UVa 11265 The Sultan's Problem

Link To The Problem

Solution : 半平面交、多边形面积

Code:

// UVa 11265 The Sultan's Problem// HalfPlane Intersection//#include<iostream>#include<cstdio>#include<cstring>#include<algorithm>#include<cmath>#include<vector>#include<deque>#include<queue>using namespace std;#define FOR(i,a,b) for(int (i)=(a);(i)<=(b);(i)++)#define DOR(i,a,b) for(int (i)=(a);(i)>=(b);(i)--)#define oo 1e6#define eps 1e-6#define nMax 100000#define pb push_back#define pf push_front#define F first#define S second#define bug puts("OOOOh.....");#define zero(x) (((x)>0?(x):-(x))<eps)#define LL long long#define DB doubleint dcmp(double x){    if(fabs(x)<eps) return 0;    return x>0?1:-1;}class point {public:    double x,y;    point (double x=0,double y=0):x(x),y(y) {}    void make(double _x,double _y) {x=_x;y=_y;}    void read() { scanf("%lf%lf",&x,&y); }    void out() { printf("%.2lf %.2lf\n",x,y);}    double len() { return sqrt(x*x+y*y); }    point friend operator - (point const& u,point const& v) {        return point(u.x-v.x,u.y-v.y);    }    point friend operator + (point const& u,point const& v) {        return point(u.x+v.x,u.y+v.y);    }    double friend operator * (point const& u,point const& v) {        return u.x*v.y-u.y*v.x;    }    double friend operator ^ (point const& u,point const& v) {        return u.x*v.x+u.y*v.y;    }    point friend operator * (point const& u,double const& k) {        return point(u.x*k,u.y*k);    }friend bool operator < (point const& u,point const& v){if(dcmp(v.x-u.x)==0) return dcmp(u.y-v.y)<0;return dcmp(u.x-v.x)<0;}friend bool operator != (point const& u,point const& v){return dcmp(u.x-v.x) || dcmp(u.y-v.y);}};double const pi = acos(-1.0);typedef point vec;//点在半平面的左边typedef class HalfPlane{public:point P;vec V;double arg;HalfPlane(){};HalfPlane(point a,point b):P(a){V = b-a;arg = atan2(V.y,V.x);}} HP;double const inf = 1e6;deque<HP> que;deque<point> deq;vector<HP> init(double w,double h) {                                  // Initwhile(!que.empty()) que.pop_back();while(!deq.empty()) deq.pop_back();vector<HP> ret;ret.clear();ret.pb(HP(point(0,0),point(w,0)));ret.pb(HP(point(w,0),point(w,h)));ret.pb(HP(point(w,h),point(0,h)));ret.pb(HP(point(0,h),point(0,0)));return ret;} int  satisfy(HP u, point a){return dcmp(u.V*(a-u.P)) >= 0;}int cmp(HP a,HP b){int ret = dcmp(a.arg-b.arg);if(ret == 0) return satisfy(b,a.P);return ret < 0;}int parrell(HP a,HP b){return dcmp(a.V*b.V) == 0;}int same_dir(HP a,HP b){return dcmp(a.V ^ b.V) >= 0;}int Same(HP a,HP b){return (dcmp((a.P-b.P)*a.V)==0);}point Intersection(HP a,HP b){point u = a.P-b.P;double t = (b.V*u)/(a.V*b.V);return a.P + a.V*t;}int erase_back(HP v){while(deq.size() && !satisfy(v,deq.back())) {if(parrell(v,que.back())) return 0;deq.pop_back();que.pop_back();}return 1;}int erase_front(HP v){while(deq.size() && !satisfy(v,deq.front())) {if(parrell(v,que.front())) return 0;deq.pop_front();que.pop_front();}return 1;}int add(HP v){if(parrell(v,que.back())) return 0;                        // Can't Be such kinddeq.push_back(Intersection(v,que.back()));que.pb(v);return 1;}int n,H,W;int HP_insection(vector<HP> hp,vector<point>& ret){vector<HP> Add =init((double)W,(double)H);for(int i=0;i<4;i++) hp.pb(Add[i]);sort(hp.begin(),hp.end(),cmp);que.pb(hp[0]);for(int i=1;i<hp.size();i++) {if(dcmp(hp[i].arg - hp[i-1].arg)==0) continue;if(!erase_back(hp[i])) return 0;if(!erase_front(hp[i])) return 0;;if(!add(hp[i]))  return 0;}while(deq.size() && !satisfy(que.front(),deq.back())){deq.pop_back();que.pop_back();}while(deq.size() && !satisfy(que.back(),deq.front())) {deq.pop_front();que.pop_front();}if(!add(que.front())) return 0;ret = vector<point> (deq.begin(),deq.end());return (int) deq.size() > 2;// return vector<point> (ans.begin(),ans.end());   // if you need; you would better use unique}double Area(vector<point> p) {double ans = 0;point O(0,0);p.pb(p[0]);for(int i=0;i<p.size()-1;i++) {ans += (p[i]-O)*(p[i+1]-O);}ans /= 2.0;return ans;}#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)#define sf scanf#define ptf printfpoint p1,p2,p;vector<HP> hp;vector<point> ans;int main() {#ifndef ONLINE_JUDGEfreopen("in.txt","r",stdin);#endifint cas = 1;while(~sf("%d%d%d",&n,&W,&H)){p.read();hp.clear();rep(i,n) {p1.read(),p2.read();if(dcmp((p2-p1)*(p-p1))>=0) hp.pb(HP(p1,p2));if(dcmp((p1-p2)*(p-p2))>=0) hp.pb(HP(p2,p1));}double ret = 0;if(HP_insection(hp,ans)){ret = Area(ans);}ptf("Case #%d: %.3lf\n",cas++,ret);}return 0;}