fastutil

Extends the the Java™ Collections Framework by providing type-specific maps, sets, lists and priority queues with a small memory footprint and fast access and insertion; provides also big (64-bit) arrays, sets and lists, and fast, practical I/O classes for binary and text files. It is free software distributed under the Apache License 2.0.

## Package Specification

`fastutil` is formed by three cores:

- type-specific classes that extend naturally the Java™ Collections Framework;
- classes that support very large collections;
- classes for fast and practical access to binary and text files.

The three cores are briefly introduced in the next sections, and then discussed at length in the rest of this overview.

### `fastutil` 8 at a glance

This is a section for previous `fastutil` users who would like to skim quickly through the new features:

- Java 8+ release.
- Type-specific versions of Java 8's new {@link java.util.Iterator} and {@link java.util.Map} methods, with default methods and full support in wrapper classes (synchronized, etc.).
- `fastutil`'s {@link it.unimi.dsi.fastutil.Function} extends JDK's {@link java.util.function.Function} and type-specific functions extend corresponding JDK primitive functions, using key widening where applicable (e.g., {@link it.unimi.dsi.fastutil.shorts.Short2IntFunction} extends {@link java.util.function.IntUnaryOperator}).
- Type-specific versions of {@link java.util.function.Consumer}.
- Clean-up of all deprecated methods.
- Many abstract classes have been made obsolete by default methods in the associated interfaces, and are now deprecated.
- Type-specific {@linkplain java.util.Comparator comparators}, {@linkplain it.unimi.dsi.fastutil.Function functions}, {@linkplain java.util.function.Consumer consumers} and ({@linkplain it.unimi.dsi.fastutil.BigSwapper big}) {@linkplain it.unimi.dsi.fastutil.Swapper swappers} can be defined using lambda expressions.
- Easy ways to exploit fast iterators for maps, even in for loops, using methods such as {@link it.unimi.dsi.fastutil.ints.Int2IntMaps#fastIterable(it.unimi.dsi.fastutil.ints.Int2IntMap)}.
- Structures based on hash tables never rehash below the size specified at construction time.

### Type-specific classes

`fastutil` specializes the most useful {@link java.util.HashSet}, {@link java.util.HashMap}, {@link java.util.LinkedHashSet}, {@link java.util.LinkedHashMap}, {@link java.util.TreeSet}, {@link java.util.TreeMap}, {@link java.util.IdentityHashMap}, {@link java.util.ArrayList} and {@link java.util.Stack} classes to versions that accept a specific kind of key or value (e.g., {@linkplain it.unimi.dsi.fastutil.ints.IntSet integers}). Besides, there are also several types of {@linkplain it.unimi.dsi.fastutil.PriorityQueue priority queues} and a large collection of static objects and methods (such as {@linkplain it.unimi.dsi.fastutil.objects.ObjectSets#EMPTY_SET immutable empty containers}, {@linkplain it.unimi.dsi.fastutil.ints.IntComparators#OPPOSITE_COMPARATOR comparators implementing the opposite of the natural order}, {@linkplain it.unimi.dsi.fastutil.ints.IntIterators#wrap(int[]) iterators obtained by wrapping an array} and so on).

To understand what's going on at a glance, the best thing is to look at the examples provided. If you already used the Collections Framework, everything should look rather natural. If, in particular, you use an IDE such as Eclipse, which can suggest you the method names, all you need to know is the right name for the class you need.

### Support for very large collections

A set of classes makes it possible to handle very large collections: in particular, collections whose size exceeds 231. {@linkplain it.unimi.dsi.fastutil.BigArrays Big arrays} are arrays-of-arrays handled by a wealth of static methods that act on them as if they were monodimensional arrays with 64-bit indices; {@linkplain it.unimi.dsi.fastutil.BigList big lists} provide 64-bit list access; {@linkplain it.unimi.dsi.fastutil.ints.IntOpenHashBigSet big hash sets} provide support for sets whose size is only limited by the amount of core memory.

The usual methods from {@link java.util.Arrays} and similar classes have been extended to big arrays: have a look at the Javadoc documentation of {@link it.unimi.dsi.fastutil.BigArrays} and {@link it.unimi.dsi.fastutil.ints.IntBigArrays} to get an idea of the generic and type-specific methods available.

