Develop Reference

What is the fastest way to fill an ArrayList with null in java?

I want a List of n Sets of Integers and initially this list should be filled with null.
A lot of the Sets will be initialised later, and some will remain null.
I have tried different methods to implement this, some of them are included here:
List<HashSet<Integer>> List_of_Sets = Arrays.asList(new HashSet[n]);
ArrayList<HashSet<Integer>> List_of_Sets = new ArrayList<>(n);
while(n-- > 0) List_of_Sets.add(null);
Is there a faster way to do this?
For clarification an example for arrays would be Arrays.fill() used to be slower than:
/*
* initialize a smaller piece of the array and use the System.arraycopy
* call to fill in the rest of the array in an expanding binary fashion
*/
public static void bytefill(byte[] array, byte value) {
int len = array.length;
if (len > 0){
array[0] = value;
}
//Value of i will be [1, 2, 4, 8, 16, 32, ..., len]
for (int i = 1; i < len; i += i) {
System.arraycopy(array, 0, array, i, ((len - i) < i) ? (len - i) : i);
}
}
^above code is from Ross Drew's answer to Fastest way to set all values of an array?

Is there a faster way to do this?
As far as I am aware, no. Certainly, there is no easy way that is faster.
Based on how it works, I think (but I have not tested) that the Arrays.asList(new HashSet[n]) should be the fastest solution.
It would be possible to implement a custom List implementation that is like an ArrayList but is pre-initialized to N null values. But under the hood the initialization will be pretty much identical with what happens in the List implementation that asList returns. So I doubt that any performance improvements would be significant ... or worth the effort.
If you want to be sure of this, you could write a benchmark of the various options. However, I don't think this is the right approach in this case.
Instead I would recommend benchmarking and profiling your entire application to determine if operations on this list are a real performance hotspot.
If it is not a hotspot, my recommendation would be to just use the Arrays.asList approach and spend your time on something more important.
If it is a hotspot, you should consider replacing the List with an array. From your earlier description it seemed you are going to use the List like an array; i.e. using positional get and set operations, and no operations that change the list size. If that is the case, then using a real array should be more efficient. It saves memory, and avoids a level of indirection and (possibly) some bounds checking.
One reason not to do this would be if you needed to pass the array to some other code that requires a List.

If resizing is not important to you then implementing your own list might be fast. It might also be buggy. It would at least be interesting to benchmark compared to Java's lists. One strange effect that you might see is that standard lists might be optimised by the JIT sooner, as they could be used internally by Java's standard library.
Here is my attempt, although I suggest you don't use it. Use a standard list implementation instead.
import java.util.*;
public class FastListOfNullsDemo {
public static void main(String[] args) {
Set<Integer>[] arr = new Set[100_000]; // all set to null by default.
List<Set<Integer>> myList = new ArrayBackedList<>(arr);
myList.set(3, new TreeSet<Integer>());
myList.get(3).add(5);
myList.get(3).add(4);
myList.get(3).add(3);
myList.get(3).add(2);
myList.get(3).add(1);
// Let's just print some because 100,000 is a lot!
for (int i = 0; i < 10; i++) {
System.out.println(myList.get(i));
}
}
}
class ArrayBackedList<T> extends AbstractList<T> {
private final T[] arr;
ArrayBackedList(T[] arr) {
this.arr = arr;
}
#Override
public T get(int index) {
return arr[index];
}
#Override
public int size() {
return arr.length;
}
#Override
public T set(int index, T value) {
T result = arr[index];
arr[index] = value;
return result;
}
}
Another possibility would be implementing an always-null, fixed-size list. Use that to initialise the ArrayList. I won't promise that it is fast but you could try it out.
import java.util.*;
public class FastListOfNullsDemo {
public static void main(String[] args) {
List<Set<Integer>> allNull = new NullList<>(100_000);
List<Set<Integer>> myList = new ArrayList<>(allNull);
myList.set(3, new TreeSet<Integer>());
myList.get(3).add(5);
myList.get(3).add(4);
myList.get(3).add(3);
myList.get(3).add(2);
myList.get(3).add(1);
System.out.println(myList.size());
// Let's just print some because 100,000 is a lot!
for (int i = 0; i < 10; i++) {
System.out.println(myList.get(i));
}
}
}
class NullList<T> extends AbstractList<T> {
private int count;
NullList(int count) {
this.count = count;
}
#Override
public T get(int index) {
return null;
}
#Override
public int size() {
return count;
}
}

Can you have collections without storing the values in Java?

