LucasSeries.java

package com.thealgorithms.maths;

/**
 * https://en.wikipedia.org/wiki/Lucas_number
 */
public class LucasSeries {

    public static void main(String[] args) {
        assert lucasSeries(1) == 2 && lucasSeriesIteration(1) == 2;
        assert lucasSeries(2) == 1 && lucasSeriesIteration(2) == 1;
        assert lucasSeries(3) == 3 && lucasSeriesIteration(3) == 3;
        assert lucasSeries(4) == 4 && lucasSeriesIteration(4) == 4;
        assert lucasSeries(5) == 7 && lucasSeriesIteration(5) == 7;
        assert lucasSeries(6) == 11 && lucasSeriesIteration(6) == 11;
        assert lucasSeries(11) == 123 && lucasSeriesIteration(11) == 123;
    }

    /**
     * Calculate nth number of lucas series(2, 1, 3, 4, 7, 11, 18, 29, 47, 76,
     * 123, ....) using recursion
     *
     * @param n nth
     * @return nth number of lucas series
     */
    public static int lucasSeries(int n) {
        return n == 1 ? 2 : n == 2 ? 1 : lucasSeries(n - 1) + lucasSeries(n - 2);
    }

    /**
     * Calculate nth number of lucas series(2, 1, 3, 4, 7, 11, 18, 29, 47, 76,
     * 123, ....) using iteration
     *
     * @param n nth
     * @return nth number of lucas series
     */
    public static int lucasSeriesIteration(int n) {
        int previous = 2;
        int current = 1;
        for (int i = 1; i < n; i++) {
            int next = previous + current;
            previous = current;
            current = next;
        }
        return previous;
    }
}