Problem 29: Distinct Powers
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?
The Catch
How to store found terms and filter out duplicates so that all terms are distinct.
The Light
In mathematics, a set is a collection of distinct objects. Use Java's TreeSet class to store a collection of distinct elements and Math class for exponent operation. There is no need to sort the set because all the problem is asking for is the number of distinct elements, or the set's size.
The Code
import java.util.*;
public class Problem29
{
public static void main(String[] args)
{
TreeSet unique = new TreeSet();
for(double a = 2; a <= 100.0; a += 1.0)
{
for(double b = 2; b <= 100.0; b += 1.0)
{
double tmp = Math.pow(a,b);
unique.add(tmp);
}
}
System.out.println(unique.size());
}
}