计算几何模版

//============================================================================
// Name        : 基本函数模板.cpp
// Author      :
// Version     :
// Copyright   : Your copyright notice
// Description : Hello World in C++, Ansi-style
//============================================================================

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <queue>
#include <map>
#include <vector>
#include <set>
#include <string>
#include <math.h>

using namespace std;

const double eps = 1e-8;
const double PI = acos(-1.0);
int sgn(double x)
{
if(fabs(x) < eps)return 0;
if(x < 0)return -1;
else return 1;
}
struct Point
{
double x,y;
Point(){}
Point(double _x,double _y)
{
x = _x;y = _y;
}
Point operator -(const Point &b)const
{
return Point(x - b.x,y - b.y);
}
//叉积
double operator ^(const Point &b)const
{
return x*b.y - y*b.x;
}
//点积
double operator *(const Point &b)const
{
return x*b.x + y*b.y;
}
//绕原点旋转角度B（弧度值），后x,y的变化
void transXY(double B)
{
double tx = x,ty = y;
x = tx*cos(B) - ty*sin(B);
y = tx*sin(B) + ty*cos(B);
}
};
struct Line
{
Point s,e;
Line(){}
Line(Point _s,Point _e)
{
s = _s;e = _e;
}
//两直线相交求交点
//第一个值为0表示直线重合，为1表示平行，为0表示相交,为2是相交
//只有第一个值为2时，交点才有意义
pair<int,Point> operator &(const Line &b)const
{
Point res = s;
if(sgn((s-e)^(b.s-b.e)) == 0)
{
if(sgn((s-b.e)^(b.s-b.e)) == 0)
return make_pair(0,res);//重合
else return make_pair(1,res);//平行
}
double t = ((s-b.s)^(b.s-b.e))/((s-e)^(b.s-b.e));
res.x += (e.x-s.x)*t;
res.y += (e.y-s.y)*t;
return make_pair(2,res);
}
};
//*两点间距离
double dist(Point a,Point b)
{
return sqrt((a-b)*(a-b));
}
//*判断线段相交
bool inter(Line l1,Line l2)
{
return
max(l1.s.x,l1.e.x) >= min(l2.s.x,l2.e.x) &&
max(l2.s.x,l2.e.x) >= min(l1.s.x,l1.e.x) &&
max(l1.s.y,l1.e.y) >= min(l2.s.y,l2.e.y) &&
max(l2.s.y,l2.e.y) >= min(l1.s.y,l1.e.y) &&
sgn((l2.s-l1.e)^(l1.s-l1.e))*sgn((l2.e-l1.e)^(l1.s-l1.e)) <= 0 &&
sgn((l1.s-l2.e)^(l2.s-l2.e))*sgn((l1.e-l2.e)^(l2.s-l2.e)) <= 0;
}
//判断直线和线段相交
bool Seg_inter_line(Line l1,Line l2) //判断直线l1和线段l2是否相交
{
return sgn((l2.s-l1.e)^(l1.s-l1.e))*sgn((l2.e-l1.e)^(l1.s-l1.e)) <= 0;
}
//点到直线距离
//返回为result,是点到直线最近的点
Point PointToLine(Point P,Line L)
{
Point result;
double t = ((P-L.s)*(L.e-L.s))/((L.e-L.s)*(L.e-L.s));
result.x = L.s.x + (L.e.x-L.s.x)*t;
result.y = L.s.y + (L.e.y-L.s.y)*t;
return result;
}
//点到线段的距离
//返回点到线段最近的点
Point NearestPointToLineSeg(Point P,Line L)
{
Point result;
double t = ((P-L.s)*(L.e-L.s))/((L.e-L.s)*(L.e-L.s));
if(t >= 0 && t <= 1)
{
result.x = L.s.x + (L.e.x - L.s.x)*t;
result.y = L.s.y + (L.e.y - L.s.y)*t;
}
else
{
if(dist(P,L.s) < dist(P,L.e))
result = L.s;
else result = L.e;
}
return result;
}
//计算多边形面积
//点的编号从0~n-1
double CalcArea(Point p[],int n)
{
double res = 0;
for(int i = 0;i < n;i++)
res += (p[i]^p[(i+1)%n])/2;
return fabs(res);
}
//*判断点在线段上
bool OnSeg(Point P,Line L)
{
return
sgn((L.s-P)^(L.e-P)) == 0 &&
sgn((P.x - L.s.x) * (P.x - L.e.x)) <= 0 &&
sgn((P.y - L.s.y) * (P.y - L.e.y)) <= 0;
}
//*判断点在凸多边形内
//点形成一个凸包，而且按逆时针排序（如果是顺时针把里面的<0改为>0）
//点的编号:0~n-1
//返回值：
//-1:点在凸多边形外
//0:点在凸多边形边界上
//1:点在凸多边形内
int inConvexPoly(Point a,Point p[],int n)
{
for(int i = 0;i < n;i++)
{
if(sgn((p[i]-a)^(p[(i+1)%n]-a)) < 0)return -1;
else if(OnSeg(a,Line(p[i],p[(i+1)%n])))return 0;
}
return 1;
}
//*判断点在任意多边形内
//射线法，poly[]的顶点数要大于等于3,点的编号0~n-1
//返回值
//-1:点在凸多边形外
//0:点在凸多边形边界上
//1:点在凸多边形内
int inPoly(Point p,Point poly[],int n)
{
int cnt;
Line ray,side;
cnt = 0;
ray.s = p;
ray.e.y = p.y;
ray.e.x = -100000000000.0;//-INF,注意取值防止越界

for(int i = 0;i < n;i++)
{
side.s = poly[i];
side.e = poly[(i+1)%n];

if(OnSeg(p,side))return 0;

