Q8: LargestProduct

"""
Created on Sun May  6 22:50:24 2018

@author: Liv d'Aliberti
"""

#The four adjacent digits in the 1000-digit number that have the greatest 
#product are 9 × 9 × 8 × 9 = 5832.

large_number = """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?

large_number = large_number.replace("\n", "")
def flatten(nested_list):
    """
    Purpose: take nested lists of numbers and make a "flattened list
    that returns a list of all the elements in each of the inner lists
    Input: A list of lists (nested_list)
    Output: A new list of all elements in each of the inner lists of
    nested_list. (new_list)
    Rule: make sure the nested_list remains unchanged
    """
    new_list = []
    #new_list = []
    for i in nested_list:
        #print(i)
        for j in i:
            #print(j)
            new_list.append(j)
    #print(nested_list)
    return(new_list)
    
def greatest_product(large_number):
    """
    Input: String
    Output: Integer
    Purpose: Input the string of a very large number, and output
    the largest product of the sum of 13 adjacent digits in this
    very large number
    """
    n = 13
    j = 0
    solution_list = []
    multiplied_number = 1
    numbers_dictionary = {}
    max_number = 0
    
    #This code creates the potential solution set
    while j < 13:
        solution_list.append([large_number[i:i+n] 
        for i in range(j,len(large_number),n) ])
        j = j + 1
    
    solution_list = flatten(solution_list)
    
    for i in solution_list:
        if len(i) != 13:
            solution_list.remove(i)
    
    solution_set = set(solution_list)
    
    #This code creates a dictionary with all of the
    #multiplied possibilities
    for numbers in solution_set:

        for number in numbers:
            number = int(number)
            multiplied_number = number * multiplied_number
            #print(multiplied_number)
        numbers_dictionary[numbers] = multiplied_number
        multiplied_number = 1
        
    #This code finds the largest multipied solution from
    #the set of solutions
    for i in numbers_dictionary:
        if numbers_dictionary[i] > max_number:
            max_number = numbers_dictionary[i]
    return(max_number)

#For this particular problem, the solution is 23514624000