I have a question about java collections such as Set or List. More generally objects that you can use in a for-each loop. Is there any requirement that the elements of them actually has to be stored somewhere in a data structure or can they be described only from some sort of requirement and calculated on the fly when you need them? It feels like this should be possible to be done, but I don't see any of the java standard collection classes doing anything like this. Am I breaking any sort of contract here?
The thing I'm thinking about using these for is mainly mathematics. Say for example I want to have a set representing all prime numbers under 1 000 000. It might not be a good idea to save these in memory but to instead have a method check if a particular number is in the collection or not.
I'm also not at all an expert at java streams, but I feel like these should be usable in java 8 streams since the objects have very minimal state (the objects in the collection doesn't even exist until you try to iterate over them or check if a particular object exists in the collection).
Is it possible to have Collections or Iterators with virtually infinitely many elements, for example "all numbers on form 6*k+1", "All primes above 10" or "All Vectors spanned by this basis"? One other thing I'm thinking about is combining two sets like the union of all primes below 1 000 000 and all integers on form 2^n-1 and list the mersenne primes below 1 000 000. I feel like it would be easier to reason about certain mathematical objects if it was done this way and the elements weren't created explicitly until they are actually needed. Maybe I'm wrong.
Here's two mockup classes I wrote to try to illustrate what I want to do. They don't act exactly as I would expect (see output) which make me think I am breaking some kind of contract here with the iterable interface or implementing it wrong. Feel free to point out what I'm doing wrong here if you see it or if this kind of code is even allowed under the collections framework.
import java.util.AbstractSet;
import java.util.Iterator;
public class PrimesBelow extends AbstractSet<Integer>{
int max;
int size;
public PrimesBelow(int max) {
this.max = max;
}
#Override
public Iterator<Integer> iterator() {
return new SetIterator<Integer>(this);
}
#Override
public int size() {
if(this.size == -1){
System.out.println("Calculating size");
size = calculateSize();
}else{
System.out.println("Accessing calculated size");
}
return size;
}
private int calculateSize() {
int c = 0;
for(Integer p: this)
c++;
return c;
}
public static void main(String[] args){
PrimesBelow primesBelow10 = new PrimesBelow(10);
for(int i: primesBelow10)
System.out.println(i);
System.out.println(primesBelow10);
}
}
.
import java.util.Iterator;
import java.util.NoSuchElementException;
public class SetIterator<T> implements Iterator<Integer> {
int max;
int current;
public SetIterator(PrimesBelow pb) {
this.max= pb.max;
current = 1;
}
#Override
public boolean hasNext() {
if(current < max) return true;
else return false;
}
#Override
public Integer next() {
while(hasNext()){
current++;
if(isPrime(current)){
System.out.println("returning "+current);
return current;
}
}
throw new NoSuchElementException();
}
private boolean isPrime(int a) {
if(a<2) return false;
for(int i = 2; i < a; i++) if((a%i)==0) return false;
return true;
}
}
Main function gives the output
returning 2
2
returning 3
3
returning 5
5
returning 7
7
Exception in thread "main" java.util.NoSuchElementException
at SetIterator.next(SetIterator.java:27)
at SetIterator.next(SetIterator.java:1)
at PrimesBelow.main(PrimesBelow.java:38)
edit: spotted an error in the next() method. Corrected it and changed the output to the new one.

Well, as you see with your (now fixed) example, you can easily do it with Iterables/Iterators. Instead of having a backing collection, the example would've been nicer with just an Iterable that takes the max number you wish to calculate primes to. You just need to make sure that you handle the hasNext() method properly so you don't have to throw an exception unnecessarily from next().
Java 8 streams can be used easier to perform these kinds of things nowadays, but there's no reason you can't have a "virtual collection" that's just an Iterable. If you start implementing Collection it becomes harder, but even then it wouldn't be completely impossible, depending on the use cases: e.g. you could implement contains() that checks for primes, but you'd have to calculate it and it would be slow for large numbers.
A (somewhat convoluted) example of a semi-infinite set of odd numbers that is immutable and stores no values.
public class OddSet implements Set<Integer> {
public boolean contains(Integer o) {
return o % 2 == 1;
}
public int size() {
return Integer.MAX_VALUE;
}
public boolean add(Integer i) {
throw new OperationNotSupportedException();
}
public boolean equals(Object o) {
return o instanceof OddSet;
}
// etc. etc.
}