### Fast and practical I/O

`fastutil` provides replacements for some standard classes of {@link java.io} that are plagued by a number of problems (see, e.g., {@link it.unimi.dsi.fastutil.io.FastBufferedInputStream}). The {@link it.unimi.dsi.fastutil.io.BinIO} and {@link it.unimi.dsi.fastutil.io.TextIO} static containers contain dozens of methods that make it possible to load and save quickly (big) arrays to disks, to adapt binary and text file to iterators, and so on.

## More on type-specific classes

All data structures in `fastutil` extend their standard counterpart interface whenever possible (e.g., {@link java.util.Map} for maps). Thus, they can be just plugged into existing code, using the standard access methods (of course, any attempt to use the wrong type for keys or values will produce a {@link java.lang.ClassCastException}). However, they also provide (whenever possible) many polymorphic versions of the most used methods that avoid boxing/unboxing. In doing so, they specify more stringent interfaces that extend and strengthen the standard ones (e.g., {@link it.unimi.dsi.fastutil.ints.Int2IntSortedMap} or {@link it.unimi.dsi.fastutil.ints.IntListIterator}). All generic methods in type-specific interfaces have been deprecated.

Warning: automatic boxing and unboxing can lead you to choose the wrong method when using `fastutil`. It is also extremely inefficient. We suggest that your programming environment is set so to mark boxing/unboxing as a warning, or even better, as an error.

Of course, the main point of type-specific data structures is that the absence of wrappers around primitive types can increase speed and reduce space occupancy by several times. The presence of generics in Java does not change this fact, since there is no genericity for primitive types.

The implementation techniques used in `fastutil` are quite different than those of {@link java.util}: for instance, open-addressing hash tables, threaded AVL trees, threaded red-black trees and exclusive-or lists. An effort has also been made to provide powerful derived objects and to expose them by overriding covariantly return types: for instance, the {@linkplain it.unimi.dsi.fastutil.objects.Object2IntSortedMap#keySet() keys of sorted maps are sorted} and iterators on sorted containers are always {@linkplain it.unimi.dsi.fastutil.BidirectionalIterator bidirectional}.

More generally, the rationale behing `fastutil` is that you should never need to code explicitly natural transformations. You do to not need to define an anonymous class to iterate over an array of integers—just {@linkplain it.unimi.dsi.fastutil.ints.IntIterators#wrap(int[]) wrap it}. You do not need to write a loop to put the characters returned by an iterator into a set—just {@linkplain it.unimi.dsi.fastutil.chars.CharOpenHashSet#CharOpenHashSet(CharIterator) use the right constructor}. And so on.

### The Names

In general, class names adhere to the general pattern

valuetype collectiontype

for collections, and

keytype 2 valuetype maptype

for maps.

The word "type" here referes to a capitalized primitive type, {@link java.lang.Object} or `Reference`. In the latter case, we are treating objects, but their equality is established by reference equality (that is, without invoking `equals()`), similarly to {@link java.util.IdentityHashMap}. Of course, reference-based classes are significantly faster.

Thus, an {@link it.unimi.dsi.fastutil.ints.IntOpenHashSet} stores integers efficiently and implements {@link it.unimi.dsi.fastutil.ints.IntSet}, whereas a {@link it.unimi.dsi.fastutil.longs.Long2IntAVLTreeMap} does the same for maps from longs to integers (but the map will be sorted, tree based, and balanced using the AVL criterion), implementing {@link it.unimi.dsi.fastutil.longs.Long2IntMap}. If you need additional flexibility in choosing your {@linkplain it.unimi.dsi.fastutil.Hash.Strategy hash strategy}, you can put, say, arrays of integers in a {@link it.unimi.dsi.fastutil.objects.ObjectOpenCustomHashSet}, maybe using the ready-made {@linkplain it.unimi.dsi.fastutil.ints.IntArrays#HASH_STRATEGY hash strategy for arrays}. A {@link it.unimi.dsi.fastutil.longs.LongLinkedOpenHashSet} stores longs in a hash table, but provides a predictable iteration order (the insertion order) and access to first/last elements of the order. A {@link it.unimi.dsi.fastutil.objects.Reference2ReferenceOpenHashMap} is similar to an {@link java.util.IdentityHashMap}. You can manage a priority queue of characters in a heap using a {@link it.unimi.dsi.fastutil.chars.CharHeapPriorityQueue}, which implements {@link it.unimi.dsi.fastutil.chars.CharPriorityQueue}. {@linkplain it.unimi.dsi.fastutil.bytes.ByteArrayFrontCodedList Front-coded lists} are highly specialized immutable data structures that store compactly a large number of arrays: if you don't know them you probably don't need them.

