mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-10-06 21:59:30 +00:00
61 lines
1.6 KiB
Python
61 lines
1.6 KiB
Python
"""
|
||
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(
|
||
set(
|
||
[
|
||
int("".join(pandigital[5:9]))
|
||
for pandigital in itertools.permutations("123456789")
|
||
if isCombinationValid(pandigital)
|
||
]
|
||
)
|
||
)
|
||
|
||
|
||
if __name__ == "__main__":
|
||
print(solution())
|