import java.util.ArrayList;

/**
A utility class that provide methods to compute elements of the
recursive sequence.
@author Leah Bidlake, Isaac Shoebottom (3429069)
*/

public class Seq{
	
	/**
	Recursively computes seq(n).
	@param n Non-negative integer.
	@return int Element n in the recursive sequence.
	*/

	private static ArrayList<Integer> cache;

	public static int seqR(int n){
		if (n == 0)
			return 1;
		if (n == 1)
			return 5;
		return seqR(n-1) + seqR(n-2);
	}

	/**
	 * Sequence calculator using an memoization cache
	 * @param n The digit the sequence is to be calculated to
	 * @return The number in the sequence n refers to
	 */
	public static int seqM(int n){
		if (cache == null) {
			cache = new ArrayList<>();
			cache.add(1);
			cache.add(5);
		}

		if (cache.size() <= n)
			cache.add(seqM(n-1) + seqM( n-2));
		return cache.get(n);
	}

	/**
	 * Sequence calculator using an iterative approach
	 * @param n The digit the sequence is to be calculated to
	 * @return The number in the sequence n refers to
	 */
	public static int seqI(int n){
		int[] cache = new int[n+2]; //n+2 so seqI(0) is not out of bounds
		cache[0] = 1;
		cache[1] = 5;

		for(int i = 2; i <= n; i++) { //i = 2 because we need to skip the first two array items
			cache[i] = cache[i-1] + cache[i-2];
		}
		return cache[n];
	}
}