For a number of data structures that were not available in the Java™ Collections Framework when `fastutil` was created, an object-based version is contained in {@link it.unimi.dsi.fastutil}, and in that case the prefix `Object` is not used (see, e.g., {@link it.unimi.dsi.fastutil.PriorityQueue}).

Since there are eight primitive types in Java, and we support reference-based containers, we get around 2000 (!) classes (some nonsensical classes, such as `Boolean2BooleanAVLTreeMap`, are not generated). Many classes are generated just to mimic the hierarchy of {@link java.util} so to redistribute common code in a similar way. There are also several abstract classes that ease significantly the creation of new type-specific classes by providing automatically generic methods based on the type-specific ones.

The huge number of classes required a suitable division in subpackages. Each subpackage is characterized by the type of elements or keys: thus, for instance, {@link it.unimi.dsi.fastutil.ints.IntSet} belongs to {@link it.unimi.dsi.fastutil.ints} (the plural is required, as `int` is a keyword and cannot be used in a package name), as well as {@link it.unimi.dsi.fastutil.ints.Int2ReferenceRBTreeMap}. Note that all classes for non-primitive elements and keys are gathered in {@link it.unimi.dsi.fastutil.objects}. Finally, a number of non-type-specific classes have been gathered in {@link it.unimi.dsi.fastutil}.

### An In–Depth Look

The following table summarizes the available interfaces and implementations. To get more information, you can look at a specific implementation in {@link it.unimi.dsi.fastutil} or, for instance, {@link it.unimi.dsi.fastutil.ints}. Note that a few existing abstract classes have been deprecated and are not listed here (they are no longer necessary due to default methods in the corresponding interfaces).

Interfaces | Abstract Implementations | Implementations
--- | --- | ---
Iterable
Collection | AbstractCollection
Set | AbstractSet | OpenHashSet, OpenCustomHashSet, ArraySet, OpenHashBigSet
SortedSet | AbstractSortedSet | RBTreeSet, AVLTreeSet, LinkedOpenHashSet
Function | AbstractFunction |
Map | AbstractMap | OpenHashMap, OpenCustomHashMap, ArrayMap
SortedMap | AbstractSortedMap | RBTreeMap, AVLTreeMap, LinkedOpenHashMap
List, BigList† | AbstractList, AbstractBigList | ArrayList, BigArrayBigList, ArrayFrontCodedList
PriorityQueue† |  | HeapPriorityQueue, ArrayPriorityQueue, ArrayFIFOQueue
IndirectPriorityQueue† |  | HeapSemiIndirectPriorityQueue, HeapIndirectPriorityQueue, ArrayIndirectPriorityQueue
Stack† |  | ArrayList
Iterator, BigListIterator†
Comparator
BidirectionalIterator†
ListIterator
Consumer
Size64‡

†: this class has also a non-type-specific implementation in {@link it.unimi.dsi.fastutil}.

‡: this class has only a non-type-specific implementation in {@link it.unimi.dsi.fastutil}.

Note that abstract implementations are named by prefixing the interface name with `Abstract`. Thus, if you want to define a type-specific structure holding a set of integers without the hassle of defining object-based methods, you should inherit from {@link it.unimi.dsi.fastutil.ints.AbstractIntSet}.

The following table summarizes static containers, which usually give rise both to a type-specific and to a generic class:

Static Containers
Collections
Sets
SortedSets
Functions
Maps†
SortedMaps
Lists
BigLists
Arrays†
BigArrays†
Heaps
SemiIndirectHeaps
IndirectHeaps
PriorityQueues†
IndirectPriorityQueues†
Iterators
BigListIterators
Comparators
Hash‡
HashCommon‡
SafeMath‡

†: this class has also a non-type-specific implementation in {@link it.unimi.dsi.fastutil}.

‡: this class has only a non-type-specific implementation in {@link it.unimi.dsi.fastutil}.

