UFO 撃墜作戦

パソコン甲子園2009予選 問題10 UFO 撃墜作戦

問題はこちら。

計算幾何学＋シミュレーションの問題です。
円と線分の交差判定ができるかが問われています。

少し面倒ですが、円と直線の交点を求めて、 それが有効範囲のレザーの上(線分)にあるかどうかを判定しました。

#include<iostream>
#include<cfloat>
#include<cassert>
#include<cmath>
#include<vector>

using namespace std;

#define EPS (1e-8)
#define equals(a, b) (fabs((a) - (b)) < EPS )
#define dle(a, b) (equals(a, b) || a < b )
static const double PI = acos(-1);

class Point{
    public:
    double x, y;
    
    Point ( double x = 0, double y = 0): x(x), y(y){}
    
    Point operator + ( Point p ){ return Point(x + p.x, y + p.y); }
    Point operator - ( Point p ){ return Point(x - p.x, y - p.y); }
    Point operator * ( double a ){ return Point(x*a, y*a); }

    double abs() { return sqrt(norm());}
    double norm() { return x*x + y*y; }

    bool operator < ( const Point &p ) const {
        return x != p.x ? x < p.x : y < p.y;
    }
    bool operator == ( const Point &p ) const {
        return fabs(x-p.x) < EPS && fabs(y-p.y) < EPS;
    }
};

typedef Point Vector;

class Segment{
    public:
    Point p1, p2;
    Segment(Point s = Point(), Point t = Point()): p1(s), p2(t){}
};

typedef Segment Line;

class Circle{
    public:
    Point c;
    double r;
    Circle(Point c = Point(), double r = 0.0): c(c), r(r){}
};

double norm( Vector a ){ return a.x*a.x + a.y*a.y; }
double abs( Vector a ){ return sqrt(norm(a)); }
Point polar( double a, double r ){ return Point(cos(r)*a, sin(r)*a);}
double getDistance( Vector a, Vector b ){ return abs(a - b); }
double scalar( Vector a, Vector b ){ return a.x*b.x + a.y*b.y; }
double cross( Vector a, Vector b ){ return a.x*b.y - a.y*b.x; }

double arg(Vector p){
    return atan2(p.y, p.x);
}

double getDistanceLP(Line s, Point p){
    return abs(cross(s.p2 - s.p1, p - s.p1)/abs(s.p2 - s.p1));
}

bool isIntersect( Circle c1, Line l ){
    double d = getDistanceLP(l, c1.c);
    return ( equals(d, c1.r) || d < c1.r );
}

pair<Point, Point> getCrossPoints(Circle c1, Line l ){
    assert( isIntersect( c1, l ) );
    double d = getDistanceLP(l, c1.c);
    Point v = l.p2 - l.p1;
    if ( cross(l.p2 - l.p1, c1.c - l.p1) > EPS ){
        v = polar(abs(v), arg(v)-acos(-1)/2);
    } else {
        v = polar(abs(v), arg(v)+acos(-1)/2);
    }
    double th = acos(d/c1.r);
    Point v1 = polar(c1.r, arg(v) + th );
    Point v2 = polar(c1.r, arg(v) - th );
    return make_pair(c1.c+v1, c1.c+v2);
}

enum {NON, IN, OUT};

double R;

class UFO{
    public:
    Circle body;
    double v, dx, dy;
    int state;

    UFO( Circle c = Circle(Point(0,0),0), double v=0):body(c), v(v){
        Point ct = Point(0, 0);
        Vector a = ct - body.c;
        dx = v*cos(arg(a));
        dy = v*sin(arg(a));
        state = NON;
    }

    void move(){
        if ( state != NON ) return;
        double pred = getDistance(Point(0, 0), body.c);
        if ( v > pred || equals(v, pred)){ state = IN; return; }
        body.c.x += dx;
        body.c.y += dy;
        double d = getDistance(Point(0, 0), body.c);
        if ( R > d || equals(R, d) ) state = IN;
    }
};

#define MAX 100

UFO U[MAX];
int n;

void attack( Point p1, Point p2){
    Line l = Line(p1, p2);
    for ( int i = 0; i < n; i++ ){
        if ( U[i].state != NON ) continue;
        if ( !isIntersect(U[i].body, l) ) continue;
        pair<Point, Point> pp = getCrossPoints(U[i].body, l);
        if ( equals( arg(p2 - p1), arg(pp.first - p1)) && 
             getDistance(p1, pp.first) > R ) U[i].state = OUT;
        if ( equals( arg(p2 - p1), arg(pp.second - p1)) && 
             getDistance(p1, pp.second) > R ) U[i].state = OUT;
    }
}

int simulate(){
    while(1){
        int life = 0;
        for ( int i = 0; i < n; i++ ) {
            U[i].move();
            if ( U[i].state == NON ) life++;
        }
        if ( life == 0 ) break;

        int target = -1;
        double md = FLT_MAX;
        for ( int i = 0; i < n; i++ ){
            if ( U[i].state != NON ) continue;
            double d = getDistance(Point(0, 0), U[i].body.c);
            if ( d < md ){
                md = d;
                target = i;
            }
        }
        attack(Point(0, 0), U[target].body.c);
    }

    int cnt = 0;
    for ( int i = 0; i < n; i++ ) if ( U[i].state == IN ) cnt++;
    return cnt;
}

main(){
    double x, y, r, v;
    while( cin >> R && R ){
        cin >> n;
        for ( int i = 0; i < n; i++ ){
            cin >> x >> y >> r >> v;
            U[i] = UFO(Circle(Point(x, y), r), v);
        }
        cout << simulate() << endl;
    }
}