首页 > 代码库 > ZOJ 3720 Magnet Darts (计算几何,概率,判点是否在多边形内)
ZOJ 3720 Magnet Darts (计算几何,概率,判点是否在多边形内)
http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemCode=3720
题意:
在一个矩形区域投掷飞镖,因此飞镖只会落在整点上,投到每个点的得分是Ax+By。矩形区域里面有个多边形,如果飞镖投在多边形里面则得分,求最终的得分期望。
即:给定一个矩形内的所有整数点,判断这些点是否在一个多边形内
方法:
计算几何的判点是否在多边形内(几何模板),如果在,则令得分加(Ax+By)*以此点为中心边长为1的正方形面积
1 void solve() 2 { 3 double ans = 0; 4 for (int i = p.x; i <= q.x; i++) 5 { 6 for (int j = p.y; j <= q.y; j++) 7 { 8 if (PointInPolygon(Point2D(i, j), poly.v, poly.n)) 9 ans += (a * i + b * j) * (min(i + 0.5, q.x) - max(i - 0.5, p.x)) * (min(j + 0.5, q.y) - max(j - 0.5, p.y));10 }11 }12 printf("%.3f\n", ans / (q.x - p.x) / (q.y - p.y));13 }
代码:
1 // #pragma comment(linker, "/STACK:102400000,102400000") 2 #include <cstdio> 3 #include <iostream> 4 #include <cstring> 5 #include <string> 6 #include <cmath> 7 #include <set> 8 #include <list> 9 #include <map> 10 #include <iterator> 11 #include <cstdlib> 12 #include <vector> 13 #include <queue> 14 #include <stack> 15 #include <algorithm> 16 #include <functional> 17 using namespace std; 18 typedef long long LL; 19 #define ROUND(x) round(x) 20 #define FLOOR(x) floor(x) 21 #define CEIL(x) ceil(x) 22 const int maxn = 0; 23 const int maxm = 0; 24 const int inf = 0x3f3f3f3f; 25 const LL inf64 = 0x3f3f3f3f3f3f3f3fLL; 26 // const double INF = 1e30; 27 // const double eps = 1e-6; 28 const int P[4] = {0, 0, -1, 1}; 29 const int Q[4] = {1, -1, 0, 0}; 30 const int PP[8] = { -1, -1, -1, 0, 0, 1, 1, 1}; 31 const int QQ[8] = { -1, 0, 1, -1, 1, -1, 0, 1}; 32 33 typedef double db; 34 const double eps = 1e-7; 35 const double PI = acos(-1.0); 36 const double INF = 1e50; 37 38 const int POLYGON_MAX_POINT = 1024; 39 40 db dmin(db a, db b) 41 { 42 return a > b ? b : a; 43 } 44 db dmax(db a, db b) 45 { 46 return a > b ? a : b; 47 } 48 int sgn(db a) 49 { 50 return a < -eps ? -1 : a > eps; //返回double型的符号 51 } 52 53 struct Point2D 54 { 55 db x, y; 56 int id; 57 Point2D(db _x = 0, db _y = 0): x(_x), y(_y) {} 58 void input() 59 { 60 scanf("%lf%lf" , &x, &y); 61 } 62 void output() 63 { 64 printf("%.2f %.2f\n" , x, y); 65 } 66 // 67 db len2() 68 { 69 return x * x + y * y; 70 } 71 //到原点距离 72 double len() 73 { 74 return sqrt(len2()); 75 } 76 //逆时针转90度 77 Point2D rotLeft90() 78 { 79 return Point2D(-y, x); 80 } 81 //顺时针转90度 82 Point2D rotRight90() 83 { 84 return Point2D(y, -x); 85 } 86 //绕原点逆时针旋转arc_u 87 Point2D rot(double arc_u) 88 { 89 return Point2D( x * cos(arc_u) - y * sin(arc_u), 90 x * sin(arc_u) + y * cos(arc_u) ); 91 } 92 //绕某点逆时针旋转arc_u 93 Point2D rotByPoint(Point2D ¢er, db arc_u) 94 { 95 Point2D tmp( x - center.x, y - center.y ); 96 Point2D ans = tmp.rot(arc_u); 97 ans = ans + center; 98 return ans; 99 }100 101 bool operator == (const Point2D &t) const102 {103 return sgn(x - t.x) == 0 && sgn(y - t.y) == 0;104 }105 bool operator < (const Point2D &t) const106 {107 if ( sgn(x - t.x) == 0 ) return y < t.y;108 else return x < t.x;109 }110 Point2D operator + (const Point2D &t) const111 {112 return Point2D(x + t.x, y + t.y);113 }114 115 Point2D operator - (const Point2D &t) const116 {117 return Point2D(x - t.x, y - t.y);118 }119 120 Point2D operator * (const db &t)const121 {122 return Point2D( t * x, t * y );123 }124 125 Point2D operator / (const db &t) const126 {127 return Point2D( x / t, y / t );128 }129 //点乘130 db operator ^ (const Point2D &t) const131 {132 return x * t.x + y * t.y;133 }134 //叉乘135 db operator * (const Point2D &t) const136 {137 return x * t.y - y * t.x;138 }139 //两点之间的角度(-PI , PI]140 double rotArc(Point2D &t)141 {142 double perp_product = rotLeft90()^t;143 double dot_product = (*this)^t;144 if ( sgn(perp_product) == 0 && sgn(dot_product) == -1) return PI;145 return sgn(perp_product) * acos( dot_product / len() / t.len() );146 }147 //标准化148 Point2D normalize()149 {150 return Point2D(x / len(), y / len());151 }152 };153 154 struct POLYGON155 {156 Point2D v[POLYGON_MAX_POINT];157 int n;158 };159 struct Segment2D160 {161 Point2D s , e;162 Segment2D() {}163 Segment2D( Point2D _s, Point2D _e ): s(_s), e(_e) {}164 };165 //0: 点在多边形外166 //1: 点在多边形内167 bool PonSegment2D(Point2D p, Segment2D seg)168 {169 return sgn((seg.s - p) * (p - seg.e)) == 0 && sgn((seg.s - p) ^ (p - seg.e)) >= 0;170 }171 172 /**** 判断线段在内部相交***/173 bool SegIntersect2D(Segment2D a, Segment2D b)174 {175 //必须在线段内相交176 int d1 = sgn((a.e - a.s) * (b.s - a.s));177 int d2 = sgn((a.e - a.s) * (b.e - a.s));178 int d3 = sgn((b.e - b.s) * (a.s - b.s));179 int d4 = sgn((b.e - b.s) * (a.e - b.s));180 if (d1 * d2 < 0 && d3 * d4 < 0) return true;181 return false;182 }183 184 int PointInPolygon(Point2D p, Point2D poly[], int n)185 {186 Segment2D l, seg;187 l.s = p;188 l.e = p;189 l.e.x = INF;//作射线190 int i, cnt = 0;191 Point2D p1, p2, p3, p4;192 for (i = 0; i < n; i++)193 {194 seg.s = poly[i], seg.e = poly[(i + 1) % n];195 if (PonSegment2D(p, seg)) return 2; //点在多边形上196 p1 = seg.s, p2 = seg.e , p3 = poly[(i + 2) % n], p4 = poly[(i + 3) % n];197 if (SegIntersect2D(l, seg) ||198 PonSegment2D(p2, l) && sgn((p2 - p1) * (p - p1))*sgn((p3 - p2) * (p - p2)) > 0 ||199 PonSegment2D(p2, l) && PonSegment2D(p3, l) &&200 sgn((p2 - p1) * (p - p1))*sgn((p4 - p3) * (p - p3)) > 0 )201 cnt++;202 }203 if (cnt % 2 == 1) return 1; //点在多边形内204 return 0;//点在多边形外205 }206 207 POLYGON poly;208 Point2D p, q;209 db a, b;210 void init()211 {212 //213 }214 void input()215 {216 scanf("%d%lf%lf", &poly.n, &a, &b);217 for (int i = 0; i < poly.n; i++)218 {219 scanf("%lf%lf", &poly.v[i].x, &poly.v[i].y);220 }221 }222 void debug()223 {224 //225 }226 void solve()227 {228 double ans = 0;229 for (int i = p.x; i <= q.x; i++)230 {231 for (int j = p.y; j <= q.y; j++)232 {233 if (PointInPolygon(Point2D(i, j), poly.v, poly.n))234 ans += (a * i + b * j) * (min(i + 0.5, q.x) - max(i - 0.5, p.x)) * (min(j + 0.5, q.y) - max(j - 0.5, p.y));235 }236 }237 printf("%.3f\n", ans / (q.x - p.x) / (q.y - p.y));238 }239 void output()240 {241 //242 }243 int main()244 {245 // std::ios_base::sync_with_stdio(false);246 // #ifndef ONLINE_JUDGE247 // freopen("in.cpp", "r", stdin);248 // #endif249 250 while (~scanf("%lf%lf%lf%lf", &p.x, &p.y, &q.x, &q.y))251 {252 init();253 input();254 solve();255 output();256 }257 return 0;258 }
声明:以上内容来自用户投稿及互联网公开渠道收集整理发布,本网站不拥有所有权,未作人工编辑处理,也不承担相关法律责任,若内容有误或涉及侵权可进行投诉: 投诉/举报 工作人员会在5个工作日内联系你,一经查实,本站将立刻删除涉嫌侵权内容。