zoj 1010

#include <iostream>
#include <cmath> 
using namespace std;

// 精度容差 
const double EPS = 1e-5; 

// 允许容差的浮点数相等 
inline bool equals( double x, double y ) {
    return fabs( x - y ) < EPS;
}

// 点结构 
struct Point {
    Point() {}
    Point( double x, double y ) : posX( x ), posY( y ) {}
    void getPoint() { cin >> posX >> posY; }
    double posX, posY;
};

// 判断两点是否重合 
bool cover( Point pointA, Point pointB ) {
    return fabs( pointA.posX - pointB.posX ) +
        fabs( pointA.posY - pointB.posY ) < EPS; 
}

// 线段类 
class LineSegment {
public:
    LineSegment() {}
    // 构造函数，两点一线 
    LineSegment( Point pA, Point pB ) : pointA( pA ), pointB( pB ) {}
    // 判别点在线的哪一侧，返回值为叉积 
    double pointOnItsSide( Point );
    // 判别点是否在线上 
    bool pointOnLine( Point );
    // 判别两线是否相交 
    friend bool cross( LineSegment, LineSegment );
private:
    Point pointA, pointB;
};

double LineSegment :: pointOnItsSide( Point point ) {
    return ( point.posX - pointA.posX ) * ( pointB.posY - pointA.posY ) -
        ( point.posY - pointA.posY ) * ( pointB.posX - pointA.posX );
} 

bool LineSegment :: pointOnLine( Point point ) {
    // 若端点重合，必定相交 
    if( cover( point, pointA ) || cover( point, pointB ) ) return true;
    // 若点在线段坐标顶点方框外，必定不相交 
    if( point.posX > pointA.posX && point.posX > pointB.posX ||
        point.posX < pointA.posX && point.posX < pointB.posX ||
        point.posY > pointA.posY && point.posY > pointB.posY ||
        point.posY < pointA.posY && point.posY < pointB.posY ) return false;
    // 否则，点必定不在延长线或端点上，只要点与直线叉积非零即不在线上
    return equals( pointOnItsSide( point ), 0.0 );
}

bool cross( LineSegment lineA, LineSegment lineB ) {
    // 若一条直线端点在另一直线上，必然相交 
    if( lineA.pointOnLine( lineB.pointA ) || lineA.pointOnLine( lineB.pointB ) ||
        lineB.pointOnLine( lineA.pointA ) || lineB.pointOnLine( lineA.pointB ) ) return true;
    double prod11 = lineA.pointOnItsSide( lineB.pointA ),
        prod12 = lineA.pointOnItsSide( lineB.pointB ),
        prod21 = lineB.pointOnItsSide( lineA.pointA ),
        prod22 = lineB.pointOnItsSide( lineA.pointB );
    return prod11 * prod12 < -EPS && prod21 * prod22 < -EPS;
}

// 多边形类
class Polygon {
public:
    Polygon() {}
    int getPolygon();
    bool isValid();
    double area(); 
private:
    int size; 
    Point vertex[1000];
    LineSegment edge[1000]; 
};

int Polygon :: getPolygon() {
    cin >> size;
    int i = 0;
    for(  i = 0; i < size; i++ )
        vertex[i].getPoint();
    for(  i = 1; i < size; i++ )
        edge[i] = LineSegment( vertex[i - 1], vertex[i] );
    edge[0] = LineSegment( vertex[size - 1], vertex[0] );
    return size;
}

bool Polygon :: isValid() {
    if( size < 3 )
        return false;
    if( size == 3 )
        return !fabs( LineSegment( vertex[0], vertex[1] ).pointOnItsSide( vertex[2] ) ) < EPS;
    for( int j = 2; j < size - 1; j++ )
        if( cross( edge[0], edge[j] ) ) return false;
        for( int i = 1; i < size - 2; i++ )
            for( int j = i + 2; j < size; j++ )
                if( cross( edge[i], edge[j] ) )
                    return false;
                return true;
} 

double Polygon :: area() {
    double ans = 0.0;
    if( size < 3 ) return ans;
    for( int i = 2; i < size; i++ )
        ans += edge[i].pointOnItsSide( vertex[0] );
    return fabs( ans / 2.0 );
}

int main() 
{
    Polygon Pattern;
    int T = 1;
    cout.setf( ios :: fixed );
    cout.precision( 2 );
    while( Pattern.getPolygon() ) {
        if( T != 1 ) cout << endl;
        cout << "Figure " << T++ << ": ";
        if( !Pattern.isValid() )
            cout << "Impossible" << endl;
        else cout << Pattern.area() << endl;
    }
    return 0;
}

 

 代码一用c++的风格，代码二用c风格。

#include<stdio.h>
#define max(a,b) ((a)>(b)?(a):(b))
#define min(a,b) ((a)<(b)?(a):(b))
double x[1000],y[1000];

//叉积,p0p1 X p0p2,>0 p0p2沿着p0右旋得到p0p1,<0 左旋得到，=0 共线
double multi(int p1,int p2,int p0)
{
 return (x[p1]-x[p0])*(y[p2]-y[p0])-(x[p2]-x[p0])*(y[p1]-y[p0]);
}
int isIntersected(int s1,int e1,int s2,int e2)//线段s1e1与s2e2是否相交
{
 if(max(x[s1],x[e1])<min(x[s2],x[e2]))
  return 0;
 if(max(x[s2],x[e2])<min(x[s1],x[e1]))
  return 0;
 if(max(y[s1],y[e1])<min(y[s2],y[e2]))
  return 0;
 if(max(y[s2],y[e2])<min(y[s1],y[e1]))
  return 0;
 if(multi(s2,e1,s1)*multi(e1,e2,s1)<0)
  return 0;
 if(multi(s1,e2,s2)*multi(e2,e1,s2)<0)
  return 0;
 return 1;
}
double polygonArea(int n)//计算多边形面积，凹凸多边形皆可
{
 double area=0;
 int i;
 for(i=1;i<n;i++)
  area+=x[i-1]*y[i]-x[i]*y[i-1];
 area+=x[n-1]*y[0]-x[0]*y[n-1];
 if(area<0)   // 得到的是有向面积，取绝对值
  area*=-1;
 return area/2;
}
int main()
{
 freopen("in.txt","r",stdin);
 int n,caseNum=0,i,j;
 double area=0;
begin: while(scanf("%d",&n)&&n)
  {
   caseNum++;
   if(caseNum>1)
    printf("\n");
   for(i=0;i<n;i++)
    scanf("%lf %lf",&x[i],&y[i]);
   if(n<3)   //小于三个点不可能组成多边形
   {
    printf("Figure %d: Impossible\n",caseNum);
    continue;
   }
   for(i=1;i<=n-1;i++)  //判断能否组成多边形
   {
    for(j=1;j<=i-2;j++)
     if(isIntersected(i-1,i,j-1,j))
     {
      printf("Figure %d: Impossible\n",caseNum);
      goto begin;
     }
   }
   for(i=2;i<n-1;i++)
    if(isIntersected(n-1,0,i-1,i))
    {
     printf("Figure %d: Impossible\n",caseNum);
     goto begin;
    }
   //计算多边形面积
   printf("Figure %d: %.2lf\n",caseNum,polygonArea(n));
  }
  return 0;
}