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Euler8.py
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Euler8.py
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# -*- coding: utf-8 -*-
"""
Largest product in a series
Problem 8
The four adjacent digits in the 1000-digit number that have the greatest
product are 9 × 9 × 8 × 9 = 5832.
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
Find the thirteen adjacent digits in the 1000-digit number that have the
greatest product. What is the value of this product?
Math solution:
The product of 13 numbers is maximized when the sum is maximized. Storing sums
requires less memory than products, so we compute the sum instead of product.
Answer: 5377010688
Ricky Kwok, [email protected], 2014-10-15
"""
import re
def get_max_product13(number):
pattern = re.compile(r"[1-9]+0 |[1-9]+\n", re.X)
nums = re.findall(pattern, number)
max_sum, digits13, max_prod, num13, = 0, 0, 1, []
for num in nums:
if len(num) > 13:
num = num[:len(num)-1] # exclude 0 or \n
num13.append(num) # add consecutive digits of at least
# 13 to num13
for num in num13:
""" Finds the 13 adjacent digits with the maximum sum """
for i in range(len(num)-12):
# iterate through all possible 13 adjacent numbers of num
num_sum = 0
for c in num[i:i+13]:
# add up the digits of those 13 numbers
num_sum += int(c)
if max_sum < num_sum:
max_sum = num_sum
digits13 = num[i:i+13]
for k in digits13:
max_prod *= int(k)
return max_prod
def main():
number = """73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450 """
max_prod = get_max_product13(number)
print max_prod
if __name__ == "__main__":
main()