pe8.py

############################################################################################################################
#
# Problem 8
#
# The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.
#
# Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. 
# What is the value of this product?
#
# Ans: 23514624000
############################################################################################################################
from typing import Optional


def toProduct(nums: Optional) -> int:
    '''
    Parameters
    ----------
    nums : Optional
        An iterable collection of integers. e.g. '123', [1, 2, 3], 
        ['1', '2', '3'],  {1, 2, 3}. 
    Returns
    -------
    int
        The product of all input elements.
    '''
    prod = 1           # identity element
    for i in nums:
        prod *= int(i) # convert str to int
    return prod 

def adjacentProduct(n: int, num_str: str) -> int:
    '''
    Args:
        n (int): the window of digits to consider
        
    Returns:
        (int): The four adjacent digits in num that have the 
               greatest product
    '''
    # A generator of all the subsets of n adjacent digits in num 
    subsets = (num_str[i:i+n] for i in range(len(num_str)))
    
    # A generator of all the products of the adjacent digits
    x = (toProduct(subset) for subset in subsets)
    return max(x)


if __name__ == "__main__":
    num_str = '7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450'
    print(adjacentProduct(13, num_str))