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UVA 11437 Triangle Fun
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UVA 11800 Determine the Shape 4边形判定
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UVA 11646 Athletics Track
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UVA 11817 Tunnelling the Earth 球面距离
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UVA 1473 Dome of Circus
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UVA 11524 InCircle
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UVA 11731 Ex-circles 旁切圆
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UVA 12300 Smallest Regular Polygon
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UVA 10566 Crossed Ladders
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UVA 11186 Circum Triangle
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UVA 12165 Triangle Hazard
UVA 11437 Triangle Fun
#include 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 #define ForD(i,n) for(int i=n;i;i--) #define ForkD(i,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,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 #define pi pair #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.xconst double eps= 1e⑴0; int dcmp( double x) { if ( fabs(x) 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));
} V Normal(V A) { double L = Length(A); return V(-A.y/L,A.x/L);
} namespace complex_G{ typedef complex<double> Point; 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)); }
} 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 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 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 B) {
V v=B-A; return A+v*(Dot(v,p-A)/Dot(v,v));
} 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;
} 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;
} 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 angdouble a) { return p+v*a;
}
}; int getLineCircleIntersection(Line L,C cir,double &t1,double &t2,vector
& sol) { if (dcmp(DistanceToLine(cir.c,L.p,L.p+L.v)-cir.r)==0) {
sol.pb(GetLineProjection(cir.c,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
& sol) { double d = Length(C1.c-C2.c); if (dcmp(d)==0) { if (dcmp(C1.r - C2.r)==0) return -1; 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;
} int getTangents(P p,C c,V* v) {
V u= c.c-p; double dist = Length(u); if (distreturn 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;
}
} int getTangents(C A,C B,P* a,P* b) { int cnt=0; if (A.rint 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 (d2return 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;
} 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));
} C InscribedCircle(P p1,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);
} 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);
} 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 v) {
sort(v.begin(),v.end()); putchar('['); int n=v.size();
Rep(i,n) {
print(v[i]); if (i1) putchar(',');
} puts("]");
} Line LineTranslation(Line l,V v) {
l.p=l.p+v; return l;
} void CircleThroughAPointAndTangentToALineWithRadius(P p,Line l,double r,vector
& 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,sol);
} void CircleTangentToTwoLinesWithRadius(Line l1,Line l2,vector
& 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,vector
& sol) {
c1.r+=r; c2.r+=r;
getCircleCircleIntersection(c1,c2,sol);
}
P getP(P A,P C) {
P D=B+(C-B)/3;
P E=C+(A-C)/3; return GetLineIntersection(A,D-A,B,E-B);
} int main()
{ int T=read(); while(T--){
P A=read_point(),B=read_point(),C=read_point();
P p[3]={getP(A,C),getP(B,C,A),getP(C,A,B)}; printf("%0.lfn",PolygonArea(p,3));
} return 0;
}
UVA 11800 Determine the Shape 4边形判定
#include using namespace std; #define For(i,sol);
}
P p[4]; bool ConvexPolygon(P &A,P &B,P &C,P &D) { if (SegmentProperIntersection(A,D)) return 1;
swap(B,C); if (SegmentProperIntersection(A,D)) return 1;
swap(D,D)) return 1; return 0;
} bool IsParallel(P A,P C,P D) { return dcmp(Cross(B-A,D-C))==0;
} bool IsPerpendicular(V A,V B) { return dcmp(Dot(A,B))==0;
} bool IsTrapezium(P A,P D){ return IsParallel(A,D)^IsParallel(B,D);
} bool IsParallelogram(P A,P D) { return IsParallel(A,D)&&IsParallel(B,D);
} bool IsRhombus(P A,P D) { return IsParallelogram(A,D)&&dcmp(Length(B-A)-Length(C-B))==0;
} bool IsRectangle(P A,D)&&IsPerpendicular(B-A,D-A);
} bool IsSquare(P A,D-A)&&dcmp(Length(B-A)-Length(C-B))==0;
} int main()
{ int T=read();
For(kcase,T) {
Rep(i,4) p[i]=read_point(); cout<<"Case "<": "; 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,D)) puts("Square"); else if (IsRectangle(A,D)) puts("Rectangle"); else if (IsRhombus(A,D)) puts("Rhombus"); else if (IsParallelogram(A,D)) puts("Parallelogram"); else if (IsTrapezium(A,D)) puts("Trapezium"); else puts("Ordinary Quadrilateral");
}
} return 0;
}
UVA 11646 Athletics Track
#include using namespace std; #define For(i,n) for(int i=1;i<=n;i++) #define Fork(i,n) for(int i=k;i<=n;i++) #define Rep(i,n) for(int i=0;i #define ForD(i,n) for(int i=n;i;i--) #define ForkD(i,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,sizeof(a)); #define MEMI(a) memset(a,sizeof(a)); #define MEMi(a) memset(a,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 #define pi pair #define SI(a) ((a).size()) typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,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()
{ double a,b; int kcase=1; while(scanf("%lf : %lfn",&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 %.10lfn",kcase++,a*x,b*x);
} return 0;
}
UVA 11817 Tunnelling the Earth 球面距离
#include using namespace std; #define For(i,const P& b) {return a.x
（编辑：李大同）
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