几何基础专题

UVA 11437 Triangle Fun
UVA 11800 Determine the Shape 四边形判定
UVA 11646 Athletics Track
UVA 11817 Tunnelling the Earth 球面距离
UVA 1473 Dome of Circus
UVA 11524 InCircle
UVA 11731 Ex-circles 旁切圆
UVA 12300 Smallest Regular Polygon
UVA 10566 Crossed Ladders
UVA 11186 Circum Triangle
UVA 12165 Triangle Hazard

UVA 11437 Triangle Fun

#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);
}

P getP(P A,P B,P C) {
    P D=B+(C-B)/3;
    P E=C+(A-C)/3;
    return GetLineIntersection(A,D-A,B,E-B);

}
int main()
{
//  freopen("uva11437.in","r",stdin);
//  freopen(".out","w",stdout);

    int T=read();
    while(T--){
        P A=read_point(),B=read_point(),C=read_point();
        P p[3]={getP(A,B,C),getP(B,C,A),getP(C,A,B)};
        printf("%0.lf\n",PolygonArea(p,3));
    }

    return 0;
}

UVA 11800 Determine the Shape 四边形判定

#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);
}

P p[4];
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;
}

int main()
{
//  freopen("uva11800.in","r",stdin);
//  freopen(".out","w",stdout);
    int T=read();
    For(kcase,T) {
        Rep(i,4) p[i]=read_point();

        cout<<"Case "<<kcase<<": ";
        if (!ConvexPolygon(p[0],p[1],p[2],p[3])) puts("Ordinary Quadrilateral");
        else {
            P A=p[0],B=p[1],C=p[2],D=p[3];
            if (IsSquare(A,B,C,D)) puts("Square");
            else if (IsRectangle(A,B,C,D)) puts("Rectangle");
            else if (IsRhombus(A,B,C,D)) puts("Rhombus");
            else if (IsParallelogram(A,B,C,D)) puts("Parallelogram");
            else if (IsTrapezium(A,B,C,D)) puts("Trapezium");
            else puts("Ordinary Quadrilateral");

        }
    }

    return 0;
}

UVA 11646 Athletics Track

#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;
}
int main()
{
//  freopen("uva11646.in","r",stdin);
//  freopen(".out","w",stdout);
    double a,b;
    int kcase=1;
    while(scanf("%lf : %lf\n",&a,&b)!=EOF) {
        double r=sqrt(a*a+b*b)/2;
        double xita=asin(b/2.0/r)*2;
        double rxita=r*xita;
        double x=200.0/(a +rxita);
        printf("Case %d: %.10lf %.10lf\n",kcase++,a*x,b*x);
    }

    return 0;
}

UVA 11817 Tunnelling the Earth 球面距离

#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;
}
int main()
{
//  freopen("uva11817.in","r",stdin);
//  freopen(".out","w",stdout);
    double a,b;
    int T=read();
    const double r=6371009;
    double lat,lng,lat2,lng2;
    while(scanf("%lf%lf%lf%lf",&lat,&lng,&lat2,&lng2)!=EOF) {

        double x,y,z,x2,y2,z2;
        get_coord(r,lat,lng,x,y,z);
        get_coord(r,lat2,lng2,x2,y2,z2);
        double chord=sqrt(sqr(x-x2)+sqr(y-y2)+sqr(z-z2));
        double ans=round(ArcDis(chord,r)-chord);
        printf("%0.lf\n",ans);
    }

    return 0;
}

UVA 1473 Dome of Circus

#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())
#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<‘ ‘; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \
                        For(j,m-1) cout<<a[i][j]<<‘ ‘;                        cout<<a[i][m]<<endl;                         }
typedef long long ll;
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;
}
const int MAXN = 10000+10;
int n;
double r[MAXN],z[MAXN];
double getR(double H) {
    double R=0;
    Rep(i,n) R=max(R,z[i]*r[i]/(H-z[i])+r[i]);
    return R;
}
int main()
{
//  freopen("uva1473.in","r",stdin);
//  freopen(".out","w",stdout);

