Project Euler Problem 29 Solution

Project Euler Problem 29 Solution

Distinct powers

by {BetaProjects} | Project Euler & HackerRank

Project Euler Problem 29 Statement

Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:

22=4, 23=8, 24=16, 25=32
32=9, 33=27, 34=81, 35=243
42=16, 43=64, 44=256, 45=1024
52=25, 53=125, 54=625, 55=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?

Solution

HackerRank version

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Solves all test cases for Hackerrank Project Euler Problem 29

HackerRank Project Euler 29 increases the limit to 2 ≤ a,b ≤ 105.

Python Source Code

N = int(input())
seen = [False]*(N+1)
s = 0
for a in range(2, N+1):
    if not seen[a]:
        b = 2 
        powers = set()
        while a**b <= N:
            seen[a**b] = True
            powers.update(p for p in range(2*b, N*b+1, b) if p > N)
            b+= 1
        s+=len(powers) + N-1
print(s)

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