Project Euler: Problem 8

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

(see the number below)

Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?

Use NumPy for this computation



In [2]:

    
import numpy as np



In [3]:

    
d1000 = """
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
"""



In [8]:

    
def greatest_product(text):
    #Change text from str to int list
    new = list(text)
    for i in range(len(d1000)):
        if text[i] == "\n":
            new.remove("\n")
            i = 0
    #Put list into an array

    text_array = np.array(new, dtype=np.float)
    
    # Create variables for a 13 digit product
    a= 0
    b= 13
    
    #Initialize max value
    max_value = 0.0
    
    #While loop takes every adjacent 13 digit's product and compares to max_value
    while b <= len(text_array):
        if b < len(text_array) and text_array[a:b].cumprod()[-1] > max_value:
            max_value = text_array[a:b].cumprod()[-1]
            a += 1
            b += 1
            
        # a and b are incremented together to keep it a 13 digit product
        
        elif b == len(text) and text_array[a:].cumprod()[-1] > max_value:
            max_value = text_array[a:].cumprod()[-1]
        else:
            a += 1
            b += 1
    return max_value

greatest_product(d1000)



#Used ellisonbg's idea of a for loop to avoid storing all products









    Out[8]:





23514624000.0



In [ ]:

    
assert True # leave this for grading