Develop Reference

Sorted Lists in Java [duplicate]

In Java there are the SortedSet and SortedMap interfaces. Both belong to the Java Collections framework and provide a sorted way to access the elements.
However, in my understanding there is no SortedList in Java. You can use java.util.Collections.sort() to sort a list.
Any idea why it is designed like that?

List iterators guarantee first and foremost that you get the list's elements in the internal order of the list (aka. insertion order). More specifically it is in the order you've inserted the elements or on how you've manipulated the list. Sorting can be seen as a manipulation of the data structure, and there are several ways to sort the list.
I'll order the ways in the order of usefulness as I personally see it:
1. Consider using Set or Bag collections instead
NOTE: I put this option at the top because this is what you normally want to do anyway.
A sorted set automatically sorts the collection at insertion, meaning that it does the sorting while you add elements into the collection. It also means you don't need to manually sort it.
Furthermore if you are sure that you don't need to worry about (or have) duplicate elements then you can use the TreeSet<T> instead. It implements SortedSet and NavigableSet interfaces and works as you'd probably expect from a list:
TreeSet<String> set = new TreeSet<String>();
set.add("lol");
set.add("cat");
// automatically sorts natural order when adding
for (String s : set) {
System.out.println(s);
}
// Prints out "cat" and "lol"
If you don't want the natural ordering you can use the constructor parameter that takes a Comparator<T>.
Alternatively, you can use Multisets (also known as Bags), that is a Set that allows duplicate elements, instead and there are third-party implementations of them. Most notably from the Guava libraries there is a TreeMultiset, that works a lot like the TreeSet.
2. Sort your list with Collections.sort()
As mentioned above, sorting of Lists is a manipulation of the data structure. So for situations where you need "one source of truth" that will be sorted in a variety of ways then sorting it manually is the way to go.
You can sort your list with the java.util.Collections.sort() method. Here is a code sample on how:
List<String> strings = new ArrayList<String>()
strings.add("lol");
strings.add("cat");
Collections.sort(strings);
for (String s : strings) {
System.out.println(s);
}
// Prints out "cat" and "lol"
Using comparators
One clear benefit is that you may use Comparator in the sort method. Java also provides some implementations for the Comparator such as the Collator which is useful for locale sensitive sorting strings. Here is one example:
Collator usCollator = Collator.getInstance(Locale.US);
usCollator.setStrength(Collator.PRIMARY); // ignores casing
Collections.sort(strings, usCollator);
Sorting in concurrent environments
Do note though that using the sort method is not friendly in concurrent environments, since the collection instance will be manipulated, and you should consider using immutable collections instead. This is something Guava provides in the Ordering class and is a simple one-liner:
List<string> sorted = Ordering.natural().sortedCopy(strings);
3. Wrap your list with java.util.PriorityQueue
Though there is no sorted list in Java there is however a sorted queue which would probably work just as well for you. It is the java.util.PriorityQueue class.
Nico Haase linked in the comments to a related question that also answers this.
In a sorted collection you most likely don't want to manipulate the internal data structure which is why PriorityQueue doesn't implement the List interface (because that would give you direct access to its elements).
Caveat on the PriorityQueue iterator
The PriorityQueue class implements the Iterable<E> and Collection<E> interfaces so it can be iterated as usual. However, the iterator is not guaranteed to return elements in the sorted order. Instead (as Alderath points out in the comments) you need to poll() the queue until empty.
Note that you can convert a list to a priority queue via the constructor that takes any collection:
List<String> strings = new ArrayList<String>()
strings.add("lol");
strings.add("cat");
PriorityQueue<String> sortedStrings = new PriorityQueue(strings);
while(!sortedStrings.isEmpty()) {
System.out.println(sortedStrings.poll());
}
// Prints out "cat" and "lol"
4. Write your own SortedList class
NOTE: You shouldn't have to do this.
You can write your own List class that sorts each time you add a new element. This can get rather computation heavy depending on your implementation and is pointless, unless you want to do it as an exercise, because of two main reasons:
It breaks the contract that List<E> interface has because the add methods should ensure that the element will reside in the index that the user specifies.
Why reinvent the wheel? You should be using the TreeSet or Multisets instead as pointed out in the first point above.
However, if you want to do it as an exercise here is a code sample to get you started, it uses the AbstractList abstract class:
public class SortedList<E> extends AbstractList<E> {
private ArrayList<E> internalList = new ArrayList<E>();
// Note that add(E e) in AbstractList is calling this one
#Override
public void add(int position, E e) {
internalList.add(e);
Collections.sort(internalList, null);
}
#Override
public E get(int i) {
return internalList.get(i);
}
#Override
public int size() {
return internalList.size();
}
}
Note that if you haven't overridden the methods you need, then the default implementations from AbstractList will throw UnsupportedOperationExceptions.

