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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:

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#include <iostream>#include <cstdio>#include <cstring>#include <cstdlib>#include <cmath>#include <algorithm>#define pi acos(-1.0)#define eps 1e-8using 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\n",CalcConvexArea(poly,m));    }    return 0;}
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POJ 2540 Hotter Colder --半平面交