1185: [HNOI2007]最小矩形覆盖 - BZOJ

 

就是一道凸包（枚举凸包的边作为矩形的一条边）的裸题，只是不太好打，所以犹豫到今天才打

不说了，说起AC都是泪啊，因为没有精度判断，没有判重（算距离时除0了）错了好久
拍了好久都和标称是一样的，因为我是随机生成数据，基本不可能有重复的点
代码请自动无视...193行pascal（都是一坨一坨的）

 const
     eps=1e-7;
 var
     x,y:array[..]of extended;
     s:array[..]of longint;
     p:array[..,..]of longint;
     n,tot:longint;
     sp:extended;

 procedure swap(var x,y:extended);
 var
     t:extended;
 begin
     t:=x;x:=y;y:=t;
 end;

 function min(x,y:extended):extended;
 begin
   if x<y then exit(x);
   exit(y);
 end;

 function cj(x1,y1,x2,y2,x3,y3:extended):extended;
 begin
     exit((y1-y2)*(x3-x1)+(x2-x1)*(y3-y1));
 end;

 function jl(x1,y1,x2,y2,x3,y3:extended):extended;
 begin
     exit(cj(x1,y1,x2,y2,x3,y3)/sqrt(sqr(x1-x2)+sqr(y1-y2)));
 end;

 procedure jiao(var x,y:extended;x1,y1,x2,y2,x3,y3:extended);
 begin
     x3:=x3-x1;
     y3:=y3-y1;
     if abs(x2)<eps then
     begin
       x:=x1;
       y:=y1+y3;
       exit;
     end;
     if abs(y2)<eps then
     begin
       x:=x1+x3;
       y:=y1;
       exit;
     end;
     x2:=y2/x2;
     y3:=y3+x3/x2;
     x3:=-/x2;
     x:=y3/(x2-x3);
     y:=x*x2;
     x:=x+x1;
     y:=y+y1;
 end;

 procedure sort(l,r:longint);
 var
     i,j:longint;
     xi,yi:extended;
 begin
     i:=l;
     j:=r;
     xi:=x[(l+r)>>];
     yi:=y[(l+r)>>];
     repeat
       while (cj(x[],y[],xi,yi,x[i],y[i])<)and(abs(cj(x[],y[],xi,yi,x[i],y[i]))>eps) do
         inc(i);
       while (cj(x[],y[],xi,yi,x[j],y[j])>)and(abs(cj(x[],y[],xi,yi,x[j],y[j]))>eps) do
         dec(j);
       if i<=j then
       begin
         swap(x[i],x[j]);
         swap(y[i],y[j]);
         inc(i);
         dec(j);
       end;
     until i>j;
     if i<r then sort(i,r);
     if j>l then sort(l,j);
 end;

 procedure init;
 var
     i:longint;
     minx,miny:extended;
 begin
     read(n);
     minx:=;
     miny:=;
     for i:= to n do
       begin
         read(x[i],y[i]);
         if (y[i]<miny)or((abs(y[i]-miny)<eps)and(x[i]<minx)) then
         begin
           minx:=x[i];
           miny:=y[i];
         end;
       end;
     i:=;
     while i<=n do
       if (abs(x[i]-minx)<eps)and(abs(y[i]-miny)<eps) then
         begin
           swap(x[i],x[n]);
           swap(y[i],y[n]);
           dec(n);
         end
       else inc(i);
     x[]:=minx;
     y[]:=miny;
     sort(,n);
     inc(n);
     x[n]:=x[];
     y[n]:=y[];
 end;