Because the concept of a List is incompatible with the concept of an automatically sorted collection. The point of a List is that after calling list.add(7, elem), a call to list.get(7) will return elem. With an auto-sorted list, the element could end up in an arbitrary position.

Since all lists are already "sorted" by the order the items were added (FIFO ordering), you can "resort" them with another order, including the natural ordering of elements, using java.util.Collections.sort().
EDIT:
Lists as data structures are based in what is interesting is the ordering in which the items where inserted.
Sets do not have that information.
If you want to order by adding time, use List. If you want to order by other criteria, use SortedSet.

Set and Map are non-linear data structure. List is linear data structure.
The tree data structure SortedSet and SortedMap interfaces implements TreeSet and TreeMap respectively using used Red-Black tree implementation algorithm. So it ensure that there are no duplicated items (or keys in case of Map).
List already maintains an ordered collection and index-based data structure, trees are no index-based data structures.
Tree by definition cannot contain duplicates.
In List we can have duplicates, so there is no TreeList(i.e. no SortedList).
List maintains elements in insertion order. So if we want to sort the list we have to use java.util.Collections.sort(). It sorts the specified list into ascending order, according to the natural ordering of its elements.

JavaFX SortedList
Though it took a while, Java 8 does have a sorted List.
http://docs.oracle.com/javase/8/javafx/api/javafx/collections/transformation/SortedList.html
As you can see in the javadocs, it is part of the JavaFX collections, intended to provide a sorted view on an ObservableList.
Update: Note that with Java 11, the JavaFX toolkit has moved outside the JDK and is now a separate library. JavaFX 11 is available as a downloadable SDK or from MavenCentral. See https://openjfx.io

For any newcomers, as of April 2015, Android now has a SortedList class in the support library, designed specifically to work with RecyclerView. Here's the blog post about it.

Another point is the time complexity of insert operations.
For a list insert, one expects a complexity of O(1).
But this could not be guaranteed with a sorted list.
And the most important point is that lists assume nothing about their elements.
For example, you can make lists of things that do not implement equals or compare.

Think of it like this: the List interface has methods like add(int index, E element), set(int index, E element). The contract is that once you added an element at position X you will find it there unless you add or remove elements before it.
If any list implementation would store elements in some order other than based on the index, the above list methods would make no sense.

In case you are looking for a way to sort elements, but also be able to access them by index in an efficient way, you can do the following:
Use a random access list for storage (e.g. ArrayList)
Make sure it is always sorted
Then to add or remove an element you can use Collections.binarySearch to get the insertion / removal index. Since your list implements random access, you can efficiently modify the list with the determined index.
Example:
/**
* #deprecated
* Only for demonstration purposes. Implementation is incomplete and does not
* handle invalid arguments.
*/
#Deprecated
public class SortingList<E extends Comparable<E>> {
private ArrayList<E> delegate;
public SortingList() {
delegate = new ArrayList<>();
}
public void add(E e) {
int insertionIndex = Collections.binarySearch(delegate, e);
// < 0 if element is not in the list, see Collections.binarySearch
if (insertionIndex < 0) {
insertionIndex = -(insertionIndex + 1);
}
else {
// Insertion index is index of existing element, to add new element
// behind it increase index
insertionIndex++;
}
delegate.add(insertionIndex, e);
}
public void remove(E e) {
int index = Collections.binarySearch(delegate, e);
delegate.remove(index);
}
public E get(int index) {
return delegate.get(index);
}
}
(See a more complete implementation in this answer)

First line in the List API says it is an ordered collection (also known as a sequence). If you sort the list you can't maintain the order, so there is no TreeList in Java.
As API says Java List got inspired from Sequence and see the sequence properties http://en.wikipedia.org/wiki/Sequence_(mathematics)
It doesn't mean that you can't sort the list, but Java strict to his definition and doesn't provide sorted versions of lists by default.

