3、ACM参考模板

#include <stdlib.h>
#include <math.h>
#define MAXN 1000
#define offset 10000
#define eps 1e-8
#define zero(x) (((x)>0?(x):-(x))<eps)
#define _sign(x) ((x)>eps?1:((x)<-eps?2:0))

struct point {
    double x,y;
};

struct line {
    point a,b;
};

double xmult(point p1,point p2,point p0) {
    return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);
}

//判定凸多边形,顶点按顺时针或逆时针给出,允许相邻边共线
int is_convex(int n,point* p) {
    int i,s[3]= {1,1,1};
    for (i=0; i<n&&s[1]|s[2]; i++)
        s[_sign(xmult(p[(i+1)%n],p[(i+2)%n],p[i]))]=0;
    return s[1]|s[2];
}

//判定凸多边形,顶点按顺时针或逆时针给出,不允许相邻边共线
int is_convex_v2(int n,point* p) {
    int i,s[3]= {1,1,1};
    for (i=0; i<n&&s[0]&&s[1]|s[2]; i++)
        s[_sign(xmult(p[(i+1)%n],p[(i+2)%n],p[i]))]=0;
    return s[0]&&s[1]|s[2];
}

//判点在凸多边形内或多边形边上,顶点按顺时针或逆时针给出
int inside_convex(point q,int n,point* p) {
    int i,s[3]= {1,1,1};
    for (i=0; i<n&&s[1]|s[2]; i++)
        s[_sign(xmult(p[(i+1)%n],q,p[i]))]=0;
    return s[1]|s[2];
}

//判点在凸多边形内,顶点按顺时针或逆时针给出,在多边形边上返回 0
int inside_convex_v2(point q,int n,point* p) {
    int i,s[3]= {1,1,1};
    for (i=0; i<n&&s[0]&&s[1]|s[2]; i++)
        s[_sign(xmult(p[(i+1)%n],q,p[i]))]=0;
    return s[0]&&s[1]|s[2];
}

//判点在任意多边形内,顶点按顺时针或逆时针给出
//on_edge 表示点在多边形边上时的返回值,offset 为多边形坐标上限
int inside_polygon(point q,int n,point* p,int on_edge=1) {
    point q2;
    int i=0,count;
    while (i<n)
        for (count=i=0,q2.x=rand()+offset,q2.y=rand()+offset; i<n; i++)
            if
            (zero(xmult(q,p[i],p[(i+1)%n]))&&(p[i].x-q.x)*(p[(i+1)%n].x-q.x)<eps&&(p[i].y-q.y)*(p[(i+1)%
                    n].y-q.y)<eps)
                return on_edge;
            else if (zero(xmult(q,q2,p[i])))
                break;
            else if
            (xmult(q,p[i],q2)*xmult(q,p[(i+1)%n],q2)<-eps&&xmult(p[i],q,p[(i+1)%n])*xmult(p[i],q2,p[(i+1)
                    %n])<-eps)
                count++;
    return count&1;
}

inline int opposite_side(point p1,point p2,point l1,point l2) {
    return xmult(l1,p1,l2)*xmult(l1,p2,l2)<-eps;
}

inline int dot_online_in(point p,point l1,point l2) {
    return zero(xmult(p,l1,l2))&&(l1.x-p.x)*(l2.x-p.x)<eps&&(l1.y-p.y)*(l2.y-p.y)<eps;
}

