328 http://inventwithpython.com/hacking

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54. 
    


55. 
    


56. def getUsefulFactors(num):


57. 
    

    Returns a list of useful factors of num. By "useful" we mean factors

    
    


58. 
    

    less than MAX_KEY_LENGTH + 1. For example, getUsefulFactors(144)

    
    


59. 
    

    returns [2, 72, 3, 48, 4, 36, 6, 24, 8, 18, 9, 16, 12]

    
    


60. 
    


61. if num < 2:


62. return [] # numbers less than 2 have no useful factors


63. 
    


64. factors = [] # the list of factors found


65. 
    


66. 
    

    When finding factors, you only need to check the integers up to

    
    


67. 
    

    MAX_KEY_LENGTH.

    
    


68. for i in range(2, MAX_KEY_LENGTH + 1): # don't test 1


69. if num % i == 0:


70. factors.append(i)


71. factors.append(int(num / i))


72. if 1 in factors:


73. factors.remove(1)


74. return list(set(factors))


75. 
    


76. 
    


77. def getItemAtIndexOne(x):


78. return x[1]


79. 
    


80. 
    


81. def getMostCommonFactors(seqFactors):


82. 
    

    First, get a count of how many times a factor occurs in seqFactors.

    
    


83. factorCounts = {} # key is a factor, value is how often if occurs


84. 
    


85. 
    

    seqFactors keys are sequences, values are lists of factors of the

    
    


86. 
    

    spacings. seqFactors has a value like: {'GFD': [2, 3, 4, 6, 9, 12,

    
    


87. 
    

    18, 23, 36, 46, 69, 92, 138, 207], 'ALW': [2, 3, 4, 6, ...], ...}

    
    


88. for seq in seqFactors:


89. factorList = seqFactors[seq]


90. for factor in factorList:


91. if factor not in factorCounts:


92. factorCounts[factor] = 0


93. factorCounts[factor] += 1


94. 
    


95. 
    

    Second, put the factor and its count into a tuple, and make a list

    
    


96. 
    

    of these tuples so we can sort them.

    
    


97. factorsByCount = []


98. for factor in factorCounts:


99. 
    

    exclude factors larger than MAX_KEY_LENGTH