POJ 2540 Hotter Colder --半平面交

题意： 一个(0,0)到(10,10)的矩形，目标点不定，从(0,0)开始走，如果走到新一点是"Hotter",那么意思是离目标点近了，如果是"Colder“，那么就是远了，"Same"是相同。要你推测目标点的可能位置的面积。

解法：半平面交水题。从一个点到另一个点远了，说明目标点在两点之间连线的中垂线的离源点较近的一侧，即我们每次都可以得到一条直线来切割平面，要么切割左侧，要么切割右侧，要么都切，再求一个半平面交就可以得出可能面积了。

代码：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#define pi acos(-1.0)
#define eps 1e-8
using namespace std;

struct Point{
    double x,y;
    Point(double x=0, double y=0):x(x),y(y) {}
    void input() { scanf("%lf%lf",&x,&y); }
};
typedef Point Vector;
struct Line{
    Point p;
    Vector v;
    double ang;
    Line(){}
    Line(Point p, Vector v):p(p),v(v) { ang = atan2(v.y,v.x); }
    Point point(double t) { return Point(p.x + t*v.x, p.y + t*v.y); }
    bool operator < (const Line &L)const { return ang < L.ang; }
};
int dcmp(double x) {
    if(x < -eps) return -1;
    if(x > eps) return 1;
    return 0;
}
template <class T> T sqr(T x) { return x * x;}
Vector operator + (Vector A, Vector B) { return Vector(A.x + B.x, A.y + B.y); }
Vector operator - (Vector A, Vector B) { return Vector(A.x - B.x, A.y - B.y); }
Vector operator * (Vector A, double p) { return Vector(A.x*p, A.y*p); }
Vector operator / (Vector A, double p) { return Vector(A.x/p, A.y/p); }
bool operator < (const Point& a, const Point& b) { return a.x < b.x || (a.x == b.x && a.y < b.y); }
bool operator >= (const Point& a, const Point& b) { return a.x >= b.x && a.y >= b.y; }
bool operator <= (const Point& a, const Point& b) { return a.x <= b.x && a.y <= b.y; }
bool operator == (const Point& a, const Point& b) { return dcmp(a.x-b.x) == 0 && dcmp(a.y-b.y) == 0; }
double Dot(Vector A, Vector B) { return A.x*B.x + A.y*B.y; }
double Length(Vector A) { return sqrt(Dot(A, A)); }
double Angle(Vector A, Vector B) { return acos(Dot(A, B) / Length(A) / Length(B)); }
double Cross(Vector A, Vector B) { return A.x*B.y - A.y*B.x; }
Vector VectorUnit(Vector x){ return x / Length(x);}
Vector Normal(Vector x) { return Point(-x.y, x.x) / Length(x);}
double angle(Vector v) { return atan2(v.y, v.x); }

Point GetLineIntersection(Line A, Line B) {
    Vector u = A.p - B.p;
    double t = Cross(B.v, u) / Cross(A.v, B.v);
    return A.p + A.v*t;
}
double DisP(Point A,Point B) {
    return Length(B-A);
}
double CalcConvexArea(Point* p,int n) {        //凸包面积
    double area = 0.0;
    for(int i=1;i<n-1;i++)
        area += Cross(p[i]-p[0],p[i+1]-p[0]);
    return fabs(area*0.5);
}
bool OnLeft(Line L, Point p) { return dcmp(Cross(L.v,p-L.p)) > 0; }
bool CmpPolarLine(Line a,Line b) {        //直线极角排序
    return angle(a.v) < angle(b.v);
}
int HalfPlaneIntersection(Line* L, int n, Point* poly) {    //半平面交点存入poly
    sort(L,L+n,CmpPolarLine);
    int first,last;
    Point *p = new Point[n];
    Line  *q = new Line[n];
    q[first=last=0] = L[0];
    for(int i=1;i<n;i++) {
        while(first < last && !OnLeft(L[i],p[last-1])) last--;
        while(first < last && !OnLeft(L[i],p[first]))  first++;
        q[++last] = L[i];
        if(dcmp(Cross(q[last].v, q[last-1].v)) == 0) {
            last--;
            if(OnLeft(q[last], L[i].p)) q[last] = L[i];
        }
        if(first < last) p[last-1] = GetLineIntersection(q[last-1],q[last]);
    }
    while(first < last && !OnLeft(q[first],p[last-1])) last--;
    if(last-first <= 1) return 0;       //点或线或无界平面，返回0
    p[last] = GetLineIntersection(q[last],q[first]);
    int m = 0;
    for(int i=first;i<=last;i++) poly[m++] = p[i];
    delete p; delete q;
    return m;
}

Line L[102],TL[103];
Point poly[104];

int main()
{
    int i,j,tot = -1;
    Point n,p;
    char ss[10];
    p.x = p.y = 0.0;
    TL[++tot] = Line(Point(0,0),Vector(10,0));
    TL[++tot] = Line(Point(10,0),Vector(0,10));
    TL[++tot] = Line(Point(10,10),Vector(-10,0));
    TL[++tot] = Line(Point(0,10),Vector(0,-10));
    while(scanf("%lf%lf%s",&n.x,&n.y,ss)!=EOF)
    {
        if(ss[0] == 'H')
            TL[++tot] = Line(Point((n.x+p.x)/2.0,(n.y+p.y)/2.0),Vector(Normal(p-n)));
        else if(ss[0] == 'C')
            TL[++tot] = Line(Point((n.x+p.x)/2.0,(n.y+p.y)/2.0),Vector(Normal(n-p)));
        else {
            TL[++tot] = Line(Point((n.x+p.x)/2.0,(n.y+p.y)/2.0),Vector(Normal(p-n)));
            TL[++tot] = Line(Point((n.x+p.x)/2.0,(n.y+p.y)/2.0),Vector(Normal(n-p)));
        }
        p = n;
        for(i=0;i<=tot;i++) L[i] = TL[i];
        int m = HalfPlaneIntersection(L,tot+1,poly);
        if(!m) puts("0.00");
        else   printf("%.2f
",CalcConvexArea(poly,m));
    }
    return 0;
}