from six.moves import map, range, reduce

"""
Explanation: The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?
<!-- TEASER_END -->
End of explanation
"""


n = \
73167176531330624919225119674426574742355349194934\
96983520312774506326239578318016984801869478851843\
85861560789112949495459501737958331952853208805511\
12540698747158523863050715693290963295227443043557\
66896648950445244523161731856403098711121722383113\
62229893423380308135336276614282806444486645238749\
30358907296290491560440772390713810515859307960866\
70172427121883998797908792274921901699720888093776\
65727333001053367881220235421809751254540594752243\
52584907711670556013604839586446706324415722155397\
53697817977846174064955149290862569321978468622482\
83972241375657056057490261407972968652414535100474\
82166370484403199890008895243450658541227588666881\
16427171479924442928230863465674813919123162824586\
17866458359124566529476545682848912883142607690042\
24219022671055626321111109370544217506941658960408\
07198403850962455444362981230987879927244284909188\
84580156166097919133875499200524063689912560717606\
05886116467109405077541002256983155200055935729725\
71636269561882670428252483600823257530420752963450

n

"""
Explanation: Version 1 - Sliding Window
Let's first set a variable to the number
End of explanation
"""


num_to_list = lambda n: list(map(int, list(str(n))))

"""
Explanation: Now let's form an array with elements representing the digits of the number.
End of explanation
"""


num_to_list(n)[:10]

"""
Explanation: This solution is kind of hacky and relies on specific characteristics of these Python built-in functions. Ideally, we'd build an array from the integer itself without all this type casting. But this will do for now.
End of explanation
"""


window = lambda lst, n: map(list, zip(*[lst[i:-n+i] for i in range(n)]))

"""
Explanation: Now we need to iterate over this array with some kind of sliding "window" of length $L=13$.
End of explanation
"""


pairwise = lambda lst: window(lst, 2)
[x+y for x, y in pairwise(range(10))]

list(window(num_to_list(n), 13))[:10]

prod = lambda iterable: reduce(lambda x, y: x*y, iterable)

"""
Explanation: Example: Partial function application and creating a list of odd numbers
End of explanation
"""


prod(range(1, 9))

list(map(prod, window(num_to_list(n), 13)))[:20]

max(map(prod, window(num_to_list(n), 13)))

max(map(prod, window(num_to_list(n), 4)))

"""
Explanation: Example: Compute $8!$
End of explanation
"""


from collections import Counter
Counter(map(prod, window(num_to_list(n), 13))).most_common(10)

"""
Explanation: Given the frequency of 0's when applying the sliding window, the next optimization to consider is skipping over windows containing at least one zero.
End of explanation
"""


