package com.euler;
/*

Consider all integer combinations of a^b 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?

*/

import java.math.*;
import java.util.*;
import static org.junit.Assert.*;

// See also Problem29a which solves without using BigInteger.
public class Problem29 implements Problem {

    @Override
    public String call() {
        assertEquals(15, getNumDistinctTerms(5, 5));
        return Integer.valueOf(getNumDistinctTerms(100, 100)).toString();
    }

    private int getNumDistinctTerms(long maxA, long maxB) {
        Set<BigInteger> terms = new HashSet<>();
        for (long a = 2; a <= maxA; ++a) {
            BigInteger term = BigInteger.valueOf(a);
            for (long b = 2; b <= maxB; ++b) {
                term = term.multiply(BigInteger.valueOf(a));
                terms.add(term);
                // System.out.format("DEBUG a=%d b=%d term=%s%n",
                //     a, b, term.toString());
            }
        }
        return terms.size();
    }

}
