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 [105]:

    
import numpy as np



In [106]:

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









    



  File "<ipython-input-106-443acf66f1e4>", line 1
    d1000=
          ^
SyntaxError: invalid syntax



In [107]:

    
num = 7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450



In [108]:

    
# YOUR CODE HERE
#raise NotImplementedError()
#Returns greatest product of 13 adjacent digits in d1000
def max_mult(number):
    w=[]
    y=[]
    z=[]
    #creates 1-D array full of 1000 zeros
    x = np.zeros(1000)
    s=0
    for i in str(number):
        #replaces every zero in x with corresponding digit in d1000
        x[s]= float(i)
        #appends arrays, each consisting of 13 adjacent digits, to y
        #loop allows for all possibilities
        a=x[s:s+13]
        y.append(a)
        s+=1 
    #makes new arrays from cumulative sum of each array in y
    #appends new arrays to z
    for j in y:
        b = j.cumprod()
        z.append(b)
    #takes max of each array in z and appends it to w
    for l in z:
        w.append(max(l))
    #w now consists of the products of all possible 13 adjacent digits in d1000
    return (int(max(w)))



In [109]:

    
max_mult(num)









    Out[109]:





23514624000



In [110]:

    
assert True # leave this for grading