I think all the above do not answer this question due to following reasons,
Since same functionality can be achieved by using other collections such as TreeSet, Collections, PriorityQueue..etc (but this is an alternative which will also impose their constraints i.e. Set will remove duplicate elements. Simply saying even if it does not impose any constraint, it does not answer the question why SortedList was not created by java community)
Since List elements do not implements compare/equals methods (This holds true for Set & Map also where in general items do not implement Comparable interface but when we need these items to be in sorted order & want to use TreeSet/TreeMap,items should implement Comparable interface)
Since List uses indexing & due to sorting it won't work (This can be easily handled introducing intermediate interface/abstract class)
but none has told the exact reason behind it & as I believe these kind of questions can be best answered by java community itself as it will have only one & specific answer but let me try my best to answer this as following,
As we know sorting is an expensive operation and there is a basic difference between List & Set/Map that List can have duplicates but Set/Map can not.
This is the core reason why we have got a default implementation for Set/Map in form of TreeSet/TreeMap. Internally this is a Red Black Tree with every operation (insert/delete/search) having the complexity of O(log N) where due to duplicates List could not fit in this data storage structure.
Now the question arises we could also choose a default sorting method for List also like MergeSort which is used by Collections.sort(list) method with the complexity of O(N log N). Community did not do this deliberately since we do have multiple choices for sorting algorithms for non distinct elements like QuickSort, ShellSort, RadixSort...etc. In future there can be more. Also sometimes same sorting algorithm performs differently depending on the data to be sorted. Therefore they wanted to keep this option open and left this on us to choose. This was not the case with Set/Map since O(log N) is the best sorting complexity.

https://github.com/geniot/indexed-tree-map
Consider using indexed-tree-map . It's an enhanced JDK's TreeSet that provides access to element by index and finding the index of an element without iteration or hidden underlying lists that back up the tree. The algorithm is based on updating weights of changed nodes every time there is a change.

We have Collections.sort(arr) method which can help to sort ArrayList arr. to get sorted in desc manner we can use Collections.sort(arr, Collections.reverseOrder())

SortedList that maintains order like SortedSet but also permits duplicate elements [duplicate]

In Java there are the SortedSet and SortedMap interfaces. Both belong to the Java Collections framework and provide a sorted way to access the elements.
However, in my understanding there is no SortedList in Java. You can use java.util.Collections.sort() to sort a list.
Any idea why it is designed like that?