//判线段在任意多边形内,顶点按顺时针或逆时针给出,与边界相交返回 1
int inside_polygon(point l1,point l2,int n,point* p) {
    point t[MAXN],tt;
    int i,j,k=0;
    if (!inside_polygon(l1,n,p)||!inside_polygon(l2,n,p))
        return 0;
    for (i=0; i<n; i++)
        if (opposite_side(l1,l2,p[i],p[(i+1)%n])&&opposite_side(p[i],p[(i+1)%n],l1,l2))
            return 0;
        else if (dot_online_in(l1,p[i],p[(i+1)%n]))
            t[k++]=l1;
        else if (dot_online_in(l2,p[i],p[(i+1)%n]))
            t[k++]=l2;
        else if (dot_online_in(p[i],l1,l2))
            t[k++]=p[i];
    for (i=0; i<k; i++)
        for (j=i+1; j<k; j++) {
            tt.x=(t[i].x+t[j].x)/2;
            tt.y=(t[i].y+t[j].y)/2;
            if (!inside_polygon(tt,n,p))
                return 0;
        }
    return 1;
}

point intersection(line u,line v) {
    point ret=u.a;
    double t=((u.a.x-v.a.x)*(v.a.y-v.b.y)-(u.a.y-v.a.y)*(v.a.x-v.b.x))
             /((u.a.x-u.b.x)*(v.a.y-v.b.y)-(u.a.y-u.b.y)*(v.a.x-v.b.x));
    ret.x+=(u.b.x-u.a.x)*t;
    ret.y+=(u.b.y-u.a.y)*t;
    return ret;
}

point barycenter(point a,point b,point c) {
    line u,v;
    u.a.x=(a.x+b.x)/2;
    u.a.y=(a.y+b.y)/2;
    u.b=c;
    v.a.x=(a.x+c.x)/2;
    v.a.y=(a.y+c.y)/2;
    v.b=b;
    return intersection(u,v);
}

//多边形重心
point barycenter(int n,point* p) {
    point ret,t;
    double t1=0,t2;
    int i;
    ret.x=ret.y=0;
    for (i=1; i<n-1; i++)
        if (fabs(t2=xmult(p[0],p[i],p[i+1]))>eps) {
            t=barycenter(p[0],p[i],p[i+1]);
            ret.x+=t.x*t2;
            ret.y+=t.y*t2;
            t1+=t2;
        }
    if (fabs(t1)>eps)
        ret.x/=t1,ret.y/=t1;
    return ret;
}

//多边形切割
//可用于半平面交
#define MAXN 100
#define eps 1e-8
#define zero(x) (((x)>0?(x):-(x))<eps)

struct point {
    double x,y;
};

double xmult(point p1,point p2,point p0) {
    return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);
}

int same_side(point p1,point p2,point l1,point l2) {
    return xmult( ,p1,l2)*xmult(l1,p2,l2)>eps;
}

point intersection(point u1,point u2,point v1,point v2) {
    point ret=u1;
    double t=((u1.x-v1.x)*(v1.y-v2.y)-(u1.y-v1.y)*(v1.x-v2.x))
             /((u1.x-u2.x)*(v1.y-v2.y)-(u1.y-u2.y)*(v1.x-v2.x));
    ret.x+=(u2.x-u1.x)*t;
    ret.y+=(u2.y-u1.y)*t;
    return ret;
}

//将多边形沿 l1,l2 确定的直线切割在 side 侧切割,保证 l1,l2,side 不共线
void polygon_cut(int& n,point* p,point l1,point l2,point side) {
    point pp[100];
    int m=0,i;
    for (i=0; i<n; i++) {
        if (same_side(p[i],side,l1,l2))
            pp[m++]=p[i];
        if
        (!same_side(p[i],p[(i+1)%n],l1,l2)&&!(zero(xmult(p[i],l1,l2))&&zero(xmult(p[(i+1)%n],l1,l2))))
            pp[m++]=intersection(p[i],p[(i+1)%n],l1,l2);
    }
    for (n=i=0; i<m; i++)
        if (!i||!zero(pp[i].x-pp[i-1].x)||!zero(pp[i].y-pp[i-1].y))
            p[n++]=pp[i];
    if (zero(p[n-1].x-p[0].x)&&zero(p[n-1].y-p[0].y))
        n--;
    if (n<3)
        n=0;
}

