bzoj1185

一遇到数学题和计算几何题我就要调半天……

玛雅，我真是太弱了……

基本思路很简单，先上凸包，然后矩形与凸包一边重合，然后旋转卡壳即可

然而我没怎么写过计算几何题，一开始写的各种囧，后来看了hzwer的写法才写得正常一些

一开始写囧，是找矩形的左右边界，用勾股定理算的，囧得不行；

后来发现可以用点积来判断，点积的几何意义：向量A在向量B上投影的长度*向量B的长度

然后就很好做了

const eps=1e-8;
type point=record
       x,y:double;
     end;

var a:array[0..50010] of point;
    q:array[0..50010] of longint;
    p:array[0..4] of point;
    n,f1,f2,h,r,t,k,i:longint;
    tmp,ans,d,l,l1,l2:double;

procedure swap(var a,b:point);
  var c:point;
  begin
    c:=a;
    a:=b;
    b:=c;
  end;

function cmp(a,b:point):boolean;
  begin
    if abs(a.y-b.y)<eps then exit(a.x<b.x);
    exit(a.y<b.y);
  end;

function cross(i,j,k,p:longint):double;
  begin
    exit((a[i].x-a[j].x)*(a[k].y-a[p].y)-(a[i].y-a[j].y)*(a[k].x-a[p].x));
  end;

procedure sort(l,r:longint);
  var i,j:longint;
      x:point;
  begin
    i:=l;
    j:=r;
    x:=a[(l+r) shr 1];
    repeat
      while cmp(a[i],x) do inc(i);
      while cmp(x,a[j]) do dec(j);
      if not(i>j) then
      begin
        swap(a[i],a[j]);
        inc(i);
        dec(j);
      end;
    until i>j;
    if l<j then sort(l,j);
    if i<r then sort(i,r);
  end;

function dis(a,b:point):double;
  begin
    exit(sqrt(sqr(a.x-b.x)+sqr(a.y-b.y)));
  end;

function mul(i,j,p,q:longint):double;
  begin
    exit((a[i].x-a[j].x)*(a[p].x-a[q].x)+(a[i].y-a[j].y)*(a[p].y-a[q].y));
  end;

begin
  readln(n);
  for i:=1 to n do
    readln(a[i].x,a[i].y);
  sort(1,n);
  ans:=1e15;
  t:=1;
  q[1]:=1;
  for i:=2 to n do
  begin
    while (t>1) and (cross(q[t],q[t-1],i,q[t-1])<eps) do dec(t);
    inc(t);
    q[t]:=i;
  end;
  k:=t;
  for i:=n-1 downto 1 do
  begin
    while (t>k) and (cross(q[t],q[t-1],i,q[t-1])<eps) do dec(t);
    inc(t);
    q[t]:=i;
  end;
//  q[t+1]:=q[1];
{  for i:=1 to t do
    writeln(a[q[i]].x,' ',a[q[i]].y);
  writeln(k); }
  k:=2;
  h:=2;
  r:=2;
  for i:=1 to t-1 do
  begin
    d:=dis(a[q[i]],a[q[i+1]]);
    while cross(q[i+1],q[i],q[k mod t+1],q[i])-cross(q[i+1],q[i],q[k],q[i])>-eps do k:=k mod t+1;
    while (mul(q[i+1],q[i],q[r mod t+1],q[i])-mul(q[i+1],q[i],q[r],q[i])>-eps) do r:=r mod t+1;
    if i=1 then h:=r;
    while (mul(q[i+1],q[i],q[h mod t+1],q[i])-mul(q[i+1],q[i],q[h],q[i])<eps) do h:=h mod t+1;
    l1:=mul(q[i+1],q[i],q[h],q[i])/d;
    l2:=mul(q[i+1],q[i],q[r],q[i])/d;
    l:=abs(cross(q[i+1],q[i],q[k],q[i]))/d;
    tmp:=(l2-l1)*l;
    if ans>tmp then
    begin
      ans:=tmp;
     // writeln(tmp,' ',a[q[i]].x,' ',a[q[i]].y,' ',l2/d);
      p[0].x:=a[q[i]].x+(a[q[i+1]].x-a[q[i]].x)*l2/d;
      p[0].y:=a[q[i]].y+(a[q[i+1]].y-a[q[i]].y)*l2/d;
     // writeln(p[0].x,' ',p[0].y);
      p[1].x:=p[0].x+(a[q[r]].x-p[0].x)*l/dis(p[0],a[q[r]]);
      p[1].y:=p[0].y+(a[q[r]].y-p[0].y)*l/dis(p[0],a[q[r]]);
      p[2].x:=p[1].x-(p[0].x-a[q[i]].x)*(l2-l1)/dis(p[0],a[q[i]]);
      p[2].y:=p[1].y-(p[0].y-a[q[i]].y)*(l2-l1)/dis(p[0],a[q[i]]);
      p[3].x:=p[2].x-(p[1].x-p[0].x);
      p[3].y:=p[2].y-(p[1].y-p[0].y);
    end;
  end;
  writeln(ans:0:5);
  h:=0;
  for i:=1 to 3 do
    if cmp(p[i],p[h]) then h:=i;
  for i:=0 to 3 do
    writeln(p[(h+i) mod 4].x:0:5,' ',p[(h+i) mod 4].y:0:5);
end.