List iterators guarantee first and foremost that you get the list's elements in the internal order of the list (aka. insertion order). More specifically it is in the order you've inserted the elements or on how you've manipulated the list. Sorting can be seen as a manipulation of the data structure, and there are several ways to sort the list.
I'll order the ways in the order of usefulness as I personally see it:
1. Consider using Set or Bag collections instead
NOTE: I put this option at the top because this is what you normally want to do anyway.
A sorted set automatically sorts the collection at insertion, meaning that it does the sorting while you add elements into the collection. It also means you don't need to manually sort it.
Furthermore if you are sure that you don't need to worry about (or have) duplicate elements then you can use the TreeSet<T> instead. It implements SortedSet and NavigableSet interfaces and works as you'd probably expect from a list:
TreeSet<String> set = new TreeSet<String>();
set.add("lol");
set.add("cat");
// automatically sorts natural order when adding
for (String s : set) {
System.out.println(s);
}
// Prints out "cat" and "lol"
If you don't want the natural ordering you can use the constructor parameter that takes a Comparator<T>.
Alternatively, you can use Multisets (also known as Bags), that is a Set that allows duplicate elements, instead and there are third-party implementations of them. Most notably from the Guava libraries there is a TreeMultiset, that works a lot like the TreeSet.
2. Sort your list with Collections.sort()
As mentioned above, sorting of Lists is a manipulation of the data structure. So for situations where you need "one source of truth" that will be sorted in a variety of ways then sorting it manually is the way to go.
You can sort your list with the java.util.Collections.sort() method. Here is a code sample on how:
List<String> strings = new ArrayList<String>()
strings.add("lol");
strings.add("cat");
Collections.sort(strings);
for (String s : strings) {
System.out.println(s);
}
// Prints out "cat" and "lol"
Using comparators
One clear benefit is that you may use Comparator in the sort method. Java also provides some implementations for the Comparator such as the Collator which is useful for locale sensitive sorting strings. Here is one example:
Collator usCollator = Collator.getInstance(Locale.US);
usCollator.setStrength(Collator.PRIMARY); // ignores casing
Collections.sort(strings, usCollator);
Sorting in concurrent environments
Do note though that using the sort method is not friendly in concurrent environments, since the collection instance will be manipulated, and you should consider using immutable collections instead. This is something Guava provides in the Ordering class and is a simple one-liner:
List<string> sorted = Ordering.natural().sortedCopy(strings);
3. Wrap your list with java.util.PriorityQueue
Though there is no sorted list in Java there is however a sorted queue which would probably work just as well for you. It is the java.util.PriorityQueue class.
Nico Haase linked in the comments to a related question that also answers this.
In a sorted collection you most likely don't want to manipulate the internal data structure which is why PriorityQueue doesn't implement the List interface (because that would give you direct access to its elements).
Caveat on the PriorityQueue iterator
The PriorityQueue class implements the Iterable<E> and Collection<E> interfaces so it can be iterated as usual. However, the iterator is not guaranteed to return elements in the sorted order. Instead (as Alderath points out in the comments) you need to poll() the queue until empty.
Note that you can convert a list to a priority queue via the constructor that takes any collection:
List<String> strings = new ArrayList<String>()
strings.add("lol");
strings.add("cat");
PriorityQueue<String> sortedStrings = new PriorityQueue(strings);
while(!sortedStrings.isEmpty()) {
System.out.println(sortedStrings.poll());
}
// Prints out "cat" and "lol"
4. Write your own SortedList class
NOTE: You shouldn't have to do this.
You can write your own List class that sorts each time you add a new element. This can get rather computation heavy depending on your implementation and is pointless, unless you want to do it as an exercise, because of two main reasons:
It breaks the contract that List<E> interface has because the add methods should ensure that the element will reside in the index that the user specifies.
Why reinvent the wheel? You should be using the TreeSet or Multisets instead as pointed out in the first point above.
However, if you want to do it as an exercise here is a code sample to get you started, it uses the AbstractList abstract class:
public class SortedList<E> extends AbstractList<E> {
private ArrayList<E> internalList = new ArrayList<E>();
// Note that add(E e) in AbstractList is calling this one
#Override
public void add(int position, E e) {
internalList.add(e);
Collections.sort(internalList, null);
}
#Override
public E get(int i) {
return internalList.get(i);
}
#Override
public int size() {
return internalList.size();
}
}
Note that if you haven't overridden the methods you need, then the default implementations from AbstractList will throw UnsupportedOperationExceptions.

Because the concept of a List is incompatible with the concept of an automatically sorted collection. The point of a List is that after calling list.add(7, elem), a call to list.get(7) will return elem. With an auto-sorted list, the element could end up in an arbitrary position.

Since all lists are already "sorted" by the order the items were added (FIFO ordering), you can "resort" them with another order, including the natural ordering of elements, using java.util.Collections.sort().
EDIT:
Lists as data structures are based in what is interesting is the ordering in which the items where inserted.
Sets do not have that information.
If you want to order by adding time, use List. If you want to order by other criteria, use SortedSet.

Set and Map are non-linear data structure. List is linear data structure.
The tree data structure SortedSet and SortedMap interfaces implements TreeSet and TreeMap respectively using used Red-Black tree implementation algorithm. So it ensure that there are no duplicated items (or keys in case of Map).
List already maintains an ordered collection and index-based data structure, trees are no index-based data structures.
Tree by definition cannot contain duplicates.
In List we can have duplicates, so there is no TreeList(i.e. no SortedList).
List maintains elements in insertion order. So if we want to sort the list we have to use java.util.Collections.sort(). It sorts the specified list into ascending order, according to the natural ordering of its elements.

JavaFX SortedList
Though it took a while, Java 8 does have a sorted List.
http://docs.oracle.com/javase/8/javafx/api/javafx/collections/transformation/SortedList.html
As you can see in the javadocs, it is part of the JavaFX collections, intended to provide a sorted view on an ObservableList.
Update: Note that with Java 11, the JavaFX toolkit has moved outside the JDK and is now a separate library. JavaFX 11 is available as a downloadable SDK or from MavenCentral. See https://openjfx.io

For any newcomers, as of April 2015, Android now has a SortedList class in the support library, designed specifically to work with RecyclerView. Here's the blog post about it.