//浮点几何函数库
#include <math.h>
#define eps 1e-8
#define zero(x) (((x)>0?(x):-(x))<eps)

struct point {
    double x,y;
};

struct line {
    point a,b;
};

//计算 cross product (P1-P0)x(P2-P0)
double xmult(point p1,point p2,point p0) {
    return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);
}

double xmult(double x1,double y1,double x2,double y2,double x0,double y0) {
    return (x1-x0)*(y2-y0)-(x2-x0)*(y1-y0);
}

//计算 dot product (P1-P0).(P2-P0)
double dmult(point p1,point p2,point p0) {
    return (p1.x-p0.x)*(p2.x-p0.x)+(p1.y-p0.y)*(p2.y-p0.y);
}

double dmult(double x1,double y1,double x2,double y2,double x0,double y0) {
    return (x1-x0)*(x2-x0)+(y1-y0)*(y2-y0);
}

//两点距离
double distance(point p1,point p2) {
    return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y));
}

double distance(double x1,double y1,double x2,double y2) {
    return sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
}

//判三点共线
int dots_inline(point p1,point p2,point p3) {
    return zero(xmult(p1,p2,p3));
}

int dots_inline(double x1,double y1,double x2,double y2,double x3,double y3) {
    return zero(xmult(x1,y1,x2,y2,x3,y3));
}

//判点是否在线段上,包括端点
int dot_online_in(point p,line l) {
    return zero(xmult(p,l.a,l.b))&&(l.a.x-p.x)*(l.b.x-p.x)<eps&&(l.a.y-p.y)*(l.b.y-p.y)<eps;
}

int dot_online_in(point p,point l1,point l2) {
    return zero(xmult(p,l1,l2))&&(l1.x-p.x)*(l2.x-p.x)<eps&&(l1.y-p.y)*(l2.y-p.y)<eps;
}

int dot_online_in(double x,double y,double x1,double y1,double x2,double y2) {
    return zero(xmult(x,y,x1,y1,x2,y2))&&(x1-x)*(x2-x)<eps&&(y1-y)*(y2-y)<eps;
}

//判点是否在线段上,不包括端点
int dot_online_ex(point p,line l) {
    return
        dot_online_in(p,l)&&(!zero(p.x-l.a.x)||!zero(p.y-l.a.y))&&(!zero(p.x-l.b.x)||!zero(p.y-l.b.y));
}

int dot_online_ex(point p,point l1,point l2) {
    return
        dot_online_in(p,l1,l2)&&(!zero(p.x-l1.x)||!zero(p.y-l1.y))&&(!zero(p.x-l2.x)||!zero(p.y-l2.y));
}

int dot_online_ex(double x,double y,double x1,double y1,double x2,double y2) {
    return
        dot_online_in(x,y,x1,y1,x2,y2)&&(!zero(x-x1)||!zero(y-y1))&&(!zero(x-x2)||!zero(y-y2));
}

//判两点在线段同侧,点在线段上返回 0
int same_side(point p1,point p2,line l) {
    return xmult(l.a,p1,l.b)*xmult(l.a,p2,l.b)>eps;
}

int same_side(point p1,point p2,point l1,point l2) {
    return xmult(l1,p1,l2)*xmult(l1,p2,l2)>eps;
}

//判两点在线段异侧,点在线段上返回 0
int opposite_side(point p1,point p2,line l) {
    return xmult(l.a,p1,l.b)*xmult(l.a,p2,l.b)<-eps;
}

int opposite_side(point p1,point p2,point l1,point l2) {
    return xmult(l1,p1,l2)*xmult(l1,p2,l2)<-eps;
}

//判两直线平行
int parallel(line u,line v) {
    return zero((u.a.x-u.b.x)*(v.a.y-v.b.y)-(v.a.x-v.b.x)*(u.a.y-u.b.y));
}

int parallel(point u1,point u2,point v1,point v2) {
    return zero((u1.x-u2.x)*(v1.y-v2.y)-(v1.x-v2.x)*(u1.y-u2.y));
}

