March 2014 update

Task/Prime-decomposition/Java/prime-decomposition-4.java

@@ -1,11 +1,43 @@
-public static List<BigInteger> primeFactorBig(BigInteger a){
-    List<BigInteger> ans = new LinkedList<BigInteger>();
+private static final BigInteger TWO = BigInteger.valueOf(2);
+private static final BigInteger THREE = BigInteger.valueOf(3);
+private static final BigInteger FIVE = BigInteger.valueOf(5);
 
-    for(BigInteger divisor = BigInteger.valueOf(2);
-    	a.compareTo(ONE) > 0; divisor = divisor.add(ONE))
-		while(a.mod(divisor).equals(ZERO)){
-			 ans.add(divisor);
-			 a = a.divide(divisor);
+public static ArrayList<BigInteger> primeDecomp(BigInteger n){
+	if(n.compareTo(TWO) < 0) return null;
+	ArrayList<BigInteger> factors = new ArrayList<BigInteger>();
+	
+	// handle even values
+	while(n.and(BigInteger.ONE).equals(BigInteger.ZERO)){
+		n = n.shiftRight(1);
+		factors.add(TWO);
+	}
+	
+	// handle values divisible by three
+	while(n.mod(THREE).equals(BigInteger.ZERO)){
+		factors.add(THREE);
+		n = n.divide(THREE);
+	}
+	
+	// handle values divisible by five
+	while(n.mod(FIVE).equals(BigInteger.ZERO)){
+		factors.add(FIVE);
+		n = n.divide(FIVE);
+	}
+	
+	// much like how we can skip multiples of two, we can also skip
+	// multiples of three and multiples of five. This increment array
+	// helps us to accomplish that
+	int[] pattern = {4,2,4,2,4,6,2,6};
+	int pattern_index = 0;
+	BigInteger current_test = BigInteger.valueOf(7);
+	while(!n.equals(BigInteger.ONE)){
+		while(n.mod(current_test).equals(BigInteger.ZERO)){
+			factors.add(current_test);
+			n = n.divide(current_test);
 		}
-    return ans;
+		current_test = current_test.add(BigInteger.valueOf(pattern[pattern_index]));
+		pattern_index = (pattern_index + 1) & 7;
+	}
+	
+	return factors;
 }

Task/Prime-decomposition/Java/prime-decomposition-5.java

@@ -0,0 +1,11 @@
+public static List<BigInteger> primeFactorBig(BigInteger a){
+    List<BigInteger> ans = new LinkedList<BigInteger>();
+
+    for(BigInteger divisor = BigInteger.valueOf(2);
+    	a.compareTo(ONE) > 0; divisor = divisor.add(ONE))
+		while(a.mod(divisor).equals(ZERO)){
+			 ans.add(divisor);
+			 a = a.divide(divisor);
+		}
+    return ans;
+}