LEM1 - COIN

Tác giả: flashmt

Ngôn ngữ: Pascal

const fi='';
      fo='';
      maxn=10005;
      ep=0.000000001;
      pi2=6.283185307;
var n:longint;
    a:array[1..maxn] of real;
    re:real;

procedure rf;
var i:longint;
begin
     assign(input,fi); reset(input);
     readln(n);
     for i:=1 to n do read(a[i]);
     close(input);
end;

function calc(x:real):longint;
var i,z:longint; goc,cosin,tg,b,c,d:real;
begin
     goc:=0;
     for i:=1 to n do
     begin
          z:=i+1;
          if z=n+1 then z:=1;
          b:=x+a[i]; c:=x+a[z]; d:=a[i]+a[z];
          cosin:=(b*b+c*c-d*d)/(2*b*c);
          tg:=sqrt((1-sqr(cosin))/sqr(cosin));
          if cosin>=0 then goc:=goc+arctan(tg)
          else goc:=goc+pi2/2-arctan(tg);
     end;
     if abs(goc-pi2)<=ep then calc:=0
     else
         if goc>pi2 then calc:=1
         else calc:=-1;
end;

procedure pr;
var l,m,r:real; t:longint;
begin
     l:=0; r:=1000000000000000000000000;
     while r-l>=ep do
     begin
          m:=(l+r)/2;
          t:=calc(m);
          if t=0 then break;
          if t>0 then l:=m
          else r:=m;
     end;
     re:=m;
end;

procedure wf;
begin
     assign(output,fo); rewrite(output);
     writeln(re:0:3);
     close(output);
end;

begin
     rf;
     pr;
     wf;
end.

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