//判两直线垂直
int perpendicular(line u,line v) {
    return zero((u.a.x-u.b.x)*(v.a.x-v.b.x)+(u.a.y-u.b.y)*(v.a.y-v.b.y));
}

int perpendicular(point u1,point u2,point v1,point v2) {
    return zero((u1.x-u2.x)*(v1.x-v2.x)+(u1.y-u2.y)*(v1.y-v2.y));
}

//判两线段相交,包括端点和部分重合
int intersect_in(line u,line v) {
    if (!dots_inline(u.a,u.b,v.a)||!dots_inline(u.a,u.b,v.b))
        return !same_side(u.a,u.b,v)&&!same_side(v.a,v.b,u);
    return dot_online_in(u.a,v)||dot_online_in(u.b,v)||dot_online_in(v.a,u)||dot_online_in(v.b,u);
}

int intersect_in(point u1,point u2,point v1,point v2) {
    if (!dots_inline(u1,u2,v1)||!dots_inline(u1,u2,v2))
        return !same_side(u1,u2,v1,v2)&&!same_side(v1,v2,u1,u2);
    return
        dot_online_in(u1,v1,v2)||dot_online_in(u2,v1,v2)||dot_online_in(v1,u1,u2)||dot_online_in(v2,u1,u
                2);
}

//判两线段相交,不包括端点和部分重合
int intersect_ex(line u,line v) {
    return opposite_side(u.a,u.b,v)&&opposite_side(v.a,v.b,u);
}

int intersect_ex(point u1,point u2,point v1,point v2) {
    return opposite_side(u1,u2,v1,v2)&&opposite_side(v1,v2,u1,u2);
}

//计算两直线交点,注意事先判断直线是否平行!
//线段交点请另外判线段相交(同时还是要判断是否平行!)
point intersection(line u,line v) {
    point ret=u.a;
    double t=((u.a.x-v.a.x)*(v.a.y-v.b.y)-(u.a.y-v.a.y)*(v.a.x-v.b.x))
             /((u.a.x-u.b.x)*(v.a.y-v.b.y)-(u.a.y-u.b.y)*(v.a.x-v.b.x));
    ret.x+=(u.b.x-u.a.x)*t;
    ret.y+=(u.b.y-u.a.y)*t;
    return ret;
}

point intersection(point u1,point u2,point v1,point v2) {
    point ret=u1;
    double t=((u1.x-v1.x)*(v1.y-v2.y)-(u1.y-v1.y)*(v1.x-v2.x))
             /((u1.x-u2.x)*(v1.y-v2.y)-(u1.y-u2.y)*(v1.x-v2.x));
    ret.x+=(u2.x-u1.x)*t;
    ret.y+=(u2.y-u1.y)*t;
    return ret;
}

//点到直线上的最近点
point ptoline(point p,line l) {
    point t=p;
    t.x+=l.a.y-l.b.y,t.y+=l.b.x-l.a.x;
    return intersection(p,t,l.a,l.b);
}

point ptoline(point p,point l1,point l2) {
    point t=p;
    t.x+=l1.y-l2.y,t.y+=l2.x-l1.x;
    return intersection(p,t,l1,l2);
}

//点到直线距离
double disptoline(point p,line l) {
    return fabs(xmult(p,l.a,l.b))/distance(l.a,l.b);
}

double disptoline(point p,point l1,point l2) {
    return fabs(xmult(p,l1,l2))/distance(l1,l2);
}

double disptoline(double x,double y,double x1,double y1,double x2,double y2) {
    return fabs(xmult(x,y,x1,y1,x2,y2))/distance(x1,y1,x2,y2);
}