Another point is the time complexity of insert operations.
For a list insert, one expects a complexity of O(1).
But this could not be guaranteed with a sorted list.
And the most important point is that lists assume nothing about their elements.
For example, you can make lists of things that do not implement equals or compare.

Think of it like this: the List interface has methods like add(int index, E element), set(int index, E element). The contract is that once you added an element at position X you will find it there unless you add or remove elements before it.
If any list implementation would store elements in some order other than based on the index, the above list methods would make no sense.

In case you are looking for a way to sort elements, but also be able to access them by index in an efficient way, you can do the following:
Use a random access list for storage (e.g. ArrayList)
Make sure it is always sorted
Then to add or remove an element you can use Collections.binarySearch to get the insertion / removal index. Since your list implements random access, you can efficiently modify the list with the determined index.
Example:
/**
* #deprecated
* Only for demonstration purposes. Implementation is incomplete and does not
* handle invalid arguments.
*/
#Deprecated
public class SortingList<E extends Comparable<E>> {
private ArrayList<E> delegate;
public SortingList() {
delegate = new ArrayList<>();
}
public void add(E e) {
int insertionIndex = Collections.binarySearch(delegate, e);
// < 0 if element is not in the list, see Collections.binarySearch
if (insertionIndex < 0) {
insertionIndex = -(insertionIndex + 1);
}
else {
// Insertion index is index of existing element, to add new element
// behind it increase index
insertionIndex++;
}
delegate.add(insertionIndex, e);
}
public void remove(E e) {
int index = Collections.binarySearch(delegate, e);
delegate.remove(index);
}
public E get(int index) {
return delegate.get(index);
}
}
(See a more complete implementation in this answer)

First line in the List API says it is an ordered collection (also known as a sequence). If you sort the list you can't maintain the order, so there is no TreeList in Java.
As API says Java List got inspired from Sequence and see the sequence properties http://en.wikipedia.org/wiki/Sequence_(mathematics)
It doesn't mean that you can't sort the list, but Java strict to his definition and doesn't provide sorted versions of lists by default.

I think all the above do not answer this question due to following reasons,
Since same functionality can be achieved by using other collections such as TreeSet, Collections, PriorityQueue..etc (but this is an alternative which will also impose their constraints i.e. Set will remove duplicate elements. Simply saying even if it does not impose any constraint, it does not answer the question why SortedList was not created by java community)
Since List elements do not implements compare/equals methods (This holds true for Set & Map also where in general items do not implement Comparable interface but when we need these items to be in sorted order & want to use TreeSet/TreeMap,items should implement Comparable interface)
Since List uses indexing & due to sorting it won't work (This can be easily handled introducing intermediate interface/abstract class)
but none has told the exact reason behind it & as I believe these kind of questions can be best answered by java community itself as it will have only one & specific answer but let me try my best to answer this as following,
As we know sorting is an expensive operation and there is a basic difference between List & Set/Map that List can have duplicates but Set/Map can not.
This is the core reason why we have got a default implementation for Set/Map in form of TreeSet/TreeMap. Internally this is a Red Black Tree with every operation (insert/delete/search) having the complexity of O(log N) where due to duplicates List could not fit in this data storage structure.
Now the question arises we could also choose a default sorting method for List also like MergeSort which is used by Collections.sort(list) method with the complexity of O(N log N). Community did not do this deliberately since we do have multiple choices for sorting algorithms for non distinct elements like QuickSort, ShellSort, RadixSort...etc. In future there can be more. Also sometimes same sorting algorithm performs differently depending on the data to be sorted. Therefore they wanted to keep this option open and left this on us to choose. This was not the case with Set/Map since O(log N) is the best sorting complexity.

https://github.com/geniot/indexed-tree-map
Consider using indexed-tree-map . It's an enhanced JDK's TreeSet that provides access to element by index and finding the index of an element without iteration or hidden underlying lists that back up the tree. The algorithm is based on updating weights of changed nodes every time there is a change.

