1185: [HNOI2007]最小矩形覆盖

 

 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[0..50010]of extended;
    s:array[0..50010]of longint;
    p:array[0..50010,1..4]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:=-1/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)>>1];
    yi:=y[(l+r)>>1];
    repeat
      while (cj(x[0],y[0],xi,yi,x[i],y[i])<0)and(abs(cj(x[0],y[0],xi,yi,x[i],y[i]))>eps) do
        inc(i);
      while (cj(x[0],y[0],xi,yi,x[j],y[j])>0)and(abs(cj(x[0],y[0],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:=99999999999999999999999999999999999999;
    miny:=99999999999999999999999999999999999999;
    for i:=1 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:=1;
    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[0]:=minx;
    y[0]:=miny;
    sort(1,n);
    inc(n);
    x[n]:=x[0];
    y[n]:=y[0];
end;
 
procedure work;
var
    i:longint;
begin
    for i:=1 to n do
      begin
        while (tot>0)and(cj(x[s[tot-1]],y[s[tot-1]],x[s[tot]],y[s[tot]],x[i],y[i])<0) do
          dec(tot);
        inc(tot);
        s[tot]:=i;
        if (abs(x[s[tot]]-x[s[tot-1]])<eps)and(abs(y[s[tot]]-y[s[tot-1]])<eps) then dec(tot);
      end;
    for i:=1 to tot do
      begin
        x[i]:=x[s[i]];
        y[i]:=y[s[i]];
      end;
    n:=tot;
    for i:=1 to n do
      begin
        if jl(-y[0],x[0],-y[1],x[1],x[i],y[i])<jl(-y[0],x[0],-y[1],x[1],x[p[0,2]],y[p[0,2]]) then p[0,2]:=i;
        if jl(x[0],y[0],x[1],y[1],x[i],y[i])>jl(x[0],y[0],x[1],y[1],x[p[0,3]],y[p[0,3]]) then p[0,3]:=i;
        if jl(-y[0],x[0],-y[1],x[1],x[i],y[i])>jl(-y[0],x[0],-y[1],x[1],x[p[0,4]],y[p[0,4]]) then p[0,4]:=i;
      end;
    for i:=1 to n-1 do
      begin
        p[i]:=p[i-1];
        p[i,1]:=i;
        while jl(-y[i],x[i],-y[i+1],x[i+1],x[(p[i,2]+1)mod n],y[(p[i,2]+1)mod n])<jl(-y[i],x[i],-y[i+1],x[i+1],x[p[i,2]],y[p[i,2]]) do
          p[i,2]:=(p[i,2]+1)mod n;
        while jl(x[i],y[i],x[i+1],y[i+1],x[(p[i,3]+1)mod n],y[(p[i,3]+1)mod n])>jl(x[i],y[i],x[i+1],y[i+1],x[p[i,3]],y[p[i,3]]) do
          p[i,3]:=(p[i,3]+1)mod n;
        while jl(-y[i],x[i],-y[i+1],x[i+1],x[(p[i,4]+1)mod n],y[(p[i,4]+1)mod n])>jl(-y[i],x[i],-y[i+1],x[i+1],x[p[i,4]],y[p[i,4]]) do
          p[i,4]:=(p[i,4]+1)mod n;
      end;
    sp:=99999999999999999999999999999999999999999999999999999;
    for i:=0 to n-1 do
      sp:=min(sp,abs((jl(x[i],y[i],x[i+1],y[i+1],x[p[i,1]],y[p[i,1]])-jl(x[i],y[i],x[i+1],y[i+1],x[p[i,3]],y[p[i,3]]))*(jl(-y[i],x[i],-y[i+1],x[i+1],x[p[i,2]],y[p[i,2]])-jl(-y[i],x[i],-y[i+1],x[i+1],x[p[i,4]],y[p[i,4]]))));
    writeln(sp:0:5);
    for i:=0 to n-1 do
      if abs(abs((jl(x[i],y[i],x[i+1],y[i+1],x[p[i,1]],y[p[i,1]])-jl(x[i],y[i],x[i+1],y[i+1],x[p[i,3]],y[p[i,3]]))*(jl(-y[i],x[i],-y[i+1],x[i+1],x[p[i,2]],y[p[i,2]])-jl(-y[i],x[i],-y[i+1],x[i+1],x[p[i,4]],y[p[i,4]])))-sp)<eps then break;
    jiao(x[n+1],y[n+1],x[i],y[i],x[i+1]-x[i],y[i+1]-y[i],x[p[i,2]],y[p[i,2]]);
    jiao(x[n+2],y[n+2],x[p[i,2]],y[p[i,2]],y[i]-y[i+1],x[i+1]-x[i],x[p[i,3]],y[p[i,3]]);
    jiao(x[n+3],y[n+3],x[p[i,3]],y[p[i,3]],x[i+1]-x[i],y[i+1]-y[i],x[p[i,4]],y[p[i,4]]);
    jiao(x[n+4],y[n+4],x[p[i,4]],y[p[i,4]],y[i]-y[i+1],x[i+1]-x[i],x[i],y[i]);
    x[0]:=999999999999999999999999999999999999999999;
    y[0]:=999999999999999999999999999999999999999999;
    for i:=1 to 4 do
      if (y[n+i]<y[0])or((abs(y[0]-y[n+i])<eps)and(x[n+i]<x[0])) then
      begin
        x[0]:=x[n+i];
        y[0]:=y[n+i];
      end;
    for i:=1 to 4 do
      if (abs(x[0]-x[n+i])<eps)and(abs(y[0]-y[n+i])<eps) then break;
    swap(x[n+4],x[n+i]);
    swap(y[n+4],y[n+i]);
    writeln(x[0]+eps:0:5,' ',y[0]+eps:0:5);
    sort(n+1,n+3);
    for i:=1 to 3 do
      writeln(x[n+i]+eps:0:5,' ',y[n+i]+eps:0:5);
end;
 
begin
    init;
    work;
end.