    while(cin>>n) {
        Rep(i,n) {
            double x,y;
            cin>>x>>y>>z[i];
            r[i]=sqrt(x*x+y*y);
        }
        double L=0,R=1e9;
        Rep(i,n) L=max(L,z[i]);
        while(R-L>1e-9) {
            double m1=L+(R-L)/3;
            double m2=R-(R-L)/3;
            double r1=getR(m1),r2=getR(m2);
            if (r1*r1*m1<r2*r2*m2) R=m2; else L=m1;
        }
        cout<<setiosflags(ios::fixed)<<setprecision(3);
        cout<<L<<‘ ‘<<getR(L)<<endl;
    }

    return 0;
}

UVA 11524 InCircle

内切圆面积公式S=(a+b+c)r2

海伦公式S=p(p?a)(p?b)(p?c)?????????????????√,p=(a+b+c)/2

#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())
#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<‘ ‘; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \
                        For(j,m-1) cout<<a[i][j]<<‘ ‘;                        cout<<a[i][m]<<endl;                         }
typedef long long ll;
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;
}
int main()
{
//  freopen("uva11524.in","r",stdin);
//  freopen(".out","w",stdout);

    const double eps=1e-5;
    int T=read();
    while(T--) {
        double r,m1,n1,m2,n2,m3,n3;
        cin>>r>>m1>>n1>>m2>>n2>>m3>>n3;
        double a=1.0;
        double b=1./(m1+n1)*m1/n3*(m3+n3);
        double c=1./(m1+n1)*n1/m2*(m2+n2);
        double S=r*(a+b+c)/2;
        double p=(a+b+c)/2;
        double S2=sqrt(p*(p-a)*(p-b)*(p-c));
        double k=S2/S;
        cout<<setiosflags(ios::fixed)<<setprecision(4);
        cout<<S/k<<endl;
    }

    return 0;
}

UVA 11731 Ex-circles 旁切圆

旁切圆半径：2S△?a+b+c

旁切圆座标：Ja=(?ax1+bx2+cx3?a+b+c,?ay1+by2+cy3?a+b+c)

盘切圆圆心角：∠A旁切=π/2?∠C

#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())
#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<‘ ‘; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \
                        For(j,m-1) cout<<a[i][j]<<‘ ‘;                        cout<<a[i][m]<<endl;                         }
typedef long long ll;
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;
}
double angle(double a,double b,double c) {
    return acos((a*a+b*b-c*c)/2/a/b);
}
double S;
double getR(double a,double b,double c) {
    return 2*S/(-a+b+c);
}
double PI=acos(-1);
int main()
{
//  freopen("uva11731.in","r",stdin);
//  freopen(".out","w",stdout);

    int a,b,c,kcase=1;
    while(cin>>a>>b>>c&&a) {
        double p=(a+b+c)/2.0;
        S=sqrt(p*(p-a)*(p-b)*(p-c));
        double r1=getR(a,b,c),r2=getR(b,c,a),r3=getR(c,a,b);
        double ans1=S+(a*r1+b*r2+c*r3)/2;
        double ans2=(PI-angle(b,c,a))/2*r1*r1
                    +(PI-angle(a,c,b))/2*r2*r2
                    +(PI-angle(a,b,c))/2*r3*r3;
        ans2/=2;
        printf("Case %d: %.2f %.2f\n",kcase++,ans1,ans2);
    }

    return 0;
}

UVA 12300 Smallest Regular Polygon

根据外接圆半径算

贪心：对角线中最长的。

#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())
#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<‘ ‘; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \
                        For(j,m-1) cout<<a[i][j]<<‘ ‘;                        cout<<a[i][m]<<endl;                         }
typedef long long ll;
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;
}
double PI = acos(-1);
int main()
{
//  freopen("uva12300.in","r",stdin);
//  freopen(".out","w",stdout);
    double a,b,c,d;
    int n;
    while(cin>>a>>b>>c>>d>>n&&n) {
        double dis=sqrt((c-a)*(c-a)+(b-d)*(b-d));