We have Collections.sort(arr) method which can help to sort ArrayList arr. to get sorted in desc manner we can use Collections.sort(arr, Collections.reverseOrder())

Does the ArrayList's contains() method work faster if the ArrayList is ordered?

I suspect it doesn't. If I want to use the fact that the list is ordered, should I implement my own contains() method, using binary search, for example? Are there any methods that assume that the list is ordered?
This question is different to the possible duplicate because the other question doesn't ask about the contains() method.

No, because ArrayList is backed by array and internally calls indexOf(Object o) method where it searches sequentially. Thus sorting is not relevant to it. Here's the source code:
/**
* Returns the index of the first occurrence of the specified element
* in this list, or -1 if this list does not contain the element.
* More formally, returns the lowest index <tt>i</tt> such that
* <tt>(o==null ? get(i)==null : o.equals(get(i)))</tt>,
* or -1 if there is no such index.
*/
public int indexOf(Object o) {
if (o == null) {
for (int i = 0; i < size; i++)
if (elementData[i]==null)
return i;
} else {
for (int i = 0; i < size; i++)
if (o.equals(elementData[i]))
return i;
}
return -1;
}

Use binary search of collections to search in an ordered array list
Collections.<T>binarySearch(List<T> list, T key)
Arraylist.contains will consider this as a normal list and it would take the same amount of time as any unordered list that is O(n) whereas complexity of binary search would be O(logn) in worst case

No. contains uses indexOf:
public boolean contains(Object var1) {
return this.indexOf(var1) >= 0;
}
and indexOf just simply iterates over the internal array:
for(var2 = 0; var2 < this.size; ++var2) {
if (var1.equals(this.elementData[var2])) {
return var2;
}
}
Collections.binarySearch is what you're looking for:
Searches the specified list for the specified object using the binary
search algorithm. The list must be sorted into ascending order
according to the natural ordering of its elements (as by the
sort(List) method) prior to making this call. If it is not sorted, the
results are undefined.
Emphasis mine
Also consider using a SortedSet such as a TreeSet which will provide stronger guarantees that the elements are kept in the correct order, unlike a List which must rely on caller contracts (as highlighted above)

Does the ArrayList's contains() method work faster if the ArrayList is ordered?
It doesn't. The implementation of ArrayList does not know if the list is ordered or not. Since it doesn't know, it cannot optimize in the case when it is ordered. (And an examination of the source code bears this out.)
Could a (hypothetical) array-based-list implementation know? I think "No" for the following reasons:
Without either a Comparator or a requirement that elements implement Comparable, the concept of ordering is ill-defined.
The cost of checking that a list is ordered is O(N). The cost of incrementally checking that a list is still ordered is O(1) ... but still one or two calls to compare on each update operation. That is a significant overhead ... for a general purpose data structure to incur in the hope of optimizing (just) one operation in the API.
But that's OK. If you (the programmer) are able to ensure (ideally by efficient algorithmic means) that a list is always ordered, then you can use Collections.binarySearch ... with zero additional checking overhead in update operations.

Just to keep it simple.
If you have an array [5,4,3,2,1] and you order it to [1,2,3,4,5] will forks faster if you look for 1 but it will take longer to find 5. Consequently, from the mathematical point of view if you order an array, searching for an item inside will anyway require to loop from 1 to, in the worst case, n.
May be that for your problem sorting may help, say you receive unordered timestamps but
if your array is not too small
want to avoid the additional cost of sorting per each new entry in the array
you just want to find quickly an object
you know the Object properties you are searching for
you can create a KeyObject containing the properties you are looking for implements equals & hashCode for it then store your items into a Map. Using a Map.containsKey(new KeyObject(prop1, prop2)) would be in any case faster than looping the array. If you do not have the real object you can always create a fake KeyObject, filled with the properties you expect, to check the Map.