As DwB stated, this is not possible to do with Java's Collections API, as every element must be stored in memory. However, there is an alternative: this is precisely why Java's Stream API was implemented!
Streams allow you to iterate across an infinite amount of objects that are not stored in memory unless you explicitly collect them into a Collection.
From the documentation of IntStream#iterate:
Returns an infinite sequential ordered IntStream produced by iterative application of a function f to an initial element seed, producing a Stream consisting of seed, f(seed), f(f(seed)), etc.
The first element (position 0) in the IntStream will be the provided seed. For n > 0, the element at position n, will be the result of applying the function f to the element at position n - 1.
Here are some examples that you proposed in your question:
public class Test {
public static void main(String[] args) {
IntStream.iterate(1, k -> 6 * k + 1);
IntStream.iterate(10, i -> i + 1).filter(Test::isPrime);
IntStream.iterate(1, n -> 2 * n - 1).filter(i -> i < 1_000_000);
}
private boolean isPrime(int a) {
if (a < 2) {
return false;
}
for(int i = 2; i < a; i++) {
if ((a % i) == 0) {
return false;
}
return true;
}
}
}

Why java concurrentmap gives slight difference in calculating doubles using multithread

I am doing matrix multiplication by trying using multi-threads approach, but the calculation between doubles are not always the same for the same matrix.
there are the codes:
for the matrix:
private ConcurrentMap<Position, Double> matrix = new ConcurrentHashMap<>();
public Matrix_2() {}
public double get(int row, int column) {
Position p = new Position(row, column);
return matrix.getOrDefault(p, 0.0);
}
public void set(int row, int column, double num) {
Position p = new Position(row, column);
if(matrix.containsKey(p)){
double a = matrix.get(p);
a += num;
matrix.put(p, a);
}else {
matrix.put(p, num);
}
}
for multiplication
public static Matrix multiply(Matrix a, Matrix b) {
List<Thread> threads = new ArrayList<>();
Matrix c = new Matrix_2();
IntStream.range(0, a.getNumRows()).forEach(r ->
IntStream.range(0, a.getNumColumns()).forEach(t ->
IntStream.range(0, b.getNumColumns())
.forEach(
v ->
threads.add(new Thread(() -> c.set(r, v, b.get(t, v) * a.get(r, t)))))
));
threads.forEach(Thread::start);
threads.forEach(r -> {
try {
r.join();
} catch (InterruptedException e) {
System.out.println("bad");
}
}
);
return c;
}
where get method get the double at specific row and column, get(row, column), and the set method add the given number to the double at that row and column.
This code works fine at the integer level but when it comes to double with a lot precision, it will have different answers for the multiplication of same two matrices, sometimes can be as large as 0.5 to 1.5 for a number. Why is that.

While I haven't fully analyzed your code for multiply, and John Bollinger makes a good point (in the comments) regarding the rounding-error inherent to floating-point primitives, your set method would seem to have a possible race condition.
Namely, while your use of java.util.ConcurrentHashMap guarantees thread safety within Map API calls, it does nothing to ensure that the mappings could not have changed in between invocations, such as between the time that you invoke containsKey and the time that you invoke put, or between the time that you invoke get and the time that you invoke put.
As of Java 8 (which your use of lambdas and streams indicates you are using), one option to rectify this problem is to make the check-existing + get + set sequence atomic via the compute API call. compute allows you to provide a key and a lambda (or method reference) specifying how to mutate the value mapped to that key, and ConcurrentHashMap guarantees that the lambda, which encompasses your full check-and-set logic, will be executed atomically. Using that approach, your code would look something like:
public void set(int row, int column, double num) {
Position p = new Position(row, column);
matrix.compute(p, (Position positionKey, Double doubleValue)->{
if (doubleValue == null) {
return num;
} else {
return num + doubleValue;
}
});
}

