UVa 11265 The Sultan's Problem

Link To The Problem

Solution : 半平面交、多邊形面積

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 double

int 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;

//點在半平面的左邊
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) {                                  // Init
	while(!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 kind
	deq.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 printf

point p1,p2,p;
vector<HP> hp;
vector<point> ans;

int main() {
#ifndef ONLINE_JUDGE
	freopen("in.txt","r",stdin);
#endif

	int 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;
}