Initial Commit

Submissions/As7/IsaacShoebottom_As7_Report/Seq.java

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+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];
+	}
+}

Submissions/As7/IsaacShoebottom_As7_Report/TestSeq.java

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+import java.text.NumberFormat;
+import java.util.Scanner;
+
+/**
+ A simple driver that uses the Seq class to compute the
+ nth element of the sequence.
+ @author Isaac Shoebottom (3429069)
+*/
+
+public class TestSeq{
+
+	public static void main(String[] args){
+		
+		int n, seqRec, seqMem, seqIter;
+		
+		Scanner scan = new Scanner(System.in);
+		System.out.print("Enter a positive integer: ");
+		n = scan.nextInt();
+					
+		seqRec = Seq.seqR(n);
+		seqMem = Seq.seqM(n);
+		seqIter = Seq.seqI(n);
+		System.out.println("seqR(" + n + ") is: " + seqRec);
+		System.out.println("seqM(" + n + ") is: " + seqMem);
+		System.out.println("seqI(" + n + ") is: " + seqIter);
+
+		NumberFormat form = NumberFormat.getInstance();
+		form.setMaximumFractionDigits(7);
+		form.setMinimumFractionDigits(7);
+		System.out.println();
+		System.out.println("Execution Times in Milliseconds (ms)");
+		System.out.println("Seq(n) \tRecursive \tMemoization \tItertive");
+		long start, end;
+		int seqA;
+		double time;
+		for(int i = 20; i <= 40; i+=10){
+			start = System.nanoTime();
+			seqA = Seq.seqR(i);
+			end = System.nanoTime();
+			time = (double)(end-start)/1000000;
+			System.out.print(i + "\t" + form.format(time));
+
+
+			start = System.nanoTime();
+			seqA = Seq.seqM(i);
+			end = System.nanoTime();
+			time = (double)(end-start)/1000000;
+			System.out.print(i + "\t" + form.format(time));
+
+			start = System.nanoTime();
+			seqA = Seq.seqI(i);
+			end = System.nanoTime();
+			time = (double)(end-start)/1000000;
+			System.out.print(i + "\t" + form.format(time));
+
+			System.out.println();
+		}
+	}
+}