The static containers provide also special-purpose implementations for all kinds of {@linkplain it.unimi.dsi.fastutil.objects.ObjectSets#EMPTY_SET empty structures} (including {@linkplain it.unimi.dsi.fastutil.objects.ObjectArrays#EMPTY_ARRAY arrays}) and {@linkplain it.unimi.dsi.fastutil.ints.Int2IntMaps#singleton(int,int) singletons}.

### Warnings

All classes are not synchronized. If multiple threads access one of these classes concurrently, and at least one of the threads modifies it, it must be synchronized externally. Iterators will behave unpredictably in the presence of concurrent modifications. Reads, however, can be carried out concurrently.

Reference-based classes violate the {@link java.util.Map} contract. They intentionally compare objects by reference, and do not use the `equals()` method. They should be used only when reference-based equality is desired (for instance, if all objects involved are canonized, as it happens with interned strings).

Setting the default return value for maps with both non-primitive keys and non-primitive values violates the {@link java.util.Map} contract, as you might not get `null` on missing keys.

Linked classes do not implement wholly the {@link java.util.SortedMap} interface. They provide methods to get the first and last element in iteration order, and to start a bidirectional iterator from any element, but any submap or subset method will cause an {@link java.lang.UnsupportedOperationException} (this may change in future versions).

Substructures in sorted classes allow the creation of arbitrary substructures. In {@link java.util}, instead, you can only create contained sub-substructures (BTW, why?). For instance, `(new TreeSet()).tailSet(1).tailSet(0)` will throw an exception, but {@link it.unimi.dsi.fastutil.ints.IntRBTreeSet (new IntRBTreeSet()).tailSet(1).tailSet(0)} won't.

### Additional Features and Methods

The new interfaces add some very natural methods and strengthen many of the old ones. Moreover, whenever possible, the object returned is type-specific, or implements a more powerful interface.

More in detail:

- Keys and values of a map are of the `fastutil` type you would expect (e.g., the keys of an {@link it.unimi.dsi.fastutil.ints.Int2LongSortedMap} are an {@link it.unimi.dsi.fastutil.ints.IntSortedSet} and the values are a {@link it.unimi.dsi.fastutil.longs.LongCollection}).
- Hash-based and tree-based maps that return primitive numeric values have an `addTo()` method (see, e.g., {@link it.unimi.dsi.fastutil.ints.Int2IntOpenHashMap#addTo(int,int)}) that adds an increment to the current value of a key; it is most useful to avoid the inefficient procedure of getting a value, incrementing it and then putting it back into the map (typically, when counting the number of occurrences of elements in a sequence).
- Hash-set implementations have an additional {@link it.unimi.dsi.fastutil.objects.ObjectOpenHashSet#get(Object) get()} method that returns the actual object in the collection that is equal to the query key.
- Linked hash-based maps and sets have a wealth of additional methods that make it easy to use them as caches. See, for instance, {@link it.unimi.dsi.fastutil.ints.Int2IntLinkedOpenHashMap#putAndMoveToLast(int,int)}, {@link it.unimi.dsi.fastutil.ints.IntLinkedOpenHashSet#addAndMoveToLast(int)} or {@link it.unimi.dsi.fastutil.ints.Int2IntLinkedOpenHashMap#removeFirstInt()}.
- Submaps of a sorted map and subsets of a sorted sets are of the `fastutil` type you would expect, too.
- Iterators returned by `iterator()` are type-specific.
- Sorted structures in `fastutil` return type-specific {@linkplain it.unimi.dsi.fastutil.BidirectionalIterator bidirectional iterators}. This means that you can move back and forth among entries, keys or values.
- Some classes for maps (check the specification) return a fast entry set (see, e.g., {@link it.unimi.dsi.fastutil.ints.Int2IntOpenHashMap#int2IntEntrySet()}); fast entry sets can, in turn, provide a {@linkplain it.unimi.dsi.fastutil.ints.Int2IntMap.FastEntrySet#fastIterator() fast iterator} that is guaranteed not to create a large number of objects, possibly by returning always the same entry (of course, mutated). There's a also companion {@link it.unimi.dsi.fastutil.ints.Int2IntMap.FastEntrySet#fastForEach(java.util.function.Consumer) fastForEach()}. To make it possible to access these fast iterators in `for` loops, there are static helper methods available (e.g., {@link it.unimi.dsi.fastutil.ints.Int2IntMaps#fastIterable(it.unimi.dsi.fastutil.ints.Int2IntMap)}).
- The type-specific sorted set interfaces, moreover, feature an optional method `iterator(from)` which creates a type-specific {@link it.unimi.dsi.fastutil.BidirectionalIterator} starting from a given element of the domain (not necessarily in the set). See, for instance, {@link it.unimi.dsi.fastutil.ints.IntSortedSet#iterator(int)}. The method is implemented by all type-specific sorted sets and subsets.
- Finally, there are constructors that allow you to build easily sets using array and iterators. This means, for instance, that you can create quickly a set of strings with a statement like

