Hdu 4458 Shoot the Airplane（判断点在多边形内）

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题目地址：http://acm.hdu.edu.cn/showproblem.php?pid=4458

思路：以飞机为参考系，则飞机相对静止，子弹加上水平方向速度-v。则只需枚举时间，判断该时间时点（子弹）是否在多边形（飞机）内。注意g可以为0，分匀变速和匀速。另外本题精度要求较高，判断点在线段上用坐标差值，避免使用Dot 。

#include<cstdio>#include<cstring>#include<iostream>#include<algorithm>#define debuusing namespace std;const double eps = 1e-10;const int maxn=25;struct Point{    double x, y;    Point(double x = 0, double y = 0) : x(x), y(y) {}};typedef Point Vector;int n,v,b,g;Point p[maxn];Vector operator - (const Point &A, const Point &B){    return Vector(A.x - B.x, A.y - B.y);}int dcmp(double x){    if(fabs(x) < eps) return 0;    else return x < 0 ? -1 : 1;}double Dot(const Vector &A, const Vector &B){    return A.x * B.x + A.y * B.y;}double Cross(const Vector &A, const Vector B){    return A.x * B.y - A.y * B.x;}bool OnSegment(const Point &p, const Point &a1, const Point &a2){    //return dcmp(Cross(a1 - p, a2 - p)) == 0 && dcmp(Dot(a1 - p, a2 - p)) < 0;    if(dcmp(Cross(a1-p,a2-p))) return 0;    else if(dcmp(p.x-min(a1.x,a2.x))>=0&&dcmp(p.x-max(a1.x,a2.x))<=0&&dcmp(p.y-min(a1.y,a2.y))>=0&&dcmp(p.y-max(a1.y,a2.y))<=0) return 1;    else return 0;}int  isPointInPolygon(Point p, Point *poly, int n){    int wn = 0;    for(int i = 0; i < n; ++i)    {        if(OnSegment(p, poly[i], poly[(i+1)%n])) return 0;        int k=dcmp(Cross(poly[(i+1)%n]-poly[i], p-poly[i]));        int d1=dcmp(poly[i].y-p.y);        int d2=dcmp(poly[(i+1)%n].y-p.y);        if(k>0&&d1<=0&&d2>0) wn++;        if(k<0&&d2<=0&&d1>0) wn--;    }    if(wn!=0)  return 1;    else return 0;}int main(){#ifdef debug    freopen("in.in","r",stdin);#endif // debug    while(scanf("%d%d%d",&v,&b,&g)==3)    {        if(v==0&&b==0&&g==0) break;        scanf("%d",&n);        double maxy=0.0;        for(int i=0; i<n; i++)        {            scanf("%lf%lf",&p[i].x,&p[i].y);            maxy=max(maxy,p[i].y);        }        int flag=0;        double Time=dcmp(g)?(2.0*b/g):(1.0*maxy/b);        //cout<<Time<<endl;        for(double i=0.0; i<=Time; i+=0.001)        {            Point tmp;            tmp.x=-v*i,tmp.y=b*i-0.5*g*i*i;            if(isPointInPolygon(tmp,p,n))            {                printf("%.2f\n",i);                flag=1;                break;            }        }        if(!flag) printf("Miss!\n");    }    return 0;}

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