StepsNumWays.java

import java.util.ArrayList;
import java.util.Collection;
import java.util.List;

public class StepsNumWays {
    public static void main(String[] args) {
        StepsNumWays solution = new StepsNumWays();
        System.out.println(solution.solve(2, List.of(1, 2)));
        System.out.println(solution.solve(3, List.of(1, 2)));
        System.out.println(solution.solve(3, List.of(1, 2, 3)));
        System.out.println(solution.solve(4, List.of(1, 2, 3)));
        System.out.println(solution.solve(4, List.of(1, 2)));
    }

    public int solve(int steps, Collection<Integer> ways) {
        System.out.printf("solving for %s (%s)%n", steps, ways);
        return solve(steps, new ArrayList<>(), ways);
    }

    private int solve(int steps, ArrayList<Integer> taken, Collection<Integer> ways) {
        int sum = 0;
        for (Integer way : ways) {
            if (way == steps) {
                sum += 1;
                taken.add(way);
                System.out.println("way: " + taken);
                taken.remove(taken.size() - 1);
            } else if (way < steps) {
                taken.add(way);
                int solve = solve(steps - way, taken, ways);
                taken.remove(taken.size() - 1);
                sum += solve;
            }
        }
        return sum;
    }
}

StepsNumWaysTest.java

import org.junit.jupiter.params.ParameterizedTest;
import org.junit.jupiter.params.provider.CsvSource;

import java.util.List;
import java.util.stream.Stream;

import static org.junit.jupiter.api.Assertions.assertEquals;

class StepsNumWaysTest {

    StepsNumWays solution = new StepsNumWays();

    @ParameterizedTest
    @CsvSource({
            "2,2,1:2",
            "3,3,1:2",
            "4,3,1:2:3",
            "7,4,1:2:3",
            "5,4,1:2"
    })
    void test(int expected, int input, String waysString) {
        List<Integer> ways = Stream.of(waysString.split(":"))
                .map(Integer::parseInt)
                .toList();

        assertEquals(expected, solution.solve(input, ways));
    }

}