Finding the maximum product from 13 contiguous digits in 10,000 digit numbers

Question

Unable to understand what happened to my code (Project Euler 8 problem). I want to find the maximum product of 13 adjacent digits in the decimal digit below, and I get the wrong answer.

my_list = list('7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450')

for i in range(1000):
    my_list[i] = int(my_list[i])

previous_product = 1
for x in range(13):
  previous_product *= my_list[x]
current_product = previous_product*my_list[13]/my_list[0]

for i in range(1, 987):
  if current_product > previous_product:
    maximum_product = current_product
  previous_product = current_product
  if my_list[i]==0:
    current_product = 1
    for x in range(13):
      current_product *= my_list[i+x+1]
  else:
    current_product = previous_product*my_list[i+x+1]/my_list[i]

print(maximum_product)

Edit: Solved! maximum_product was not defined correctly ... it takes on the value of the most recent "current product", which turned out to be higher than the previous product, and not the largest product.

The correct, though not super-efficient code:

   my_list = list('7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450')

for i in range(1000):
    my_list[i] = int(my_list[i])

previous_product = 1
for x in range(13):
  previous_product *= my_list[x]
current_product = previous_product*my_list[13]/my_list[0]

large_products = []

for i in range(1, 987):
  if current_product > previous_product:
    large_products.append(current_product)
  previous_product = current_product
  if my_list[i]==0:
    current_product = 1
    for x in range(13):
      current_product *= my_list[i+x+1]
  else:
    current_product = previous_product*my_list[i+x+1]/my_list[i]

print(max(large_products))

Answer 1

I have not tested why your approach does not work, but you can easily solve this with:

import operator
from functools import reduce

my_int_list = [int(char) for char in my_list]

max(map(lambda *x: reduce(operator.mul, x), 
        my_int_list[0:], 
        my_int_list[1:], 
        my_int_list[2:], 
        my_int_list[3:], 
        my_int_list[4:], 
        my_int_list[5:], 
        my_int_list[6:], 
        my_int_list[7:], 
        my_int_list[8:], 
        my_int_list[9:], 
        my_int_list[10:], 
        my_int_list[11:], 
        my_int_list[12:]))

, , itertools.islice [idx:].

Answer 2

, , , :

def max_product(s,k):
    s = [int(d) for d in s]
    p = 1
    for d in s[:k]:
        p *= d
    m = p
    for i,d in enumerate(s[k:]):
        p *= d
        p //= s[i]
        if p > m: m = p
    return p

s k (k = 13 ). k . . enumerate on s[k:], i 0 - , .

data = '7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450'

, 13 :

chunks = [s for s in data.split('0') if len(s) >= 13]

24 . , :

print(max(max_product(s,13) for s in chunks))

23514624000

Answer 3

, , -, - , , , . .

, : 7316717. 3 . . , Python .

• 3- :

  seqs = [731, 316, 167, 671, 717]
  

• :

  products = [21, 18, 42, 42, 49]
  

• .

  answer = max(products)
  

Answer 4

.

But an easy way to solve your problem is to generate all possible fragments with 13 adjacent numbers from your input data, then find the product of their elements, and then find the maximum product from them.

Here's how to do it:

data = '7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450'

def product(a):
    prod = 1
    for k in a:
        prod *= int(k)
    return prod

def max_adjacent_number(data, suit=13):
    return max(product(data[k:k+suit]) for k in range(len(data)) if '0' not in data[k:k+suit])


from time import time
start = time()
val = max_adjacent_number(data)
elapsed = time() - start
print("Solution: {0} \telapsed: {1:.5f}ms".format(val, elapsed*1000))

Conclusion:

# Best time
Solution: 23514624000   elapsed: 1.31226ms

Answer 5

You can improve code performance by using list comprehension as follows:

import time
n = str(x) #x is the long number
a = time.time()
result = max(reduce(lambda x, y: x * y, map(int, n[i:i+13])) for i in xrange(len(n)-12) if '0' not in n[i:i+13])
b = time.time()
print "Maximum adjacent numbers product: %d" % result
print "Time taken:", (b-a)*1000, "ms"

Conclusion:

Maximum adjacent numbers product: 23514624000
Time taken: 4.34899330139 ms