Project Euler: Problem 8

https://projecteuler.net/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 [1]:
import numpy as np

In [20]:
d1000 = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450"

In [22]:
# YOUR CODE HERE
d = np.array(range(1000))
for x in range(1000):
    d[x] = d1000[x]
print(d)


[7 3 1 6 7 1 7 6 5 3 1 3 3 0 6 2 4 9 1 9 2 2 5 1 1 9 6 7 4 4 2 6 5 7 4 7 4
 2 3 5 5 3 4 9 1 9 4 9 3 4 9 6 9 8 3 5 2 0 3 1 2 7 7 4 5 0 6 3 2 6 2 3 9 5
 7 8 3 1 8 0 1 6 9 8 4 8 0 1 8 6 9 4 7 8 8 5 1 8 4 3 8 5 8 6 1 5 6 0 7 8 9
 1 1 2 9 4 9 4 9 5 4 5 9 5 0 1 7 3 7 9 5 8 3 3 1 9 5 2 8 5 3 2 0 8 8 0 5 5
 1 1 1 2 5 4 0 6 9 8 7 4 7 1 5 8 5 2 3 8 6 3 0 5 0 7 1 5 6 9 3 2 9 0 9 6 3
 2 9 5 2 2 7 4 4 3 0 4 3 5 5 7 6 6 8 9 6 6 4 8 9 5 0 4 4 5 2 4 4 5 2 3 1 6
 1 7 3 1 8 5 6 4 0 3 0 9 8 7 1 1 1 2 1 7 2 2 3 8 3 1 1 3 6 2 2 2 9 8 9 3 4
 2 3 3 8 0 3 0 8 1 3 5 3 3 6 2 7 6 6 1 4 2 8 2 8 0 6 4 4 4 4 8 6 6 4 5 2 3
 8 7 4 9 3 0 3 5 8 9 0 7 2 9 6 2 9 0 4 9 1 5 6 0 4 4 0 7 7 2 3 9 0 7 1 3 8
 1 0 5 1 5 8 5 9 3 0 7 9 6 0 8 6 6 7 0 1 7 2 4 2 7 1 2 1 8 8 3 9 9 8 7 9 7
 9 0 8 7 9 2 2 7 4 9 2 1 9 0 1 6 9 9 7 2 0 8 8 8 0 9 3 7 7 6 6 5 7 2 7 3 3
 3 0 0 1 0 5 3 3 6 7 8 8 1 2 2 0 2 3 5 4 2 1 8 0 9 7 5 1 2 5 4 5 4 0 5 9 4
 7 5 2 2 4 3 5 2 5 8 4 9 0 7 7 1 1 6 7 0 5 5 6 0 1 3 6 0 4 8 3 9 5 8 6 4 4
 6 7 0 6 3 2 4 4 1 5 7 2 2 1 5 5 3 9 7 5 3 6 9 7 8 1 7 9 7 7 8 4 6 1 7 4 0
 6 4 9 5 5 1 4 9 2 9 0 8 6 2 5 6 9 3 2 1 9 7 8 4 6 8 6 2 2 4 8 2 8 3 9 7 2
 2 4 1 3 7 5 6 5 7 0 5 6 0 5 7 4 9 0 2 6 1 4 0 7 9 7 2 9 6 8 6 5 2 4 1 4 5
 3 5 1 0 0 4 7 4 8 2 1 6 6 3 7 0 4 8 4 4 0 3 1 9 9 8 9 0 0 0 8 8 9 5 2 4 3
 4 5 0 6 5 8 5 4 1 2 2 7 5 8 8 6 6 6 8 8 1 1 6 4 2 7 1 7 1 4 7 9 9 2 4 4 4
 2 9 2 8 2 3 0 8 6 3 4 6 5 6 7 4 8 1 3 9 1 9 1 2 3 1 6 2 8 2 4 5 8 6 1 7 8
 6 6 4 5 8 3 5 9 1 2 4 5 6 6 5 2 9 4 7 6 5 4 5 6 8 2 8 4 8 9 1 2 8 8 3 1 4
 2 6 0 7 6 9 0 0 4 2 2 4 2 1 9 0 2 2 6 7 1 0 5 5 6 2 6 3 2 1 1 1 1 1 0 9 3
 7 0 5 4 4 2 1 7 5 0 6 9 4 1 6 5 8 9 6 0 4 0 8 0 7 1 9 8 4 0 3 8 5 0 9 6 2
 4 5 5 4 4 4 3 6 2 9 8 1 2 3 0 9 8 7 8 7 9 9 2 7 2 4 4 2 8 4 9 0 9 1 8 8 8
 4 5 8 0 1 5 6 1 6 6 0 9 7 9 1 9 1 3 3 8 7 5 4 9 9 2 0 0 5 2 4 0 6 3 6 8 9
 9 1 2 5 6 0 7 1 7 6 0 6 0 5 8 8 6 1 1 6 4 6 7 1 0 9 4 0 5 0 7 7 5 4 1 0 0
 2 2 5 6 9 8 3 1 5 5 2 0 0 0 5 5 9 3 5 7 2 9 7 2 5 7 1 6 3 6 2 6 9 5 6 1 8
 8 2 6 7 0 4 2 8 2 5 2 4 8 3 6 0 0 8 2 3 2 5 7 5 3 0 4 2 0 7 5 2 9 6 3 4 5
 0]

In [32]:
def mult_thirteen(lst):
    prod = np.array(range(1000-12))
    for a in range(len(lst)-13):
        x=1
        for b in range(a,a+13):
             x *= lst[b]
        prod[a] = x
    return prod

In [34]:
products = mult_thirteen(d)
ind = np.argmax(products)
print(d[ind:ind+13])
print(products.max())


[7 3 1 6 7 1 7 6 5 3 1 3 3]
23514624000

In [7]:
assert True # leave this for grading