Tricky test case (even can't find its analogue). It contains such placement of draughts that you should precisely touch one or several other draughts by your move, and almost identical angles (+/- 1e-8 radians) will not give correct answer. When allow precisely touch got AC.

P.S.
Seems like one enemy draught you touch on the left side and other one - on the right side simultaneously.

Edited by author 23.04.2023 18:44

New tricky tests have been added to the problem.
All solutions have been rejudged. 152 authors (62% of all) lost their solved status for the problem.

If you get WA 30 check this:

1) correct calculation of tangent line angle (asin(2R/D), NOT asin(R/D))
2) check not only enemies circles to make your movement, but angles to your own circles too. You can destroy your circles and win by this angle (don't forget about this).

These tests helped me:

Test 1:
7.100 2.280 3.530 4.410 2.690 2.990 1.770 4.360 5.850 1.770 1.960 1.720 6.550 1.870 2.200 4.940
4.090 0.920 6.580 3.590 1.970 1.070 2.390 2.700 0.360 4.030 1.520 6.730 5.820 5.280 1.640 5.520
Answer: WHITE

Test 2:
2.670 6.880 2.140 2.820 0.830 6.960 2.180 4.600 6.220 7.170 7.130 1.290 3.010 6.320 2.880 4.690
0.350 6.670 6.680 5.820 7.230 5.020 7.160 4.100 0.120 0.430 2.950 7.780 5.630 2.400 2.290 1.310
Answer: RED

Edited by author 06.01.2023 21:45

Hint: ->, not <->

Rot13: Gur qenhtug bayl zbirf sbejneq jura chfurq, abg ovqverpgvbanyyl.

0.5 7.5 1.5 5.5 5.5 6.5 2.5 3.5 6.5 4.5 1.5 7.5 7.5 2.5 2.5 4.5
3.5 5.5 6.5 0.5 4.5 1.5 0.5 5.5 1.5 4.5 0.5 2.5 0.5 0.5 4.5 7.5

5.5 6.5 1.5 2.5 1.5 3.5 4.5 1.5 3.5 4.5 5.5 4.5 4.5 0.5 7.5 0.5
5.5 7.5 3.5 1.5 0.5 2.5 6.5 5.5 7.5 1.5 4.5 6.5 7.5 7.5 2.5 1.5

1.5 4.5 3.5 2.5 2.5 0.5 6.5 4.5 7.5 6.5 1.5 2.5 6.5 5.5 6.5 1.5
6.5 7.5 0.5 3.5 3.5 4.5 1.5 0.5 6.5 0.5 2.5 2.5 1.5 5.5 5.5 5.5

I have 4 AC solutions. Sets of answers to these tests are quite different =)

First of all, precision of 1e-8 is ok to get AC (with double type and without trigonometry).

Now about WA16 - that's the case when one of boundary rays is parallel to OX. When some angular segments crosses OX, I perform a split at 0/2PI point. In described case it was possible that I first delete a draught at point 0 and then add it. So, sorting should be not just angular, but also additions should precede deletions. This condition is automatic for regular cases, so I omitted it. But in described case special care should be taken.

Are there any tangential draughts in the input?
And when a draught during its movement gets just tangential with another draught, is the latter considered to be killed?

If both answers are yes: suppose there are two tangential draughts in the input (one left and one right), now I shoot the right one to the right, is the left one considered to be killed?

I have got WA on #22.

If one checker touches another initially, what should I do?

I use minimax and alpha-beta cutting off.

I get AC with this program. But it's wrong! Please give me some hints
to solve this problem or Accepted program (not as my) :-))

{$A-,B-,D+,E+,F-,G-,I-,L+,N+,O-,P-,Q-,R-,S-,T-,V-,X-}
Program t1163;

Const  Radius = 0.4;
       Change = Pi/180;
       N      = 8;
       L      = 8;
       Eps    = 1E-5;

Type Point  = record X,Y : extended end;
     Vector = record rX,rY : extended end;
     IMas   = array[1..N]of byte;

Var  R,W           : array[1..N]of Point;
     Ru,Wu         : IMas;
     i             : integer;
     count         : integer;

Function GetW(A : Vector) : extended;
Var tgW,W  : extended;
 begin
  if abs(A.rX)=0 then begin
    if A.rY<0 then W:=270 else W:=90;
   end else
  if abs(A.rY)=0 then begin
    if A.rX<0 then W:=180 else W:=0;
   end else begin
    tgW:=Abs(A.rY/A.rX);
    W:=ArcTan(tgW); W:=W/Change;
    if (A.rX<0)and(A.rY>0) then W:=180-W;
    if (A.rX<0)and(A.rY<0) then W:=180+W;
    if (A.rX>0)and(A.rY<0) then W:=360-W;
   end;
  GetW:=W;
 end;