//点到线段上的最近点
point ptoseg(point p,line l) {
    point t=p;
    t.x+=l.a.y-l.b.y,t.y+=l.b.x-l.a.x;
    if (xmult(l.a,t,p)*xmult(l.b,t,p)>eps)
        return distance(p,l.a)<distance(p,l.b)?l.a:l.b;
    return intersection(p,t,l.a,l.b);
}

point ptoseg(point p,point l1,point l2) {
    point t=p;
    t.x+=l1.y-l2.y,t.y+=l2.x-l1.x;
    if (xmult(l1,t,p)*xmult(l2,t,p)>eps)
        return distance(p,l1)<distance(p,l2)?l1:l2;
    return intersection(p,t,l1,l2);
}

//点到线段距离
double disptoseg(point p,line l) {
    point t=p;
    t.x+=l.a.y-l.b.y,t.y+=l.b.x-l.a.x;
    if (xmult(l.a,t,p)*xmult(l.b,t,p)>eps)
        return distance(p,l.a)<distance(p,l.b)?distance(p,l.a):distance(p,l.b);
    return fabs(xmult(p,l.a,l.b))/distance(l.a,l.b);
}

double disptoseg(point p,point l1,point l2) {
    point t=p;
    t.x+=l1.y-l2.y,t.y+=l2.x-l1.x;
    if (xmult(l1,t,p)*xmult(l2,t,p)>eps)
        return distance(p,l1)<distance(p,l2)?distance(p,l1):distance(p,l2);
    return fabs(xmult(p,l1,l2))/distance(l1,l2);
}

//矢量 V 以 P 为顶点逆时针旋转 angle 并放大 scale 倍
point rotate(point v,point p,double angle,double scale) {
    point ret=p;
    v.x-=p.x,v.y-=p.y;
    p.x=scale*cos(angle);
    p.y=scale*sin(angle);
    ret.x+=v.x*p.x-v.y*p.y;
    ret.y+=v.x*p.y+v.y*p.x;
    return ret;
}

#include <math.h>

struct point {
    double x,y;
};

//计算 cross product (P1-P0)x(P2-P0)
double xmult(point p1,point p2,point p0) {
    return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);
}

double xmult(double x1,double y1,double x2,double y2,double x0,double y0) {
    return (x1-x0)*(y2-y0)-(x2-x0)*(y1-y0);
}

//计算三角形面积,输入三顶点
double area_triangle(point p1,point p2,point p3) {
    return fabs(xmult(p1,p2,p3))/2;
}

double area_triangle(double x1,double y1,double x2,double y2,double x3,double y3) {
    return fabs(xmult(x1,y1,x2,y2,x3,y3))/2;
}

//计算三角形面积,输入三边长
double area_triangle(double a,double b,double c) {
    double s=(a+b+c)/2;
    return sqrt(s*(s-a)*(s-b)*(s-c));
}

//计算多边形面积,顶点按顺时针或逆时针给出
double area_polygon(int n,point* p) {
    double s1=0,s2=0;
    int i;
    for (i=0; i<n; i++)
        s1+=p[(i+1)%n].y*p[i].x,s2+=p[(i+1)%n].y*p[(i+2)%n].x;
    return fabs(s1-s2)/2;
}

#include <math.h>
const double pi=acos(-1);

//计算圆心角 lat 表示纬度,-90<=w<=90,lng 表示经度
//返回两点所在大圆劣弧对应圆心角,0<=angle<=pi
double angle(double lng1,double lat1,double lng2,double lat2) {
    double dlng=fabs(lng1-lng2)*pi/180;
    while (dlng>=pi+pi)
        dlng-=pi+pi;
    if (dlng>pi)
        dlng=pi+pi-dlng;
    lat1*=pi/180,lat2*=pi/180;
    return acos(cos(lat1)*cos(lat2)*cos(dlng)+sin(lat1)*sin(lat2));
}

