hello codeforces,

I have come here to ask help to dp experts. I will highly appreciate it if you can help solve this dilemma. I have been struggling with this for a while now.

THe problem can be found here.

http://mirror.codeforces.com/contest/69/problem/D

Now i am not working on a general solution. My algorithm is just for the first test case and i am confused why the result is "Anton loses" when the correct answer is "Anton wins". I have stepped through the logic of my DP formulation and i dont seem to spot the fallacy. So, can you please point out the point where my logic fails. I will highly appreciate it. Thanks for your time. I have commented out parts of my code for legibility.

import math


#For the following test case
#0 0 2 3
#1 1
#1 2
#
#
#x --> x coordinate
#y --> y coordinate
#t --> if t == True then Anton turn, if t == False then Dasha turn
#fs --> if first player or Anton has swapped, since only 1 swap is possible
#ss --> if second player or Dasha has swapped, since only 1 swap is possible


def canWin(x, y, t, fs, ss):

  if math.sqrt(float(x)*float(x) + float(y)*float(y)) > 3:
    return False

	
  if t == False and ss == False:  #if Dasha turn and if dasha hasnt swapped then can swap 1 time
    return (not (canWin(x + 1, y + 1, not t, fs, ss))) and (not canWin(x + 1, y + 2, not t, fs, ss)) and (not canWin(y, x, not t, fs, True))
  elif t == True and fs == False: #if Anton turn and if Anton hasnt swapped then can swap 1 time
    return (not (canWin(x + 1, y + 1, not t, fs, ss))) and (not canWin(x + 1, y + 2, not t, fs, ss)) and (not canWin(y, x, not t, True, ss))
  else: #since both has swapped 1 time now cannot swap further
    return (not (canWin(x + 1, y + 1, not t, fs, ss))) and (not canWin(x + 1, y + 2, not t, fs, ss))
    

print canWin(0, 0, True, False, False)

#Expected result was True since Anton wins but the result is False

Also, please note that i have removed the memoization part for now as to make the code short and easy to understand so i guess this is not a dp solution. But i am just trying to find the fallacy in my recurrence formula. Thanks!