    //real(p):实部 imag(p):虚部 conj(p):共轭     typedef Point Vector;    double Dot(Vector A,Vector B) {return real(conj(A)*B); }    double Cross(Vector A,Vector B) {return imag(conj(A)*B); }    Vector Rotate(Vector A,double rad) {return A*exp(Point(0,rad)); }}//Cross(v,w)==0(平行)时,不能调这个函数 P GetLineIntersection(P p,V v,P Q,V w){    V u = p-Q;    double t = Cross(w,u)/Cross(v,w);    return p+v*t;}P GetLineIntersectionB(P p,V v,P Q,V w){    return GetLineIntersection(p,v-p,Q,w-Q);}double DistanceToLine(P p,P A,P B) {    V v1 = B-A, v2 = p-A;    return fabs(Cross(v1,v2))/Length(v1);}double DistanceToSegment(P p,P A,P B) {    if (A==B) return Length(p-A);    V v1 = B-A, v2 = p-A, v3 = p - B;    if (dcmp(Dot(v1,v2))<0) return Length(v2);    else if (dcmp(Dot(v1,v3))>0 ) return Length(v3);    else return fabs(Cross(v1,v2) ) / Length(v1);}P GetLineProjection(P p,P A,P B) {    V v=B-A;    return A+v*(Dot(v,p-A)/Dot(v,v));}//规范相交-线段相交且交点不在端点 bool SegmentProperIntersection(P a1,P a2,P b1,P b2) {     double  c1 = Cross(a2-a1,b1-a1) , c2 = Cross(a2-a1,b2-a1),            c3 = Cross(b2-b1,a1-b1) , c4 = Cross(b2-b1,a2-b1);    return dcmp(c1)*dcmp(c2)<0 && dcmp(c3)*dcmp(c4)<0;}//点在线段上（不包含端点） bool OnSegment(P p,P a1,P a2) {    return dcmp(Cross(a1-p,a2-p)) == 0 && dcmp(Dot(a1-p,a2-p))<0;}double PolygonArea(P *p,int n) {    double area=0;    For(i,n-2) area+=Cross(p[i]-p[0],p[i+1]-p[0]);    return area/2;} /*欧拉公式： V+F-E=2 V-点数 F面数 E边数 */P read_point() {    P a;    scanf("%lf%lf",&a.x,&a.y);    return a;   } struct C{    P c;    double r,x,y;    C(P c,double r):c(c),r(r),x(c.x),y(c.y){}    P point(double a) {        return P(c.x+cos(a)*r,c.y+sin(a)*r);    }};struct Line{    P p;    V v;    double ang;    Line(){}    Line(P p,V v):p(p),v(v) {ang=atan2(v.y,v.x); }    bool operator<(const Line & L) const {        return ang<L.ang;    }    P point(double a) {        return p+v*a;    }};int getLineCircleIntersection(Line L,C cir,double &t1,double &t2,vector<P> & sol) {    if (dcmp(DistanceToLine(cir.c,L.p,L.p+L.v)-cir.r)==0) {        sol.pb(GetLineProjection(cir.c,L.p,L.p+L.v));        return 1;    }    double a = L.v.x, b = L.p.x - cir.c.x, c = L.v.y, d= L.p.y - cir.c.y;    double e = a*a+c*c, f = 2*(a*b + c*d), g = b*b+d*d-cir.r*cir.r;    double delta = f*f - 4*e*g;    if (dcmp(delta)<0) return 0;    else if (dcmp(delta)==0) {        t1 = t2 = -f / (2*e); sol.pb(L.point(t1));        return 1;    }     t1 = (-f - sqrt(delta)) / (2*e); sol.pb(L.point(t1));    t2 = (-f + sqrt(delta)) / (2*e); sol.pb(L.point(t2));    return 2;}double angle(V v) {return atan2(v.y,v.x);}int getCircleCircleIntersection(C C1,C C2,vector<P>& sol) {    double d = Length(C1.c-C2.c);    if (dcmp(d)==0) {        if (dcmp(C1.r - C2.r)==0) return -1; //2圆重合         return 0;    }    if (dcmp(C1.r+C2.r-d)<0) return 0;    if (dcmp(fabs(C1.r-C2.r)-d)>0) return 0;    double a = angle(C2.c-C1.c);    double da = acos((C1.r*C1.r+d*d - C2.r*C2.r)/ (2*C1.r*d));    P p1 = C1.point(a-da), p2 = C1.point(a+da);    sol.pb(p1);    if (p1==p2) return 1;    sol.pb(p2);    return 2; }// Tangents-切线 int getTangents(P p,C c,V* v) {    V u= c.c-p;    double dist = Length(u);    if (dist<c.r) return 0;    else if (dcmp(dist-c.r)==0) {        v[0]=Rotate(u,PI/2);        return 1;    } else {        double ang = asin(c.r / dist);        v[0]=Rotate(u,-ang);        v[1]=Rotate(u,ang);        return 2;    }       }//这个函数假设整数坐标和整数半径//double时要把int改成double int getTangents(C A,C B,P* a,P* b) {    int cnt=0;    if (A.r<B.r) {swap(A,B),swap(a,b);}    int d2 = (A.c.x-B.c.x)*(A.c.x-B.c.x) + (A.c.y-B.c.y)*(A.c.y-B.c.y);    int rdiff = A.r-B.r;    int rsum = A.r+B.r;    if (d2<rdiff*rdiff) return 0;    double base = atan2(B.y-A.y,B.x-A.x);    if (d2==0 && A.r == B.r) return -1;    if (d2 == rdiff*rdiff) {        a[cnt] = A.point(base); b[cnt] = B.point(base); ++cnt;        return 1;    }    double ang = acos((A.r-B.r)/sqrt(d2));    a[cnt] = A.point(base+ang); b[cnt] = B.point(base+ang); ++cnt;    a[cnt] = A.point(base-ang); b[cnt] = B.point(base-ang); ++cnt;    if (d2==rsum*rsum) {        a[cnt] = A.point(base); b[cnt] = B.point(PI+base); ++cnt;    }    else if (d2>rsum*rsum) {        double ang = acos((A.r+B.r)/sqrt(d2));        a[cnt] = A.point(base+ang); b[cnt] = B.point(PI+base+ang); ++cnt;        a[cnt] = A.point(base-ang); b[cnt] = B.point(PI+base-ang); ++cnt;    }    return cnt; }//Circumscribed-外接 C CircumscribedCircle(P p1,P p2,P p3) {    double Bx = p2.x-p1.x, By= p2.y-p1.y;    double Cx = p3.x-p1.x, Cy= p3.y-p1.y;    double D = 2*(Bx*Cy-By*Cx);    double cx = (Cy*(Bx*Bx+By*By)-By*(Cx*Cx+Cy*Cy))/D + p1.x;    double cy = (Bx*(Cx*Cx+Cy*Cy)-Cx*(Bx*Bx+By*By))/D + p1.y;    P p =P(cx,cy);    return C(p,Length(p1-p));}//Inscribed-内接 C InscribedCircle(P p1,P p2,P p3) {    double a = Length(p2-p3);    double b = Length(p3-p1);    double c = Length(p1-p2);    P p = (p1*a+p2*b+p3*c)/(a+b+c);    return C(p,DistanceToLine(p,p1,p2));}double torad(double deg) {    return deg/180*acos(-1);}//把 角度+-pi 转换到 [0,pi) 上 double radToPositive(double rad) {    if (dcmp(rad)<0) rad=ceil(-rad/PI)*PI+rad;    if (dcmp(rad-PI)>=0) rad-=floor(rad/PI)*PI;     return rad;} double todeg(double rad) {    return rad*180/acos(-1);}//(R,lat,lng)->(x,y,z)void get_coord(double R,double lat,double lng,double &x,double &y,double &z) {    lat=torad(lat);    lng=torad(lng);    x=R*cos(lat)*cos(lng);    y=R*cos(lat)*sin(lng);    z=R*sin(lat);}void print(double a) {    printf("%.6lf",a); }void print(P p) {    printf("(%.6lf,%.6lf)",p.x,p.y);}template<class T>void print(vector<T> v) {    sort(v.begin(),v.end());    putchar('[');    int n=v.size();    Rep(i,n) {        print(v[i]);        if (i<n-1) putchar(',');     }    puts("]");}// 把直线沿v平移// Translation-平移 Line LineTranslation(Line l,V v) {    l.p=l.p+v;    return l;}void CircleThroughAPointAndTangentToALineWithRadius(P p,Line l,double r,vector<P>& sol) {    V e=Normal(l.v);    Line l1=LineTranslation(l,e*r),l2=LineTranslation(l,e*(-r));    double t1,t2;    getLineCircleIntersection(l1,C(p,r),t1,t2,sol);    getLineCircleIntersection(l2,C(p,r),t1,t2,sol);}void CircleTangentToTwoLinesWithRadius(Line l1,Line l2,double r,vector<P>& sol) {    V e1=Normal(l1.v),e2=Normal(l2.v);    Line L1[2]={LineTranslation(l1,e1*r),LineTranslation(l1,e1*(-r))},         L2[2]={LineTranslation(l2,e2*r),LineTranslation(l2,e2*(-r))};    Rep(i,2) Rep(j,2) sol.pb(GetLineIntersection(L1[i].p,L1[i].v,L2[j].p,L2[j].v));}void CircleTangentToTwoDisjointCirclesWithRadius(C c1,C c2,double r,vector<P>& sol) {    c1.r+=r; c2.r+=r;    getCircleCircleIntersection(c1,c2,sol);}//确定4个点能否组成凸多边形，并按顺序（不一定是逆时针）返回 bool ConvexPolygon(P &A,P &B,P &C,P &D) {    if (SegmentProperIntersection(A,C,B,D)) return 1;    swap(B,C);    if (SegmentProperIntersection(A,C,B,D)) return 1;    swap(D,C);    if (SegmentProperIntersection(A,C,B,D)) return 1;    return 0;}bool IsParallel(P A,P B,P C,P D) {    return dcmp(Cross(B-A,D-C))==0;}bool IsPerpendicular(V A,V B) {    return dcmp(Dot(A,B))==0;}//先调用ConvexPolygon 求凸包并确认是否是四边形// Trapezium-梯形 Rhombus-菱形  bool IsTrapezium(P A,P B,P C,P D){    return IsParallel(A,B,C,D)^IsParallel(B,C,A,D);}bool