  > `new ObjectOpenHashSet( new String[] { "foo", "bar" } )`

  or just "unroll" the integers returned by an iterator into a list with

  > `new IntArrayList( iterator )`

There are a few quirks, however, that you should be aware of:

- The versions of the {@link java.util.Map#get(Object) get()}, {@link java.util.Map#put(Object,Object) put()} and {@link java.util.Map#remove(Object) remove()} methods that return a primitive type cannot, of course, rely on returning `null` to denote the absence of a certain pair. Rather, they return a {@linkplain it.unimi.dsi.fastutil.ints.Int2LongMap#defaultReturnValue(long) default return value}, which is set to 0 cast to the return type (`false` for booleans) at creation, but can be changed using the `defaultReturnValue()` method (see, e.g., {@link it.unimi.dsi.fastutil.ints.Int2IntMap}). Note that changing the default return value does not change anything about the data structure; it is just a way to return a reasonably meaningful result—it can be changed at any time. For uniformity reasons, even maps returning objects can use `defaultReturnValue()` (of course, in this case the default return value is initialized to `null`). A submap or subset has an independent default return value (which however is initialized to the default return value of the originator).
- For all maps that have objects as keys, the {@link java.util.Map#get(Object) get()} and {@link java.util.Map#remove(Object) remove()} methods do not admit polymorphic versions, as Java does not allow return-value polymorphism. Rather, the extended interfaces introduce new methods of the form {@link it.unimi.dsi.fastutil.objects.Object2IntOpenHashMap#getInt(Object) getvaluetype()} and {@link it.unimi.dsi.fastutil.objects.Object2IntOpenHashMap#removeInt(Object) removevaluetype()}. Similar problems occur with {@link it.unimi.dsi.fastutil.chars.CharSortedSet#firstChar() first()}, {@link it.unimi.dsi.fastutil.chars.CharSortedSet#lastChar() last()}, and so on.
- Similarly, all iterators have a suitable method {@link it.unimi.dsi.fastutil.ints.IntIterator#nextInt() nexttype()} returning directly a primitive type. And, of course, you have a type-specific version of {@link java.util.ListIterator#previous() previous()}.
- For the same reason, the method {@link java.util.Collection#toArray} as a polymorphic version accepting a type-specific array, but there is also an explicitly typed method {@link it.unimi.dsi.fastutil.bytes.ByteCollection#toByteArray() tokeytypeArray()}.
- The standard entry-set iterators for hash-based maps use an entry object that refers to the data contained in the hash table. If you retrieve an entry and delete it, the entry object will become invalid and will throw an {@link java.util.ArrayIndexOutOfBounds} exception. This does not apply to fast iterators (see above).
- A name clash between the list and collection interfaces forces the deletion method of a collection to be named {@link it.unimi.dsi.fastutil.doubles.DoubleCollection#rem(double) rem()}. At the risk of creating some confusion, {@link it.unimi.dsi.fastutil.doubles.DoubleSet#remove(double) remove()} reappears in the type-specific set interfaces, so the only really unpleasant effect is that you must use `rem()` on variables that are collections, but not sets—for instance, {@linkplain it.unimi.dsi.fastutil.ints.IntList type-specific lists}, and that a subclass of a type-specific abstract collection must override `rem()`, rather than `remove()`, to make all inherited methods work properly.
- Stacks are interfaces implemented by array-based lists: the interface, moreover, is slightly different from the implementation contained in {@link java.util.Stack}.
- In JDK 8 a number of classes appeared specifying primitive-type interfaces: examples are {@link java.util.PrimitiveIterator} and {@link java.util.function.IntToLongFunction}. Whenever possible, `fastutil` tries to extend such interfaces (e.g., {@link it.unimi.dsi.fastutil.ints.IntIterator} extends {@link java.util.PrimitiveIterator.OfInt}).
- In the specification of new methods such as {@link java.util.Map#computeIfAbsent(Object,java.util.function.Function) Map.computeIfAbsent()} we do not always have a suitable type-specific version of {@link java.util.function.Function} in the JDK: in this case, we approximate the best we can. For example, a {@link it.unimi.dsi.fastutil.bytes.Byte2ByteMap} expects an {@link java.util.function.IntUnaryOperator}. The default implementation will check that the returned argument actually fits a byte, throwing an exception otherwise. Note that we always specify also a version accepting a function returning an object, as it is useful in case one needs to return {@code null}.
- In the specification of new methods requiring a type-specific {@link java.util.function.Consumer} such as {@link java.lang.Iterable#forEach(java.util.function.Consumer)} we try to use the {@link java.util.function} correct type, if available. Otherwise, we use the `fastutil` correct type-specific version, but, as in the previous case, the `fastutil` version extends the closest {@link java.util.function.Consumer}. For example, {@link it.unimi.dsi.fastutil.chars.CharConsumer} extends {@link java.util.function.IntConsumer}.