Function GetWT(a,b,c : extended) : extended;
Var cosw,sinw,tgw,w   : extended;
 begin
  cosw:=(b*b+c*c-a*a)/(2*b*c);
  sinw:=sqrt(abs(1-cosw*cosw));
  if abs(cosw)<Eps then
   w:=90
  else begin
   tgw:=sinw/cosw;
   w:=ArcTan(tgw);
   w:=w/Change;
  end;
  GetWT:=w;
 end;

Function Dist(A,B : Point) : extended;
 begin
  Dist:=sqrt(sqr(A.X-B.X)+sqr(A.Y-B.Y));
 end;

Function Touch(begP,tP : Point; wF : extended) : boolean;
Var TVector      : Vector;
    w,aw,d,dp    : extended;
 begin
  TVector.rX:=begP.X-tP.X;
  TVector.rY:=begP.Y-tP.Y;
  w:=GetW(TVector);
  aw:=abs(w-wF);
  if aw>180 then aw:=360-aw;
  aw:=aw*Change;
  dp:=Dist(begP,tP);
  d:=sqrt(2*dp*dp*(1-cos(aw)));
  Touch:= d<=2*Radius;
 end;

Function WinGR : boolean; forward;
Function WinGW : boolean; forward;

Function WinGW : boolean;
var i,j      : integer;
    u,v,vv   : integer;
    wh1,re1  : integer;
    A        : Vector;
    w1,dw,d  : extended;
    wFLICK   : extended;
    Tr,Tw    : IMas;
    ok       : byte;
    pp       : array[1..2*n*n]of IMas;
 begin
  inc(count);
// SEE AT THIS
// IF COUNT>10000 I
//   WRITE
//  'RED' !!
//
  if count>100000 then begin
    Writeln('RED');
    Halt;
   end;
  vv:=0;
  for i:=1 to N do if Wu[i]=0 then
   for j:=N downto 1 do if Ru[j]=0 then begin
    A.rx:=W[i].X-R[j].X;
    A.ry:=W[i].Y-R[j].Y;
    w1:=GetW(A);
    d:=Dist(W[i],R[j]);
    dw:=GetWT(2*Radius,d,d);
    Wu[i]:=1;
    Tr:=Ru; Tw:=Wu;
    {go down}
    wFLICK:=w1-dw; if wFLICK<0 then wFLICK:=wFLICK+360;
    wh1:=0; re1:=0;
    for u:=1 to N do if Wu[u]=0 then if Touch(W[i],W[u],wFLICK) then
begin Wu[u]:=1; inc(wh1); end;
    for u:=1 to N do if Ru[u]=0 then if Touch(W[i],R[u],wFLICK) then
begin Ru[u]:=1; inc(re1); end;
    ok:=1;
    for u:=1 to vv do begin
      ok:=0;
      for v:=1 to 8 do if pp[u][v]<ru[v] then ok:=1;
      if ok=1 then break;
     end;
    if wh1<re1 then
    if ok=1 then begin
     inc(vv);
     for u:=1 to 8 do pp[vv][u]:=ru[u];
    if not(WinGR) then begin
      WinGW:=true;
      Wu[i]:=0;
      exit;
     end;
    end;
    Ru:=Tr; Wu:=Tw;
    {go up}
    wFLICK:=w1+dw; if wFLICK>360 then wFLICK:=wFLICK-360;
    wh1:=0; re1:=0;
    for u:=1 to N do if Wu[u]=0 then if Touch(W[i],W[u],wFLICK) then
begin Wu[u]:=1; inc(wh1); end;
    for u:=1 to N do if Ru[u]=0 then if Touch(W[i],R[u],wFLICK) then
begin Ru[u]:=1; inc(re1); end;
    ok:=1;
    for u:=1 to vv do begin
      ok:=0;
      for v:=1 to 8 do if pp[u][v]<ru[v] then ok:=1;
      if ok=1 then break;
     end;
    if ok=1 then begin
     inc(vv);
     for u:=1 to 8 do pp[vv][u]:=ru[u];
    if wh1<re1 then
    if not(WinGR) then begin
      WinGW:=true;
      Wu[i]:=0;
      exit;
     end;
    end;
    Ru:=Tr; Wu:=Tw;