start on enumerating all state combinations

examples/tictactoe.py

 # -*- coding: utf-8 -*-
 
-import mdp
+#import mdp
 
 class TicTacToeMDP(object):
     """"""
          
     def __init__(self):
         """"""
-        pass
+        self.P = {}
+        self.R = {}
+        # some board states are equal, just rotations of other states
+        self.rotorder = []
+        #self.rotorder.append([0, 1, 2, 3, 4, 5, 6, 7, 8])
+        self.rotorder.append([6, 3, 0, 7, 4, 1, 8, 5, 2])
+        self.rotorder.append([8, 7, 6, 5, 4, 3, 2, 1, 0])
+        self.rotorder.append([2, 5, 8, 1, 4, 7, 0, 3, 6])
+    
+    def rotate(self, state):
+        rotations = []
+        identity = []
+        rotations.append(state)
+        identity.append(int("".join(str(x) for x in state), 3))
+        for k in range(3):
+            rotations.append(tuple([state[self.rotorder[k][kk]]
+                                      for kk in xrange(9)]))
+            # Convert the state from base 3 number to integer.
+            identity.append(int("".join(str(x) for x in rotations[k + 1]), 3))
+        # return the rotation with the smallest identity number
+        idx = identity.index(min(identity))
+        return (identity[idx], rotations[idx])
+    
+    def unrotate(self, move, rotation):
+        rotation -= 1
+        # return the move
+        return self.rotorder[rotation][move]
     
     def isLegal(state, action):
         """"""
@@ -28,7 +54,8 @@ class TicTacToeMDP(object):
                 [0, 0, 1, 0, 1, 0, 1, 0, 0])
         # Check to see if there are any wins
         for w in wins:
-            S = sum([1 if (w[k] == 1 and state[k] == 1) else 0 for k in xrange(9)])
+            S = sum([1 if (w[k] == 1 and state[k] == 1) else 0
+                     for k in xrange(9)])
             if S == 3:
                 # We have a win
                 return True
@@ -47,8 +74,33 @@ class TicTacToeMDP(object):
     
     def run(self):
         """"""
-        pass
-     
+        nXO = ((0, 0),
+               (1, 1),
+               (2, 2),
+               (3, 3),
+               (4, 4),
+               (0, 1),
+               (1, 2),
+               (2, 3),
+               (3, 4))
+        #
+        # return (P, R)
+    
+    def transition(self, s):
+        """"""
+        idn_s = int("".join(str(x) for x in s), 3)
+        legal_a = [a for a in xrange(9) if s[a] == 0]
+        for a1 in legal_a:
+            s[a1] = 1
+            legal_m = [a for a in xrange(9) if s[a] == 0]
+            for m1 in legal_m:
+                s_new = s
+                s_new[m1] = 2
+                idn_s_new, s_new = self.rotate(s_new)
+                if self.P.has_key((idn_s, idn_s_new)):
+                    raise Exception("unexpected, P already has Pr(s,s')")
+                else:
+                    self.P[(idn_s, idn_s_new)] = 1 / len(legal_m)
 
 if __name__ == "__main__":
     P, R = TicTacToeMDP().run()