Project Euler Solution 29: Distinct powers
Project Euler Problem 29: Distinct powers we have to work with large integers. This is trivial in Python, so this problem can be solved with a single line without any insights.
Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
$2^2=4, 2^3=8, 2^4=16, 2^5=32$
$3^2=9, 3^3=27, 3^4=81, 3^5=243$
$4^2=16, 4^3=64, 4^4=256, 4^5=1024$
$5^2=25, 5^3=125, 5^4=625, 5^5=3125$If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:
4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?
Well, we just construct all these numbers in a set comprehension and take the length of that set. That's it.
def solution() -> int: return len({a**b for a in range(2, 101) for b in range(2, 101)})
It takes 4.7 ms to compute. One might be able to be a bit more clever about the deduplication, though the time is still fast enough.