数学题，看代码吧，我的注释写得很全。还有注意浮点误差，无语的误差！
CO
/*
PROGRAM: $PROGRAM
AUTHOR: Su Jiao
DATE: 2010-3-25
DESCRIPTION:
$DESCRIPTION
*/
#include <iostream>
using std::cin;
using std::cout;
#include <fstream>
using std::ifstream;
using std::ofstream;
#include <sstream>
using std::stringstream;
using std::endl;
#include <vector>
using std::vector;
#include <string>
using std::string;
#include <stack>
using std::stack;
#include <queue>
using std::queue;
#include <set>
using std::set;
#include <map>
using std::map;
using std::pair;
using std::make_pair;
#include <algorithm>
using std::sort;
#include <cassert>
//using std::assert;
#include <cmath>
using std::sqrt;
using std::floor;
using std::ceil;
template<typename Type>
class Function
{
int n;
vector<vector<Type> > matrix;
vector<Type> answer;
static Type abs(Type a)
{
return a>=0?a:-a;
}
void smaller(int step)
{
for (int i=step+1;i<n;i++)
if (abs(matrix[i][step])>abs(matrix[step][step]))
matrix[step].swap(matrix[i]);
for (int i=step+1;i<n;i++)
{
Type mul=matrix[i][step];
Type div=matrix[step][step];
for (int j=step;j<=n;j++)
matrix[i][j]-=matrix[step][j]*mul/div;
}
}
void back(int step)
{
if (step==n-1)
answer[step]=matrix[step][n]/matrix[step][step];
else
{
answer[step]=matrix[step][n];
for (int i=step+1;i<n;i++)
answer[step]-=matrix[step][i]*answer[i];
answer[step]/=matrix[step][step];
}
}
public:
void read(vector<vector<Type> >& get)
{
n=get.size();
matrix=get;
answer.resize(get.size());
}
void solve()
{
for (int i=0;i<n-1;i++) smaller(i);
for (int i=n-1;i>=0;i–) back(i);
}
void write(vector<Type>& put)
{
put=answer;
}
};
class Application
{
static const int POINTNUMBER=3;
static const int oo=1000;
vector<pair<int,int> > p;
double cross(double x1,double y1,double x2,double y2,double x3,double y3)
{
/*
1———–2
/
/
/
3
return 1->2 X 1->3
*/
double dx12=x2-x1,dy12=y2-y1,
dx13=x3-x1,dy13=y3-y1;
return dx12*dy13-dx13*dy12;
}
bool sameside(double x1,double y1,double x2,double y2,
double px1,double py1,double px2,double py2)
{
return cross(x1,y1,x2,y2,px1,py1)*cross(x1,y1,x2,y2,px2,py2)>0;
}
public:
Application()
:p(POINTNUMBER)
{
for (int i=0;i<POINTNUMBER;i++)
cin>>p[i].first>>p[i].second;
}
int run()
{
vector<vector<double> > v(POINTNUMBER,vector<double>(POINTNUMBER+1));
Function<double> f;
vector<double> answer;
for (int i=0;i<POINTNUMBER;i++)
{
//x^2+y^2+Cx+Dy+E=0
//x y 1 (-x^2-y^2)
v[i][0]=p[i].first;
v[i][1]=p[i].second;
v[i][2]=1;
v[i][3]=-(p[i].first*p[i].first+p[i].second*p[i].second);
}
f.read(v);
f.solve();
f.write(answer);
//C=answer[0]
//D=answer[1]
//E=answer[2]
//(x+C/2)^2+(y+D/2)^2=(C^2+D^2)/4-E
//O(-C/2,-D/2) R=sqrt((C^2+D^2)/4-E)
double C=answer[0],
D=answer[1],
E=answer[2];
double Ox=-C/2,
Oy=-D/2,
R=sqrt((C*C+D*D)/4-E);
/*
圆心O; 起点S; 终点E; 中间过M
O———–S
/ \
/ \
/ \
/ \
/ \
E M
*/
double Sx=p[0].first,Sy=p[0].second,
Ex=p[1].first,Ey=p[1].second,
Mx=p[2].first,My=p[2].second;
int t=-oo,b=oo,l=oo,r=-oo;
#define line(x1,y1,x2,y2) x1,y1,x2,y2
#define point(x,y) x,y
#define ZERO 0.0000001
#define update(x,y)\
{\
double X=x,Y=y;\
if (floor(X+ZERO)<l) l=floor(X+ZERO);\
if (ceil(X-ZERO)>r) r=ceil(X-ZERO);\
if (floor(Y+ZERO)<b) b=floor(Y+ZERO);\
if (ceil(Y-ZERO)>t) t=ceil(Y-ZERO);\
}
#define check_and_update(X,Y)\
if (sameside(line(Sx,Sy,Ex,Ey),point(Mx,My),point(X,Y)))\
update(X,Y);
update(Sx,Sy);
update(Ex,Ey);
update(Mx,My);
check_and_update(Ox+R,Oy);
check_and_update(Ox-R,Oy);
check_and_update(Ox,Oy+R);
check_and_update(Ox,Oy-R);
#undef check_and_update
#undef update
#undef ZERO
#undef point
#undef line
if (r>oo) r=oo;
if (l<-oo) l=-oo;
if (t>oo) t=oo;
if (b<-oo) b=-oo;
cout<<(r-l)*(t-b)<<endl;
return 0;
}
};
int main()
{
Application app;
return app.run();
}