//计算距离,r 为球半径
double line_dist(double r,double lng1,double lat1,double lng2,double lat2) {
    double dlng=fabs(lng1-lng2)*pi/180;
    while (dlng>=pi+pi)
        dlng-=pi+pi;
    if (dlng>pi)
        dlng=pi+pi-dlng;
    lat1*=pi/180,lat2*=pi/180;
    return r*sqrt(2-2*(cos(lat1)*cos(lat2)*cos(dlng)+sin(lat1)*sin(lat2)));
}

//计算球面距离,r 为球半径
inline double sphere_dist(double r,double lng1,double lat1,double lng2,double lat2) {
    return r*angle(lng1,lat1,lng2,lat2);
}

#include <math.h>

struct point {
    double x,y;
};

struct line {
    point a,b;
};

double distance(point p1,point p2) {
    return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y));
}

point intersection(line u,line v) {
    point ret=u.a;
    double t=((u.a.x-v.a.x)*(v.a.y-v.b.y)-(u.a.y-v.a.y)*(v.a.x-v.b.x))
             /((u.a.x-u.b.x)*(v.a.y-v.b.y)-(u.a.y-u.b.y)*(v.a.x-v.b.x));
    ret.x+=(u.b.x-u.a.x)*t;
    ret.y+=(u.b.y-u.a.y)*t;
    return ret;
}

//外心
point circumcenter(point a,point b,point c) {
    line u,v;
    u.a.x=(a.x+b.x)/2;
    u.a.y=(a.y+b.y)/2;
    u.b.x=u.a.x-a.y+b.y;
    u.b.y=u.a.y+a.x-b.x;
    v.a.x=(a.x+c.x)/2;
    v.a.y=(a.y+c.y)/2;
    v.b.x=v.a.x-a.y+c.y;
    v.b.y=v.a.y+a.x-c.x;
    return intersection(u,v);
}

//内心
point incenter(point a,point b,point c) {
    line u,v;
    double m,n;
    u.a=a;
    m=atan2(b.y-a.y,b.x-a.x);
    n=atan2(c.y-a.y,c.x-a.x);
    u.b.x=u.a.x+cos((m+n)/2);
    u.b.y=u.a.y+sin((m+n)/2);
    v.a=b;
    m=atan2(a.y-b.y,a.x-b.x);
    n=atan2(c.y-b.y,c.x-b.x);
    v.b.x=v.a.x+cos((m+n)/2);
    v.b.y=v.a.y+sin((m+n)/2);
    return intersection(u,v);
}

//垂心
point perpencenter(point a,point b,point c) {
    line u,v;
    u.a=c;
    u.b.x=u.a.x-a.y+b.y;
    u.b.y=u.a.y+a.x-b.x;
    v.a=b;
    v.b.x=v.a.x-a.y+c.y;
    v.b.y=v.a.y+a.x-c.x;
    return intersection(u,v);
}

//重心
//到三角形三顶点距离的平方和最小的点
//三角形内到三边距离之积最大的点
point barycenter(point a,point b,point c) {
    line u,v;
    u.a.x=(a.x+b.x)/2;
    u.a.y=(a.y+b.y)/2;
    u.b=c;
    v.a.x=(a.x+c.x)/2;
    v.a.y=(a.y+c.y)/2;
    v.b=b;
    return intersection(u,v);
}

//费马点
//到三角形三顶点距离之和最小的点
point fermentpoint(point a,point b,point c) {
    point u,v;
    double step=fabs(a.x)+fabs(a.y)+fabs(b.x)+fabs(b.y)+fabs(c.x)+fabs(c.y);
    int i,j,k;
    u.x=(a.x+b.x+c.x)/3;
    u.y=(a.y+b.y+c.y)/3;
    while (step>1e-10)
        for (k=0; k<10; step/=2,k++)
            for (i=-1; i<=1; i++)
                for (j=-1; j<=1; j++) {
                    v.x=u.x+step*i;
                    v.y=u.y+step*j;
                    if(distance(u,a)+distance(u,b)+distance(u,c)>distance(v,a)+distance(v,b)+distance(v,c))
                        u=v;
                }
    return u;
}