1 ###############################################################
 2  #######                   AndrUlkComb.py              #########
 3  ## Calculate the COMBination count for ANDroid UNLock screen ##
 4  ##              By grepall@gmail.com                         ##
 5  ###############################################################
 6
 7
 8  ###############################################################
 9  ## The Android unlock screen looks like below
10  ## -------------------------------
11  ##       o  ->  o  ->  o
12  ##
13  ##       o      o      o
14  ##
15  ##       o      o      o
16  ## --------------------------------
17  ##
18  ## We'll use:
19  ##  1. Index from 0-8 to represent all 9 nodes instead of
20  ##      using row:column format.
21  ##  2. An array (routeList in the code) to record the path of the unlock combination.
22  ##      For example, for the unlock comb which is shown in
23  ##      in the figure. There will be 3 elements in the array:
24  ##      0, 1, and 2. (Although it's NOT a valid path because of
25  ##      not long enough)
26  ##
27  ## Valid unlock path must holds true for 3 conditions:
28  ##  C1: It must pass 4 different nodes at least;
29  ##  C2: It cannot contains duplicate nodes;
30  ##  C3: This is a little tricky. Any node cannot direct link to another node, when
31  ##      any node will be past through if we connect those 2 nodes in the unlock panel. UNLESS
32  ##      the crossed node already EXISTs in the path.
33  ##      For example, path (0, 2, 5, 4) is not valid, because 0-->2 crosses node 1. But path
34  ##      (1, 0, 2, 5) is a vliad path.
35  ##      This rule holds for diagonal as well.
36
37
38
39  #######################################################################
40  # M stands for the width of the unlock panel
41  # H stands for the height of the unlock panel
42  # CAUTION: Modify this value will NOT generate correct result!!! That's TO BE DONE
43  #
44  W = 3   #Width
45  H = 3   #Height
46
47  # Unlock path
48  routeList = list()
49
50  # Combination count, which is we want to know
51  routeCount = 0
52
53
54
55  def isValidRoute(p1, route):
56      # If the candidate node exists in the unlock path
57      if route.count(p1) != 0:
58          return False
59      return True;
60
61
62  def isCrossPoint(p1, p2):
63      # Will the connection line (p1, p2) cross another node?
64      x1 = p1%W
65      y1 = p1/W
66      x2 = p2%W
67      y2 = p2/W
68      if x1 == x2 and abs(y1-y2) > 1:
69          return True # same column
70      if y1 == y2 and abs(x1-x2) > 1:
71          return True # same row
72      if abs(y1-y2) == abs(x1-x2) and abs(y1-y2)>1:
73          return True # diagonal
74      return False
75
76  def tryPoint(lastPt, route):
77      # Try next valid node for the unlock path recursively
78      global routeCount
79      for pt in range(0, W*H):
80          if isValidRoute(pt, route): #C2
81              crossPt = (lastPt+pt)/2
82              if isCrossPoint(lastPt, pt) and route.count(crossPt) == 0: #C3
83                  continue
84              route.append(pt)
85              if len(route) >3: #C1
86                  routeCount += 1
87              tryPoint(pt, route)
88              route.pop()
89
90
91  # Each node may be the start node for unlock
92  for i in range(0, W*H):
93      routeList = [i]
94      tryPoint(i, routeList)
95      print "Start from point %d, combination count is %d now..." % (i, routeCount)
96  print "Toatl combination counter for Android unlock screen: " + str(routeCount)