#Android Unlock Patterns

#

#Given an Android 3x3 key lock screen and two integers m and n, where 1 ≤ m ≤ n ≤ 9, count the total number of unlock patterns of the Android lock screen, which consist of minimum of m keys and maximum n keys.

#

#Rules for a valid pattern:

#Each pattern must connect at least m keys and at most n keys.

#All the keys must be distinct.

#If the line connecting two consecutive keys in the pattern passes through any other keys, the other keys must have previously selected in the pattern. No jumps through non selected key is allowed.

#The order of keys used matters.

#

#Explanation:

#| 1 | 2 | 3 |

#| 4 | 5 | 6 |

#| 7 | 8 | 9 |

#Invalid move: 4 - 1 - 3 - 6

#Line 1 - 3 passes through key 2 which had not been selected in the pattern.

#

#Invalid move: 4 - 1 - 9 - 2

#Line 1 - 9 passes through key 5 which had not been selected in the pattern.

#

#Valid move: 2 - 4 - 1 - 3 - 6

#Line 1 - 3 is valid because it passes through key 2, which had been selected in the pattern

#

#Valid move: 6 - 5 - 4 - 1 - 9 - 2

#Line 1 - 9 is valid because it passes through key 5, which had been selected in the pattern.

#

#Example:

#Given m = 1, n = 1, return 9.

class Solution(object):

def __init__(self):

self.keyPad = [[1,2,3],[4,5,6],[7,8,9]]

self.directions = ["up", "down", "left", "right", "diagonal-up-left", "diagonal-up-right", "diagonal-down-left", "diagonal-down-right"]

self.totalPatterns = 0

def printCombination(self, combination):

for i in range(len(combination)):

r = combination[i][0]

c = combination[i][1]

print self.keyPad[r][c],

print "->",

print ""

#gives next move based on direction

def nextMove(self, direction, row, col):

if(direction == "up"):

return row-1, col

if(direction == "down"):

return row+1, col

if(direction == "left"):

return row, col-1

if(direction == "right"):

return row, col+1

if(direction == "diagonal-up-left"):

return row-1, col-1

if(direction == "diagonal-up-right"):

return row-1, col+1

if(direction == "diagonal-down-left"):

return row+1, col-1

if(direction == "diagonal-down-right"):

return row+1, col+1

#checks the bounds

def checkBounds(self, row, col):

if(row >= 0 and row < 3):

if(col >=0 and col <3):

return True

return False

#keys is the number of keys allowed to use

def countPatterns(self, keys, row, col, combination):

#return condition

if(keys == len(combination)):

self.totalPatterns = self.totalPatterns+1

self.printCombination(combination)

return

#for every current key we have 9 moves

for direction in self.directions:

#Get next move

n_row, n_col = self.nextMove(direction, row, col)

#check bounds

#check if its present in combination or not

while(self.checkBounds(n_row, n_col) and ([n_row, n_col] in combination)):

n_row, n_col = self.nextMove(direction, n_row, n_col)

if(self.checkBounds(n_row, n_col)):

#append this new row and col to combination

combination.append([n_row, n_col])

self.countPatterns(keys, n_row, n_col, combination)

combination.pop()

def numberOfPatterns(self, m, n):

for key in range(m, n+1):

for r in range(3):

for c in range(3):

self.countPatterns(key, r, c, [[r,c]])

print "Total Patterns = ",

print self.totalPatterns

#MainProgram

o = Solution()

o.numberOfPatterns(1,3)