tasks a-s

Task/Prime-decomposition/Java/prime-decomposition-1.java

@@ -0,0 +1 @@
+public boolean prime(BigInteger i);

Task/Prime-decomposition/Java/prime-decomposition-2.java

@@ -0,0 +1,12 @@
+public static List<BigInteger> primeFactorBig(BigInteger a){
+    List<BigInteger> ans = new LinkedList<BigInteger>();
+    //loop until we test the number itself or the number is 1
+    for (BigInteger i = BigInteger.valueOf(2); i.compareTo(a) <= 0 && !a.equals(BigInteger.ONE);
+         i = i.add(BigInteger.ONE)){
+        while (a.remainder(i).equals(BigInteger.ZERO) && prime(i)) { //if we have a prime factor
+            ans.add(i); //put it in the list
+            a = a.divide(i); //factor it out of the number
+        }
+    }
+    return ans;
+}

Task/Prime-decomposition/Java/prime-decomposition-3.java

@@ -0,0 +1,32 @@
+private static final BigInteger two = BigInteger.valueOf(2);
+
+public List<BigInteger> primeDecomp(BigInteger a) {
+    // impossible for values lower than 2
+    if (a.compareTo(two) < 0) {
+        return null;
+    }
+
+    //quickly handle even values
+    List<BigInteger> result = new ArrayList<BigInteger>();
+    while (a.and(BigInteger.ONE).equals(BigInteger.ZERO)) {
+        a = a.shiftRight(1);
+        result.add(two);
+    }
+
+    //left with odd values
+    if (!a.equals(BigInteger.ONE)) {
+        BigInteger b = BigInteger.valueOf(3);
+        while (b.compareTo(a) < 0) {
+            if (b.isProbablePrime(10)) {
+                BigInteger[] dr = a.divideAndRemainder(b);
+                if (dr[1].equals(BigInteger.ZERO)) {
+                    result.add(b);
+                    a = dr[0];
+                }
+            }
+            b = b.add(two);
+        }
+        result.add(b); //b will always be prime here...
+    }
+    return result;
+}

Task/Prime-decomposition/Java/prime-decomposition-4.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;
+}