//如果平行轴则不考虑
if(sgn(side.s.y - side.e.y) == 0)
continue;

if(OnSeg(side.s,ray))
{
if(sgn(side.s.y - side.e.y) > 0)cnt++;
}
else if(OnSeg(side.e,ray))
{
if(sgn(side.e.y - side.s.y) > 0)cnt++;
}
else if(inter(ray,side))
cnt++;
}
if(cnt % 2 == 1)return 1;
else return -1;
}
//判断凸多边形
//允许共线边
//点可以是顺时针给出也可以是逆时针给出
//点的编号0~n-1
bool isconvex(Point poly[],int n)
{
bool s[3];
memset(s,false,sizeof(s));
for(int i = 0;i < n;i++)
{
s[sgn( (poly[(i+1)%n]-poly[i])^(poly[(i+2)%n]-poly[i]) )+1] = true;
if(s[0] && s[2])return false;
}
return true;
}

int main()
{

return 0;
}

//============================================================================
// Name        : 凸包.cpp
// Author      :
// Version     :
// Copyright   : Your copyright notice
// Description : Hello World in C++, Ansi-style
//============================================================================

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <math.h>
using namespace std;

const double eps = 1e-8;
const double PI = acos(-1.0);
int sgn(double x)
{
if(fabs(x) < eps)return 0;
if(x < 0)return -1;
else return 1;
}
struct Point
{
double x,y;
Point(){}
Point(double _x,double _y)
{
x = _x;
y = _y;
}
Point operator -(const Point &b)const
{
return Point(x-b.x,y-b.y);
}
double operator ^(const Point &b)const
{
return x*b.y - y*b.x;
}
double operator *(const Point &b)const
{
return x*b.x + y*b.y;
}
};
//*两点间距离
double dist(Point a,Point b)
{
return sqrt((a-b)*(a-b));
}

const int MAXN = 1010;
Point list[MAXN];
int Stack[MAXN],top;
//相对于list[0]的极角排序
bool _cmp(Point p1,Point p2)
{
double tmp = (p1-list[0])^(p2-list[0]);
if(sgn(tmp) > 0)return true;
else if(sgn(tmp) == 0 && sgn(dist(p1,list[0]) - dist(p2,list[0])) <= 0)
return true;
else return false;
}
void Graham(int n)
{
Point p0;
int k = 0;
p0 = list[0];
//找最下边的一个点
for(int i = 1;i < n;i++)
{
if( (p0.y > list[i].y) || (p0.y == list[i].y && p0.x > list[i].x) )
{
p0 = list[i];
k = i;
}
}
swap(list[k],list[0]);
sort(list+1,list+n,_cmp);
if(n == 1)
{
top = 1;
Stack[0] = 0;
return;
}
if(n == 2)
{
top = 2;
Stack[0] = 0;
Stack[1] = 1;
return ;
}
Stack[0] = 0;
Stack[1] = 1;
top = 2;
for(int i = 2;i < n;i++)
{
while(top > 1 && sgn((list[Stack[top-1]]-list[Stack[top-2]])^(list[i]-list[Stack[top-2]])) <= 0)
top--;
Stack[top++] = i;
}

}

int main() {
cout << "!!!Hello World!!!" << endl; // prints !!!Hello World!!!
return 0;
}

#include<cmath>
#include<cstdio>
#include<iostream>
#include<algorithm>
using namespace std;
#define N 100005
struct point
{
double x;
double y;
}p1
,p2
;
bool cmpx(point a,point b)//按x坐标排序
{
return a.x<b.x;
}
bool cmpy(point a,point b)//按y坐标排序
{
return a.y<b.y;
}
double dis(point a,point b)//求两点的距离
{
return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
double min(double a,double b)//取最小值
{
return a>b?b:a;
}
double mindis(int l,int r)//求最近点对
{
int i,j;
if(l+1==r)return dis(p1[l],p1[r]);//如果就两个点
if(l+2==r)return min(dis(p1[l],p1[l+1]),min(dis(p1[l],p1[r]),dis(p1[l+1],p1[r])));//就三个点的情况
int mid=(l+r)>>1;
double ans=min(mindis(l,mid),mindis(mid+1,r)); //取两边（左边或者右边）的最小值

int cn=0;
for(i=l;i<=r;i++)//选出在分界线（左右）ans内的点
{
if(p1[i].x>=p1[mid].x-ans&&p1[i].x<=p1[mid].x+ans)
p2[cn++]=p1[i];

}

sort(p2,p2+cn,cmpy);//把区域内的点按y坐标排序。
for(i=0;i<cn;i++)
{
for(j=i+1;j<cn;j++)
{
if(p2[j].y-p2[i].y>=ans)break;//优化 大于的肯定不会是解
ans=min(ans,dis(p2[i],p2[j]));
}
}
return ans;
}
int main()
{
int n;
while(scanf("%d",&n)&&n)
{
for(int i=0;i<n;i++)
scanf("%lf%lf",&p1[i].x,&p1[i].y);
sort(p1,p1+n,cmpx);//按x坐标排序

double dist=mindis(0,n-1);

printf("%.2lf\n",dist/2);
}
return 0;
}