        double xita=2*PI/n,r;
        if (n%2==0) {
            r=dis/2;
        } else {
            double phi = PI-xita/2;
            r=sqrt(dis*dis/2/(1-cos(phi)));
        }
        double S=r*r*sin(xita)*n/2;
        printf("%.6lf\n",S);
    }

    return 0;
}

UVA 10566 Crossed Ladders

#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())
#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<‘ ‘; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \
                        For(j,m-1) cout<<a[i][j]<<‘ ‘;                        cout<<a[i][m]<<endl;                         }
typedef long long ll;
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;
}
int main()
{
//  freopen("uva10566.in","r",stdin);
//  freopen(".out","w",stdout);

    double x,y,c;
    while(cin>>x>>y>>c) {
        double L=0,R=min(x,y);
        while(R-L>=1e-9) {
            double m=(L+R)/2;
            double p=1/sqrt(x*x-m*m)+1/sqrt(y*y-m*m)-1/c;
            if (p<0) L=m; else R=m;
        }
        printf("%.3lf\n",L);

    }

    return 0;
}

UVA 11186 Circum Triangle

S△abc=S△Oab+S△Obc?S△Oac

考虑每个有一个点在圆心的三角形出现的次数，容斥

#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())
#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<‘ ‘; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \
                        For(j,m-1) cout<<a[i][j]<<‘ ‘;                        cout<<a[i][m]<<endl;                         }
typedef long long ll;
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;
}
double rad[1000];
int main()
{
//  freopen("uva11186.in","r",stdin);
//  freopen(".out","w",stdout);
    int n,r;
    while(cin>>n>>r&&n) {
        Rep(i,n) {
            cin>>rad[i];
            rad[i]=rad[i]/180*acos(-1);
        }
        sort(rad,rad+n);
        double ans=0;
        Rep(i,n) Fork(j,i+1,n-1) ans+=(double)(n+2*i-2*j)*sin(rad[j]-rad[i]);
        ans*=r*r/2;
        printf("%.0lf\n",ans);

    }

    return 0;
}

UVA 12165 Triangle Hazard

梅涅劳斯定理:如果一条直线与△ABC的三边AB、BC、CA或其延长线交于F、D、E点，那么(AF/FB)×(BD/DC)×(CE/EA)=1。

对题目中

△ABD,FC 与 △ACD,BE 用定理，联立解出AR/RP

#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())
#define Pr(kcase,ans) printf("Case #%d: %lld\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<‘ ‘; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \
                        For(j,m-1) cout<<a[i][j]<<‘ ‘;                        cout<<a[i][m]<<endl;                         }
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);}

};

P read_point() {
    P a;
    scanf("%lf%lf",&a.x,&a.y);
    return a;
}
P getA(P p,P r,double m1,double m2,double m3,double m4,double m5,double m6) {
    double dr_ra=1/(m5/m6*(m1+m2)/m2);
    double dp_pa=1/(m4/m3*(m1+m2)/m1);
    double ra_da=1/(dr_ra+1);
    double pa_da=1/(dp_pa+1);
    double pr_da=pa_da-ra_da;
    double ra_pr=ra_da/pr_da;
    double pr=Length(p-r);
    double ra=pr*ra_pr;
    return r+(r-p)*ra_pr;
}
int main()
{
//  freopen("uva12165.in","r",stdin);
//  freopen(".out","w",stdout);
    int T=read();
    while(T--) {
        P p=read_point(),q=read_point(),r=read_point();
        double m[7];
        For(i,6) cin>>m[i];
        P A=getA(p,r,m[1],m[2],m[3],m[4],m[5],m[6]),
          C=getA(r,q,m[5],m[6],m[1],m[2],m[3],m[4]),
          B=getA(q,p,m[3],m[4],m[5],m[6],m[1],m[2]);
        printf("%.8lf %.8lf %.8lf %.8lf %.8lf %.8lf\n",A.x,A.y,B.x,B.y,C.x,C.y);
    }

    return 0;
}

时间： 2024-10-02 21:46:41

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