How to write a transitive comparator when "equality" implies "order doesn't matter"? [duplicate]

This question already has answers here:
Partial ordered Comparator
(6 answers)
Closed 8 years ago.
I have a set of items that are serialized to a file. Some items can rely on other items, but circular references are not allowed. Thus, they need to be serialized in a way such that if A relies on B, B is serialized first in the file.
I wrote my Comparator that uses a reliesOn() function to determine if two items are linked:
Collections.sort(itemsToSort, new Comparator<Item>() {
#Override
public int compare(Item first, Item second) {
boolean firstReliesOnSecond = reliesOn(first, second);
if (firstReliesOnSecond) {
return 1;
}
boolean secondReliesOnFirst = reliesOn(second, first);
if (secondReliesOnFirst) {
return -1;
}
return 0;
}
});
This works for some cases, but not all. In debugging, it's obvious that the sort relies on the transitive nature of the Comparator, and understandably does not compare every possible pairing of items.
For example, with five items A through E, if:
A -> B
B -> E
C
D
E
Then one possible ordering would be:
E, B, A, C, D
At the very least, E comes before B, and B comes before A.
However, during the comparison phase (paraphrasing as an example), what happens is that C is compared to E, returning 0 because they have no relation. And then C is compared to B, and also returns 0.
And as a result, the sorting algorithm assumes B = E, which is not the case. (Even though I broke the Comparator contract.) How can I write my compare() method in a way that ensures transitivity?
Edit: It was pointed out that I'm performing a topological sort on a directed acyclic graph. I'm having flashbacks to my Data Structures course. Fortunately Wikipedia seems to have a good linear-time algorithm for performing this sort - I'll give it a shot.

How can I write my compare() method in a way that ensures transitivity?
As you've discovered the contract of a Comparator forces you to make a decision based on two given objects, while their relation in the overall sort may involve other objects.
What you have here is a DAG and what you're trying to do is a topological sort. The only way I see that it would be possible to do using a Comparator would be to first do a topological sort, and then using the indexes of the objects in this sorting as keys when implementing the comparator. But then of course there's no need for the comparator since you have already sorted the elements.

Breaking the contract of Comparator does little to help you, since the standard sorting algorithms assume that you honor it.
Besides implementing a topological sort algorithm from Wikipedia you can also take a look at this lib (which gets mentioned often when someone speaks of directed graphs and topological sorting) or that implementation.

Given a set of objects that have 2 values. Sort the set with respect to the 1st value and then with the 2nd value

Eg.:
{2,3},{1,2},(2,2},{3,1},{2,1} to {1,2},{2,1},{2,2},{2,3},{3,1}
Here's what I'm thinking:
Do a merge sort on the first column of values. Iterate over the set to see if there are any duplicate values in the first column. If there are, enqueue them onto a list.
Merge sort this list on the second column and then integrate them into the main set. While it does seem feasible to do, it seems overly complicated. This should run in O(NlogN), so if somebody can think of a faster/same complexity algorithm that's also simpler, please post it!
Thanks!

Simply implement a Comparator<T> which compares any two objects of your type by first comparing the first field, and then moving on to the second field if the first fields are equal. You can then copy the set into a list, call Collections.sort and give it the list and your comparator. There's no need to implement sorting yourself.
The comparator would be something like:
public class TwoFieldComparator implements Comparator<Foo>
{
public int compare(Foo first, Foo second)
{
// TODO: null checks
int firstComparison = Integer.compare(first.x, second.x);
return firstComparison != 0 ? firstComparison
: Integer.compare(first.y, second.y);
}
}
Alternatively, you could make your class implement Comparable<T> in the same sort of way.

What you have to do is performing a stable sort on the second column then once more on the first column.
If the range of the numbers can be determined, O(N) can be achieved with some linear sort.
EDIT:
Take 'merge sort' as an example(for it's stable):
1, Run a merge sort on the second column, then number pairs will be arranged according to the value of second column.
2, Run a merge sort again on the first column, number pairs will be arranged in the order of first column value. However, because the sorting method is stable, that means if the first number is the same, the second number will be sorted as well(we did it in the first sort).
Thus, the num pair array is in order now. No more action is needed.
Merge sort is O(NlogN), thus 2*O(NlogN) is still O(NlogN).
EDIT2:
Well, I might make this problem complicated. Even if the sorting method is needed to be implemented by our own, as long as the data stucture has been determined, filling the compare code by Jon Skeet in the corresponding part of the hand-make sorting method will be the most convenient way.

As you mentioned in one of your commments, this is interview question. Solution by John Skeet shows that you don't have to worry about having two values in your item - just implement correct comparator.
Assuming that you are asked this at 2011, it would be good do find out how your sort is meant to be used. Depending on environment where this sort will be used, you may consider parallel processing (using multiple threads). That may drive your choice of sorting algorithm.