Project Euler: Problem 29 – Distinct powers

Problem 29:

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?

Idea:

Generating the numbers is easy with the BigInteger class. As for not counting duplicates, I just chose a data type that doesn’t allow for duplicates. Some wasted computations (on the duplicates and adding them to the set), but much easier to follow and understand.

int answer = -1;

Set<BigInteger> terms = new HashSet<BigInteger>();

for(int i = 2; i <= 100; i++) {
   BigInteger base = BigInteger.valueOf(i);
   for(int j = 2; j <= 100; j++) {
      terms.add(base.pow(j));
   }
}

answer = terms.size();

System.out.println("Answer: "+answer);
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