IsParallelogram(P A,P B,P C,P D) {    return IsParallel(A,B,C,D)&&IsParallel(B,C,A,D);}bool IsRhombus(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&dcmp(Length(B-A)-Length(C-B))==0;}bool IsRectangle(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&IsPerpendicular(B-A,D-A);}bool IsSquare(P A,P B,P C,P D) {    return IsParallelogram(A,B,C,D)&&IsPerpendicular(B-A,D-A)&&dcmp(Length(B-A)-Length(C-B))==0;}//chord-弦 arc-弧 double ArcDis(double chord,double r) {    return 2*asin(chord/2/r)*r;} typedef vector<P> Polygon ;int isPointInPolygon(P p,Polygon poly) {    int wn=0;    int n=poly.size();    Rep(i,n) {        if (OnSegment(p,poly[i],poly[(i+1)%n])) return -1;        int k=dcmp(Cross(poly[(i+1)%n]-poly[i],p-poly[i]));        int d1 = dcmp(poly[i].y-p.y);        int d2 = dcmp(poly[(i+1)%n].y-p.y);        if ( k > 0 && d1 <= 0 && d2 > 0 ) wn++;        if ( k < 0 && d2 <= 0 && d1 > 0 ) wn--;    }    if (wn!=0) return 1;    return 0;}int ConvexHull(P *p,int n,P *ch) {    sort(p,p+n);    int m=0;    Rep(i,n) {        while(m>1 && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;        ch[m++]=p[i];    }    int k=m;    RepD(i,n-2) {        while(m>k && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0) m--;        ch[m++]=p[i];    }    if ( n > 1 ) m--;    return m;}//把两点式转为一般式 ax+by+c=0 void Two_pointFormToGeneralForm(P A,P B,double &a,double &b,double &c){    a = A.y - B.y;    b = B.x - A.x;    c = Cross(A,B);}//ax+by+c>0 的 P,V有向线段 void GeneralFormToPointVectorForm(P &p,V &v,double a,double b,double c){    v=V(b,-a);    if (fabs(a)>fabs(b)) p=P(-c/a,0);    else p=P(0,-c/b);}//有向直线A->B 切割多边行poly 可能返回单点线段 O(n)Polygon CutPolygon(Polygon poly,P A,P B){    Polygon newpoly;    int n=poly.size();    Rep(i,n) {        P C = poly[i];        P D = poly[(i+1)%n];        if (dcmp(Cross(B-A,C-A))>=0)  newpoly.pb(C);        if (dcmp(Cross(B-A,C-D))) {            P ip = GetLineIntersection(A,B-A,C,D-C);            if (OnSegment(ip,C,D)) newpoly.pb(ip);        }    }}//线上不算 bool OnLeft(Line L,P p) {    return Cross(L.v,p-L.p) > 0;} P GetIntersection(Line a,Line b) {    V u=a.p-b.p;    double t = Cross(b.v,u) / Cross(a.v, b.v);    return a.p + a.v*t;}int HalfplaneIntersection(Line *L, int n, P* poly) {    sort(L,L+n);    int fi,la;    P *p = new P[n];    Line *q = new Line[n];    q[fi=la=0 ] = L[0];    For(i,n-1) {        while (fi < la && !OnLeft(L[i],p[la-1])) la--;        while (fi < la && !OnLeft(L[i],p[fi])) fi++;        q[++la] = L[i];        if (fabs(Cross(q[la].v, q[la-1].v))<eps) {            la--;            if (OnLeft(q[la],L[i].p)) q[la] = L[i];        }        if (fi<la) p[la-1] = GetIntersection(q[la-1],q[la]);    }    while(fi < la && !OnLeft(q[fi],p[la-1])) la--;    if (la-fi<=1) return 0;     p[la] = GetIntersection(q[la],q[fi]);    int m=0;    Fork(i,fi,la) poly[m++]=p[i];    return m;} // hypot(double x,double y); return sqrt(x*x+y*y)#define MAXN (50000+10)P p[MAXN],poly[MAXN];Line L[MAXN];int n;int main(){//  freopen("uva1475.in","r",stdin);//  freopen(".out","w",stdout);    while(cin>>n) {        Rep(i,n) {            p[i]=read_point();          }        int l=0,r=n-2,ans=n-2;        while(l<=r) {            int m=(l+r)/2;              int lc=0;            Rep(i,n) {                P A=p[i];                P B=p[(i+1+m)%n];                L[lc++] = Line(B,A-B);                      }            if(!HalfplaneIntersection(L,lc,poly)) r=m-1,ans=m;else l=m+1;        }        cout<<ans<<endl;    }    return 0;}

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