### Functions

{@link it.unimi.dsi.fastutil.Function} (and its type-specific versions) is an interface geared towards mathematical functions (e.g., hashes) which associates values to keys, but in which enumerating keys or values is not possible. It is essentially a {@link java.util.Map} that does not provide access to set representations. It is of course unfortunate that Java 8 introduced an identically named interface with a different signature: differences and interoperability issues are discussed in the {@linkplain it.unimi.dsi.fastutil.Function class documentation}.

`fastutil` provides interfaces, abstract implementations and the usual array of wrappers in the suitable static container (e.g., {@link it.unimi.dsi.fastutil.ints.Int2IntFunctions}). Implementations will be provided by other projects (e.g., Sux4J). Type-specific functions require just to define their {@code get()} methods: thus, they can be defined by lambda expressions.

All `fastutil` type-specific maps extend their respective type-specific functions: but, alas, we cannot have {@link java.util.Map} extending {@link it.unimi.dsi.fastutil.Function}. Moreover, type-specific functions extend the existing type-specific function from {@link java.util.function} that can accommodate the argument and the result with the least widening: for example, {@link it.unimi.dsi.fastutil.shorts.Short2CharFunction} extends {@link java.util.function.IntUnaryOperator}.

### Static Container Classes

`fastutil` provides a number of static methods and singletons, much like {@link java.util.Collections}. To avoid creating classes with hundreds of methods, there are separate containers for sets, lists, maps and so on. Generic containers are placed in {@link it.unimi.dsi.fastutil}, whereas type-specific containers are in the appropriate package. You should look at the documentation of the static classes contained in {@link it.unimi.dsi.fastutil}, and in type-specific static classes such as {@link it.unimi.dsi.fastutil.chars.CharSets}, {@link it.unimi.dsi.fastutil.floats.Float2ByteSortedMaps}, {@link it.unimi.dsi.fastutil.longs.LongArrays}, {@link it.unimi.dsi.fastutil.floats.FloatHeaps}. Presently, you can easily obtain {@linkplain it.unimi.dsi.fastutil.objects.ObjectSets#EMPTY_SET empty collections}, {@linkplain it.unimi.dsi.fastutil.longs.Long2IntMaps#EMPTY_MAP empty type-specific collections}, {@linkplain it.unimi.dsi.fastutil.ints.IntLists#singleton(int) singletons}, {@linkplain it.unimi.dsi.fastutil.objects.Object2ReferenceSortedMaps#synchronize(Object2ReferenceSortedMap) synchronized versions} of any type-specific container and unmodifiable versions of {@linkplain it.unimi.dsi.fastutil.objects.ObjectLists#unmodifiable(ObjectList) containers} and {@linkplain it.unimi.dsi.fastutil.ints.IntIterators#unmodifiable(IntBidirectionalIterator) iterators} (of course, unmodifiable containers always return unmodifiable iterators).