A concurrent collection can help you write thread-safe code, but it does not make your code automatically thread-safe. And your code -- principally your set() method -- is not thread safe.
In fact, your set() method does not even make sense, at least not under that name. If the implementation is indeed what you intend, then it seems to be more of an increment() method.
My first suggestion would be to simplify your approach by eliminating the middle IntStream, or at least moving it into the threads. The objective here would be to avoid any two threads ever manipulating the same element of the map. You could then also use a bona fide set() method in conjunction, as there would be no contention for individual matrix elements. The ConcurrentMap would still be helpful in that case. Most likely that would run faster, too.
If you must keep the structure of the computation the same, however, then you need a better set() method, one that accounts for the possibility that another thread updates an element between your get() and put(). If you don't account for that then updates can be lost. Something along these lines would be an improvement:
public void increment(int row, int column, double num) {
Position p = new Position(row, column);
Double current = matrix.putIfAbsent(p, num);
if (current != null) {
// there was already a value at the designated position
double newval = current + num;
while (!matrix.replace(p, current, newval)) {
// Failed to replace -- indicates that the value at the designated
// position is no longer the one we most recently read
current = matrix.get(p);
newval = current + num;
}
} // else successfully set the first value for this position
}
That approach will work with any version of Java that provides ConcurrentMap, but of course, other parts of your code already rely on Java 8. The solution offered by #Sumitsu leverages API features that were new in Java 8; it is more elegant than the above, but less illustrative.
Note also that it would not be surprising to see see small differences in your result in any case, because reordering floating-point operations can cause different rounding.

Is there any way I can return a value from a loop and continue from where I left off?

Is there any way I can return a value from a loop and continuing from where I left off ?
In the following snippet, I want to return the current value of currVm. But I am unable to do so.
In the innermost loop of the snippet :
while(c <= currVm) {
allocatedVm(currVm);
c++;
}
a function named allocatedVm is called. I want to return the value of currVm and start again from where I left off. Is there any way out ?
#Override
public int getNextAvailableVm() {
Set<String> dataCenters = confMap.keySet();
for (String dataCenter : dataCenters) {
LinkedList<DepConfAttr> list = confMap.get(dataCenter);
Collections.sort(list, new MemoryComparator());
int size = list.size() - 1;
int count = 0;
while(size >= 0) {
DepConfAttr dca = (DepConfAttr)list.get(count);
int currVm = dca.getVmCount();
int c = 0;
while(c <= currVm) {
allocatedVm(currVm); // RETURN currVm
c++;
}
count++;
size--;
}
}
}

The best approach would probably be to write a method returning an Iterable<Integer>. That's not as easy in Java as it is in languages which support generator functions (e.g. C# and Python) but it's still feasible. If the code is short, you can get away with a pair of (nested) anonymous inner classes:
public Iterable<Integer> foo() {
return new Iterable<Integer>() {
#Override public Iterator<Integer> iterator() {
return new Iterator<Integer>() {
// Implement hasNext, next and remove here
};
}
};
}
In your case I'd be tempted to break it into a separate non-anonymous class though, just for simplicity.
Anyway, the point of using Iterable is that an Iterator naturally has state - that's its purpose, basically. So it's a good fit for your requirements.
Another rather simpler approach would be to return all of the elements in one go, and make the caller perform the allocation on demand. Obviously that doesn't work well if there could be a huge number of elements, but it would be easier to understand.

not sure i understand what you need, but:
if you wish to notify the caller of the method that you've got a value during the running of the method, but don't wish to exit the method just yet, you can use listeners.
just create an interface as a parameter to your function, and have a function inside that will have the object as a parameter.
example:
interface IGotValueListener
{
public void onGotValue(MyClass obj);
}
public int getNextAvailableVm(IGotValueListener listener)
{
...
if(listener!=null)
listener.onGotValue(...);
}
now , for calling the method, you do:
int finalResult=getNextAvailableVm(new IGotValueListener ()
{
... //implement onGotValue
};

You can return from anywhere in your method , by just putting the return keyword. If you want to put a functionality to resume ur method from different places then u need to factor ur method in that way. You can use labels and if statements, set some static variables to mark the last execution place. If your application is not multi-threaded then u need not to worry with the use of static variable synchronization. Also if your method is too big and becoming hard to follow/read, then think about breaking it into smaller ones.

Refactor this recursive method?

