tasks a-s

Task/Catalan-numbers/Java/catalan-numbers.java

@@ -0,0 +1,65 @@
+import java.util.HashMap;
+import java.util.Map;
+
+public class Catalan {
+	private static final Map<Long, Double> facts = new HashMap<Long, Double>();
+	private static final Map<Long, Double> catsI = new HashMap<Long, Double>();
+	private static final Map<Long, Double> catsR1 = new HashMap<Long, Double>();
+	private static final Map<Long, Double> catsR2 = new HashMap<Long, Double>();
+	
+	static{//pre-load the memoization maps with some answers
+		facts.put(0L, 1D);
+		facts.put(1L, 1D);
+		facts.put(2L, 2D);
+		
+		catsI.put(0L, 1D);
+		catsR1.put(0L, 1D);
+		catsR2.put(0L, 1D);
+	}
+
+	private static double fact(long n){
+		if(facts.containsKey(n)){
+			return facts.get(n);
+		}
+		double fact = 1;
+		for(long i = 2; i <= n; i++){
+			fact *= i; //could be further optimized, but it would probably be ugly
+		}
+		facts.put(n, fact);
+		return fact;
+	}
+
+	private static double catI(long n){
+		if(!catsI.containsKey(n)){
+			catsI.put(n, fact(2 * n)/(fact(n+1)*fact(n)));
+		}
+		return catsI.get(n);
+	}
+	
+	private static double catR1(long n){
+		if(catsR1.containsKey(n)){
+			return catsR1.get(n);
+		}
+		double sum = 0;
+		for(int i = 0; i < n; i++){
+			sum += catR1(i) * catR1(n - 1 - i);
+		}
+		catsR1.put(n, sum);
+		return sum;
+	}
+	
+	private static double catR2(long n){
+		if(!catsR2.containsKey(n)){
+			catsR2.put(n, ((2.0*(2*(n-1) + 1))/(n + 1)) * catR2(n-1));
+		}
+		return catsR2.get(n);
+	}
+	
+	public static void main(String[] args){
+		for(int i = 0; i <= 15; i++){
+			System.out.println(catI(i));
+			System.out.println(catR1(i));
+			System.out.println(catR2(i));
+		}
+	}
+}