On a completely different side, the {@linkplain it.unimi.dsi.fastutil.ints.IntArrays type-specific static container classes for arrays} provide several useful methods that allow to treat an array much like an array-based list, hiding completely the growth logic. In many cases, using this methods and an array is even simpler then using a full-blown {@linkplain it.unimi.dsi.fastutil.doubles.DoubleArrayList type-specific array-based list} because elements access is syntactically much simpler. The version for objects uses reflection to return arrays of the same type of the argument.

For the same reason, `fastutil` provides a full implementation of methods that manipulate arrays as type-specific {@linkplain it.unimi.dsi.fastutil.ints.IntHeaps heaps}, {@linkplain it.unimi.dsi.fastutil.ints.IntSemiIndirectHeaps semi-indirect heaps} and {@linkplain it.unimi.dsi.fastutil.ints.IntIndirectHeaps indirect heaps}. There are also quicksort and mergesort implementations that use arbitrary type-specific comparators.

`fastutil` offers also a less common choice—a very tuned implementation of {@linkplain it.unimi.dsi.fastutil.ints.IntArrays#radixSort(int[],int,int) radix sort} for all primitive types. It is significantly faster than quicksort already at small sizes (say, more than 10000 elements), and should be considered the sorting algorithm of choice if you do not need a generic comparator.

There are several variants provided. First of all you can radix sort in parallel {@linkplain it.unimi.dsi.fastutil.ints.IntArrays#radixSort(int[],int[], int, int) two} or {@linkplain it.unimi.dsi.fastutil.ints.IntArrays#radixSort(int[][],int,int) even more} arrays. You can also perform {@linkplain it.unimi.dsi.fastutil.ints.IntArrays#radixSortIndirect(int[],int[],int,int,boolean) indirect} sorts, for instance if you want to compute the sorting permutation of an array.

The sorting algorithm is a tuned radix sort adapted from Peter M. McIlroy, Keith Bostic and M. Douglas McIlroy, “Engineering radix sort”, Computing Systems, 6(1), pages 5−27 (1993), and further improved using the digit-oracle idea described by Juha Kärkkäinen and Tommi Rantala in “Engineering radix sort for strings”, String Processing and Information Retrieval, 15th International Symposium, volume 5280 of Lecture Notes in Computer Science, pages 3−14, Springer (2008). The basic algorithm is not stable, but this is immaterial for arrays of primitive types. For the indirect case, there is a parameter specifying whether the algorithm should be stable.

### Iterators and Comparators

`fastutil` provides type-specific iterators and comparators. The interface of a `fastutil` iterator is slightly more powerful than that of a {@link java.util} iterator, as it contains a {@link it.unimi.dsi.fastutil.objects.ObjectIterator#skip(int) skip()} method that allows to skip over a list of elements (an {@linkplain it.unimi.dsi.fastutil.objects.ObjectBidirectionalIterator#back(int) analogous method} is provided for bidirectional iterators). For objects (even those managed by reference), the extended interface is named {@link it.unimi.dsi.fastutil.objects.ObjectIterator}; it is the return type, for instance, of {@link it.unimi.dsi.fastutil.objects.ObjectCollection#iterator()}.

A plethora of useful static methods is also provided by various type-specific static containers (e.g., {@link it.unimi.dsi.fastutil.ints.IntIterators}) and {@link it.unimi.dsi.fastutil.ints.IntComparators}: among other things, you can {@linkplain it.unimi.dsi.fastutil.ints.IntIterators#wrap(int[]) wrap arrays} and {@linkplain it.unimi.dsi.fastutil.ints.IntIterators#asIntIterator(java.util.Iterator) standard iterators} in type-specific iterators, {@linkplain it.unimi.dsi.fastutil.ints.IntIterators#fromTo(int,int) generate them} giving an interval of elements to be returned, {@linkplain it.unimi.dsi.fastutil.objects.ObjectIterators#concat(ObjectIterator[]) concatenate them} or {@linkplain it.unimi.dsi.fastutil.objects.ObjectIterators#pour(Iterator,ObjectCollection) pour them} into a set.