I'm pretty new to the idea of recursion and this is actually my first attempt at writing a recursive method.
I tried to implement a recursive function Max that passes an array, along with a variable that holds the array's size in order to print the largest element.
It works, but it just doesn't feel right!
I have also noticed that I seem to use the static modifier much more than my classmates in general...
Can anybody please provide any general tips as well as feedback as to how I can improve my code?
public class RecursiveTry{
static int[] n = new int[] {1,2,4,3,3,32,100};
static int current = 0;
static int maxValue = 0;
static int SIZE = n.length;
public static void main(String[] args){
System.out.println(Max(n, SIZE));
}
public static int Max(int[] n, int SIZE) {
if(current <= SIZE - 1){
if (maxValue <= n[current]) {
maxValue = n[current];
current++;
Max(n, SIZE);
}
else {
current++;
Max(n, SIZE);
}
}
return maxValue;
}
}

Your use of static variables for holding state outside the function will be a source of difficulty.
An example of a recursive implementation of a max() function in pseudocode might be:
function Max(data, size) {
assert(size > 0)
if (size == 1) {
return data[0]
}
maxtail = Max(data[1..size], size-1)
if (data[0] > maxtail) {
return data[0]
} else {
return maxtail
}
}
The key here is the recursive call to Max(), where you pass everything except the first element, and one less than the size. The general idea is this function says "the maximum value in this data is either the first element, or the maximum of the values in the rest of the array, whichever is larger".
This implementation requires no static data outside the function definition.
One of the hallmarks of recursive implementations is a so-called "termination condition" which prevents the recursion from going on forever (or, until you get a stack overflow). In the above case, the test for size == 1 is the termination condition.

Making your function dependent on static variables is not a good idea. Here is possible implementation of recursive Max function:
int Max(int[] array, int currentPos, int maxValue) {
// Ouch!
if (currentPos < 0) {
raise some error
}
// We reached the end of the array, return latest maxValue
if (currentPos >= array.length) {
return maxValue;
}
// Is current value greater then latest maxValue ?
int currentValue = array[currentPos];
if (currentValue > maxValue) {
// currentValue is a new maxValue
return Max(array, currentPos + 1, currentValue);
} else {
// maxValue is still a max value
return Max(array, currentPos + 1, maxValue);
}
}
...
int[] array = new int[] {...};
int currentPos = 0;
int maxValue = array[currentPos] or minimum int value;
maxValue = Max(array, currentPos, maxValue);

A "max" function is the wrong type of thing to write a recursive function for -- and the fact you're using static values for "current" and "maxValue" makes your function not really a recursive function.
Why not do something a little more amenable to a recursive algorithm, like factorial?

"not-homework"?
Anyway. First things first. The
static int[] n = new int[] {1,2,4,3,3,32,100};
static int SIZE = n.length;
have nothing to do with the parameters of Max() with which they share their names. Move these over to main and lose the "static" specifiers. They are used only once, when calling the first instance of Max() from inside main(). Their scope shouldn't extend beyond main().
There is no reason for all invocations of Max() to share a single "current" index. "current" should be local to Max(). But then how would successive recurrences of Max() know what value of "current" to use? (Hint: Max() is already passing other Max()'s lower down the line some data. Add "current" to this data.)
The same thing goes for maxValue, though the situation here is a bit more complex. Not only do you need to pass a current "maxValue" down the line, but when the recursion finishes, you have to pass it back up all the way to the first Max() function, which will return it to main(). You may need to look at some other examples of recursion and spend some time with this one.
Finally, Max() itself is static. Once you've eliminated the need to refer to external data (the static variables) however; it doesn't really matter. It just means that you can call Max() without having to instantiate an object.

As others have observed, there is no need for recursion to implement a Max function, but it can be instructive to use a familiar algorithm to experiment with a new concept. So, here is the simplified code, with an explanation below:
public class RecursiveTry
{
public static void main(String[] args)
{
System.out.println(Max(new int[] {1,2,4,3,3,32,100}, 0, 0));
}
public static int Max(int[] n, int current, int maxValue)
{
if(current < n.Length)
{
if (maxValue <= n[current] || current == 0))
{
return Max(n, current+1, n[current]);
}
return Max(n, current+1, maxValue);
}
return maxValue;
}
}
all of the static state is gone as unnecessary; instead everything is passed on the stack. the internal logic of the Max function is streamlined, and we recurse in two different ways just for fun

Here's a Java version for you.
public class Recursion {
public static void main(String[] args) {
int[] data = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };
System.out.println("Max: " + max(0, data));
}
public static int max(int i, int[] arr) {
if(i == arr.length-1) {
return arr[i];
}
int memo = max(i+1, arr);
if(arr[i] > memo) {
return arr[i];
}
return memo;
}
}
The recurrence relation is that the maximum element of an array is either the first element, or the maximum of the rest of the array. The stop condition is reached when you reach the end of the array. Note the use of memoization to reduce the recursive calls (roughly) in half.