 procedure work;
 var
     i:longint;
 begin
     for i:= to n do
       begin
         while (tot>)and(cj(x[s[tot-]],y[s[tot-]],x[s[tot]],y[s[tot]],x[i],y[i])<) do
           dec(tot);
         inc(tot);
         s[tot]:=i;
         if (abs(x[s[tot]]-x[s[tot-]])<eps)and(abs(y[s[tot]]-y[s[tot-]])<eps) then dec(tot);
       end;
     for i:= to tot do
       begin
         x[i]:=x[s[i]];
         y[i]:=y[s[i]];
       end;
     n:=tot;
     for i:= to n do
       begin
         if jl(-y[],x[],-y[],x[],x[i],y[i])<jl(-y[],x[],-y[],x[],x[p[,]],y[p[,]]) then p[,]:=i;
         if jl(x[],y[],x[],y[],x[i],y[i])>jl(x[],y[],x[],y[],x[p[,]],y[p[,]]) then p[,]:=i;
         if jl(-y[],x[],-y[],x[],x[i],y[i])>jl(-y[],x[],-y[],x[],x[p[,]],y[p[,]]) then p[,]:=i;
       end;
     for i:= to n- do
       begin
         p[i]:=p[i-];
         p[i,]:=i;
         while jl(-y[i],x[i],-y[i+],x[i+],x[(p[i,]+)mod n],y[(p[i,]+)mod n])<jl(-y[i],x[i],-y[i+],x[i+],x[p[i,]],y[p[i,]]) do
           p[i,]:=(p[i,]+)mod n;
         while jl(x[i],y[i],x[i+],y[i+],x[(p[i,]+)mod n],y[(p[i,]+)mod n])>jl(x[i],y[i],x[i+],y[i+],x[p[i,]],y[p[i,]]) do
           p[i,]:=(p[i,]+)mod n;
         while jl(-y[i],x[i],-y[i+],x[i+],x[(p[i,]+)mod n],y[(p[i,]+)mod n])>jl(-y[i],x[i],-y[i+],x[i+],x[p[i,]],y[p[i,]]) do
           p[i,]:=(p[i,]+)mod n;
       end;
     sp:=;
     for i:= to n- do
       sp:=min(sp,abs((jl(x[i],y[i],x[i+],y[i+],x[p[i,]],y[p[i,]])-jl(x[i],y[i],x[i+],y[i+],x[p[i,]],y[p[i,]]))*(jl(-y[i],x[i],-y[i+],x[i+],x[p[i,]],y[p[i,]])-jl(-y[i],x[i],-y[i+],x[i+],x[p[i,]],y[p[i,]]))));
     writeln(sp::);
     for i:= to n- do
       if abs(abs((jl(x[i],y[i],x[i+],y[i+],x[p[i,]],y[p[i,]])-jl(x[i],y[i],x[i+],y[i+],x[p[i,]],y[p[i,]]))*(jl(-y[i],x[i],-y[i+],x[i+],x[p[i,]],y[p[i,]])-jl(-y[i],x[i],-y[i+],x[i+],x[p[i,]],y[p[i,]])))-sp)<eps then break;
     jiao(x[n+],y[n+],x[i],y[i],x[i+]-x[i],y[i+]-y[i],x[p[i,]],y[p[i,]]);
     jiao(x[n+],y[n+],x[p[i,]],y[p[i,]],y[i]-y[i+],x[i+]-x[i],x[p[i,]],y[p[i,]]);
     jiao(x[n+],y[n+],x[p[i,]],y[p[i,]],x[i+]-x[i],y[i+]-y[i],x[p[i,]],y[p[i,]]);
     jiao(x[n+],y[n+],x[p[i,]],y[p[i,]],y[i]-y[i+],x[i+]-x[i],x[i],y[i]);
     x[]:=;
     y[]:=;
     for i:= to  do
       if (y[n+i]<y[])or((abs(y[]-y[n+i])<eps)and(x[n+i]<x[])) then
       begin
         x[]:=x[n+i];
         y[]:=y[n+i];
       end;
     for i:= to  do
       if (abs(x[]-x[n+i])<eps)and(abs(y[]-y[n+i])<eps) then break;
     swap(x[n+],x[n+i]);
     swap(y[n+],y[n+i]);
     writeln(x[]+eps::,' ',y[]+eps::);
     sort(n+,n+);
     for i:= to  do
       writeln(x[n+i]+eps::,' ',y[n+i]+eps::);
 end;

 begin
     init;
     work;
 end.