TheAlgorithms-Python/project_euler/problem_032/sol32.py at master · windNight/TheAlgorithms-Python · GitHub

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"""

We shall say that an n-digit number is pandigital if it makes use of all the

digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through

5 pandigital.

The product 7254 is unusual, as the identity, 39 × 186 = 7254, containing

multiplicand, multiplier, and product is 1 through 9 pandigital.

Find the sum of all products whose multiplicand/multiplier/product identity can

be written as a 1 through 9 pandigital.

HINT: Some products can be obtained in more than one way so be sure to only

include it once in your sum.

"""

import itertools

def isCombinationValid(combination):

"""

Checks if a combination (a tuple of 9 digits)

is a valid product equation.

>>> isCombinationValid(('3', '9', '1', '8', '6', '7', '2', '5', '4'))

True

>>> isCombinationValid(('1', '2', '3', '4', '5', '6', '7', '8', '9'))

False

"""

return (

int("".join(combination[0:2])) * int("".join(combination[2:5]))

== int("".join(combination[5:9]))

) or (

int("".join(combination[0])) * int("".join(combination[1:5]))

== int("".join(combination[5:9]))

)

def solution():

"""

Finds the sum of all products whose multiplicand/multiplier/product identity

can be written as a 1 through 9 pandigital

>>> solution()

45228

"""

return sum(

{

int("".join(pandigital[5:9]))

for pandigital in itertools.permutations("123456789")

if isCombinationValid(pandigital)

}

)

if __name__ == "__main__":

print(solution())

TheAlgorithms-Python/project_euler/problem_032/sol32.py at master · windNight/TheAlgorithms-Python · GitHub

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