Cod sursa(job #378391)

Utilizator GotenAmza Catalin Goten Data 28 decembrie 2009 14:47:17
Problema Rubarba Scor 20
Compilator cpp Status done
Runda Arhiva de probleme Marime 3.9 kb
#include<fstream.h>
#include<iomanip.h>
#include<math.h>
#include<iostream.h>

int x[101000],y[101000],b[101000],a[101000],sol[101000];

double distance(int i1, int i2)
{
	double l;
	l=(x[i1]-x[i2])*(x[i1]-x[i2])+(y[i1]-y[i2])*(y[i1]-y[i2]);
	return l;
}

void qs(int i, int j)
{
	int s=i,d=j,piv=a[(i+j)>>1],aux;
	while(s<=d)
	{
		while((y[a[s]]-y[1])*(x[piv]-x[1])<(y[piv]-y[1])*(x[a[s]]-x[1])||(y[a[s]]-y[1])*(x[piv]-x[1])==(y[piv]-y[1])*(x[a[s]]-x[1])&&distance(a[s],1)<distance(piv,1))
			s++;
		while((y[a[d]]-y[1])*(x[piv]-x[1])>(y[piv]-y[1])*(x[a[d]]-x[1])||(y[a[d]]-y[1])*(x[piv]-x[1])==(y[piv]-y[1])*(x[a[d]]-x[1])&&distance(a[d],1)>distance(piv,1))
			d--;
		if(s<=d)
		{
			aux=a[s];
			a[s]=a[d];
			a[d]=aux;
			s++;
			d--;
		}
	}
	if(s<j)
		qs(s,j);
	if(i<d)
		qs(i,d);
}

int det(int i1, int i2, int i3)
{
	int r=x[i1]*y[i2]+x[i2]*y[i3]+x[i3]*y[i1]-y[i2]*x[i3]-y[i3]*x[i1]-y[i1]*x[i2];
	return r;
}


void distanta(int i1, int i2, int i, double &lmax)
{
	double numa,numi,l;
	int i0;
	lmax=0;
	for(i0=1;i0<=i;i0++)
		if(i0!=i1&&i0!=i2)
		{
			numa=(x[sol[i2]]-x[sol[i1]])*(y[sol[i1]]-y[sol[i0]])-(x[sol[i1]]-x[sol[i0]])*(y[sol[i2]]-y[sol[i1]]);
			if(numa<0)
				numa=-numa;
			numi=(x[sol[i2]]-x[sol[i1]])*(x[sol[i2]]-x[sol[i1]])+(y[sol[i2]]-y[sol[i1]])*(y[sol[i2]]-y[sol[i1]]);
			numi=sqrt(numi);
			l=numa/numi;
			if(l>lmax)
				lmax=l;
		}
}

void proiectie(int i1, int i2, int i, double &l)
{
	double tg,cos,sin,xx[101000],yy[101000],sst,ddr;
	int j,st,dr;
	tg=(y[sol[i2]]-y[sol[i1]])/(x[sol[i2]]-x[sol[i1]]);
	cos=tg*tg+1;
	cos=1/cos;
	sin=1-cos;
	sin=sqrt(sin);
	cos=sqrt(cos);
	if(tg<0)
		cos=-cos;
	for(j=1;j<=i;j++)
	{
		xx[sol[j]]=x[sol[j]]*cos+y[sol[j]]*sin;
		yy[sol[j]]=y[sol[j]]*cos-x[sol[j]]*sin;
	}	
	sst=xx[sol[1]];
	ddr=sst;
	st=1;
	dr=1;
	for(j=2;j<=i;j++)
	{
		if(xx[sol[j]]<sst)
		{
			st=j;
			sst=xx[sol[j]];
		}
		if(xx[sol[j]]>ddr)
		{
			dr=j;
			ddr=xx[sol[j]];
		}
	}
	l=(ddr-sst)*(ddr-sst)+(yy[sol[st]]-yy[sol[dr]])*(yy[sol[st]]-yy[sol[dr]]);
	l=sqrt(l);	
	tg=(yy[sol[dr]]-yy[sol[st]])/(ddr-sst);
	cos=tg*tg+1;
	cos=1/cos;
	cos=sqrt(cos);
	l*=cos;
}

void projectie(int i1, int i2, int i, double &l)
{
	double tg,cos;
	int j,up,down,uup,dwn;
	uup=y[sol[1]];
	dwn=y[sol[1]];
	up=1;
	down=1;
	for(j=2;j<=i;j++)
	{
		if(y[sol[j]]>uup)
		{
			uup=y[sol[j]];
			up=j;
		}
		if(y[sol[j]]<dwn)
		{
			dwn=y[sol[j]];
			down=j;
		}
	}
	l=(x[sol[down]]-x[sol[up]])*(x[sol[down]]-x[sol[up]])+(dwn-uup)*(dwn-uup);
	l=sqrt(l);
	tg=(x[sol[up]]-x[sol[down]])/(uup-dwn);	
	cos=tg*tg+1;
	cos=1/cos;
	cos=sqrt(cos);
	l*=cos;
}

int main()
{
	int i,j,k=0,n,t=0,inc,sf,aux,i1,i2;
	double s,smax,l1,l2;
	ifstream f("rubarba.in");
	ofstream g("rubarba.out");
	f>>n;
	inc=1;
	for(i=1;i<=n;i++)
	{
		f>>x[i]>>y[i];
		if(x[i]<x[inc]||x[i]==x[inc]&&y[i]<y[inc])
			inc=i;
	}
	if(n==1||n==2)
	{
		g<<"0.00";
		return 0;
	}
	if(n==3)
	{
		g<<fixed<<setprecision(2)<<(float)abs(det(1,2,3));
		return 0;
	}
	aux=x[1];
	x[1]=x[inc];
	x[inc]=aux;
	aux=y[1];
	y[1]=y[inc];
	y[inc]=1;
	for(i=2;i<=n;i++)
		if(x[i]!=x[1])
			a[++k]=i;
		else
			b[++t]=i;
	qs(1,k);
	sf=1;
	for(i=2;i<=t;i++)
		if(y[b[i]]>y[b[sf]])
			sf=i;
	sol[1]=1;
	sol[2]=a[1];
	i=2;j=2;
	while(j<=k)
	{
		while(det(sol[i-1],sol[i],a[j])<=0&&i>1)
			i--;
		sol[++i]=a[j++];
	}
	if(t)
	{
		while(det(sol[i-1],sol[i],b[sf])<=0&&i>1)
			i--;
		sol[++i]=b[sf];
	}
	if(i==1||i==2)
	{
		g<<"0.00";
		return 0;
	}
	if(i==3)
	{
		g<<fixed<<setprecision(2)<<(float)abs(det(sol[1],sol[2],sol[3]));
		return 0;
	}
	smax=(1<<30);
	for(j=1;j<=i;j++)
	{
		i1=j;
		if(j==i)
			i2=1;
		else 
			i2=j+1;
		distanta(i1,i2,i,l1);
		if(x[sol[i1]]==x[sol[i2]])
			projectie(i1,i2,i,l2);
		else
			proiectie(i1,i2,i,l2);
		s=l1*l2;
		if(s<smax)
			smax=s;
	}
	g<<fixed<<setprecision(2)<<smax;
	return 0;
}