You are essentially writing an iterative version but using tail recursion for the looping. Also, by making so many variables static, you are essentially using global variables instead of objects. Here is an attempt at something closer to a typical recursive implementation. Of course, in real life if you were using a language like Java that doesn't optimize tail calls, you would implement a "Max" function using a loop.
public class RecursiveTry{
static int[] n;
public static void main(String[] args){
RecursiveTry t = new RecursiveTry(new int[] {1,2,4,3,3,32,100});
System.out.println(t.Max());
}
RecursiveTry(int[] arg) {
n = arg;
}
public int Max() {
return MaxHelper(0);
}
private int MaxHelper(int index) {
if(index == n.length-1) {
return n[index];
} else {
int maxrest = MaxHelper(index+1);
int current = n[index];
if(current > maxrest)
return current;
else
return maxrest;
}
}
}

In Scheme this can be written very concisely:
(define (max l)
(if (= (length l) 1)
(first l)
(local ([define maxRest (max (rest l))])
(if (> (first l) maxRest)
(first l)
maxRest))))
Granted, this uses linked lists and not arrays, which is why I didn't pass it a size element, but I feel this distills the problem to its essence. This is the pseudocode definition:
define max of a list as:
if the list has one element, return that element
otherwise, the max of the list will be the max between the first element and the max of the rest of the list

A nicer way of getting the max value of an array recursively would be to implement quicksort (which is a nice, recursive sorting algorithm), and then just return the first value.
Here is some Java code for quicksort.

Smallest codesize I could get:
public class RecursiveTry {
public static void main(String[] args) {
int[] x = new int[] {1,2,4,3,3,32,100};
System.out.println(Max(x, 0));
}
public static int Max(int[] arr, int currPos) {
if (arr.length == 0) return -1;
if (currPos == arr.length) return arr[0];
int len = Max (arr, currPos + 1);
if (len < arr[currPos]) return arr[currPos];
return len;
}
}
A few things:
1/ If the array is zero-size, it returns a max of -1 (you could have another marker value, say, -MAX_INT, or throw an exception). I've made the assumption for code clarity here to assume all values are zero or more. Otherwise I would have peppered the code with all sorts of unnecessary stuff (in regards to answering the question).
2/ Most recursions are 'cleaner' in my opinion if the terminating case is no-data rather than last-data, hence I return a value guaranteed to be less than or equal to the max when we've finished the array. Others may differ in their opinion but it wouldn't be the first or last time that they've been wrong :-).
3/ The recursive call just gets the max of the rest of the list and compares it to the current element, returning the maximum of the two.
4/ The 'ideal' solution would have been to pass a modified array on each recursive call so that you're only comparing the first element with the rest of the list, removing the need for currPos. But that would have been inefficient and would have bought down the wrath of SO.
5/ This may not necessarily be the best solution. It may be that by gray matter has been compromised from too much use of LISP with its CAR, CDR and those interminable parentheses.

First, let's take care of the static scope issue ... Your class is defining an object, but never actually instantiating one. Since main is statically scoped, the first thing to do is get an object, then execute it's methods like this:
public class RecursiveTry{
private int[] n = {1,2,4,3,3,32,100};
public static void main(String[] args){
RecursiveTry maxObject = new RecursiveTry();
System.out.println(maxObject.Max(maxObject.n, 0));
}
public int Max(int[] n, int start) {
if(start == n.length - 1) {
return n[start];
} else {
int maxRest = Max(n, start + 1);
if(n[start] > maxRest) {
return n[start];
}
return maxRest;
}
}
}
So now we have a RecursiveTry object named maxObject that does not require the static scope. I'm not sure that finding a maximum is effective using recursion as the number of iterations in the traditional looping method is roughly equivalent, but the amount of stack used is larger using recursion. But for this example, I'd pare it down a lot.
One of the advantages of recursion is that your state doesn't generally need to be persisted during the repeated tests like it does in iteration. Here, I've conceded to the use of a variable to hold the starting point, because it's less CPU intensive that passing a new int[] that contains all the items except for the first one.