### Queues

`fastutil` offers two types of queues: direct queues and indirect queues. A direct queue offers type-specific method to {@linkplain it.unimi.dsi.fastutil.longs.LongPriorityQueue#enqueue(long) enqueue} and {@linkplain it.unimi.dsi.fastutil.longs.LongPriorityQueue#dequeueLong() dequeue} elements. An indirect queue needs a reference array, specified at construction time: {@linkplain it.unimi.dsi.fastutil.IndirectPriorityQueue#enqueue(int) enqueue} and {@linkplain it.unimi.dsi.fastutil.IndirectPriorityQueue#dequeue() dequeue} operations refer to indices in the reference array. The advantage is that it may be possible to {@linkplain it.unimi.dsi.fastutil.IndirectPriorityQueue#changed(int) notify the change} of any element of the reference array, or even to {@linkplain it.unimi.dsi.fastutil.IndirectPriorityQueue#remove(int) remove an arbitrary element}.

Queues have two kind of implementations: array-based implementations, and heap-based implementations. In particular, heap-based indirect queues may be {@linkplain it.unimi.dsi.fastutil.objects.ObjectHeapIndirectPriorityQueue fully indirect} or just {@linkplain it.unimi.dsi.fastutil.objects.ObjectHeapSemiIndirectPriorityQueue semi-indirect}: in the latter case, there is no need for an explicit indirection array (which saves one integer per queue entry), but not all operations will be available. Note there there are also {@linkplain it.unimi.dsi.fastutil.ints.IntArrayFIFOQueue FIFO queues}.

### Custom Hashing

Sometimes, the behaviour of the built-in equality and hashing methods is not what you want. In particular, this happens if you store in a hash-based collection arrays, and you would like to compare them by equality. For this kind of applications, `fastutil` provides {@linkplain it.unimi.dsi.fastutil.Hash.Strategy custom hash strategies}, which define new equality and hashing methods to be used inside the collection. There are even {@linkplain it.unimi.dsi.fastutil.ints.IntArrays#HASH_STRATEGY ready-made strategies} for arrays. Note, however, that `fastutil` containers do not cache hash codes, so custom hash strategies must be efficient.

### Abstract Classes

`fastutil` provides a wide range of abstract classes, to help in implementing its interfaces. They take care, for instance, of providing wrappers for non-type-specific method calls, so that you have to write just the (usually simpler) type-specific version. When possible, such wrappers are actually default methods, so no abstract class is necessary.

## More on the support for very large collections

With the continuous increase in core memory available, Java arrays are starting to show their size limitation (indices cannot be larger than 231). `fastutil` proposes to store big arrays using arrays-of-arrays subject to certain size restrictions and a number of supporting static methods. Please read the documentation of {@link it.unimi.dsi.fastutil.BigArrays} to understand how big arrays work.

Correspondingly, `fastutil` proposes a new interface, called {@link it.unimi.dsi.fastutil.Size64}, that should be implemented by very large collections. {@link it.unimi.dsi.fastutil.Size64} contains a method {@link it.unimi.dsi.fastutil.Size64#size64()} which returns the collection size as a long integer.

`fastutil` provides {@linkplain it.unimi.dsi.fastutil.BigList big lists}, which are lists with 64-bit indices; of course, they implement {@link it.unimi.dsi.fastutil.Size64}. An implementation based on big arrays is provided (see, e.g., {@link it.unimi.dsi.fastutil.ints.IntBigArrayBigList}), as well as static containers (see, e.g., {@link it.unimi.dsi.fastutil.ints.IntBigLists}). Whereas it is unlikely that such collection will be in main memory as big arrays, there are number of situations, such as exposing large files through a list interface or storing a large amount of data using succinct data structures, in which a big list interface is natural.

Unfortunately, {@linkplain java.util.List lists} and {@linkplain it.unimi.dsi.fastutil.BigList big lists}, as well as {@linkplain java.util.ListIterator list iterators} and {@linkplain it.unimi.dsi.fastutil.BigListIterator big-list iterators}, cannot be made compatible: we thus provide adapters (see, e.g., {@link it.unimi.dsi.fastutil.ints.IntBigLists#asBigList(it.unimi.dsi.fastutil.ints.IntList)}).

Finally, `fastutil` provides {@linkplain it.unimi.dsi.fastutil.longs.LongOpenHashBigSet big hash sets}, which are based on big arrays. They are about 30% slower than non-big sets, but their size is limited only by the amount core memory.

## More on fast and practical I/O

`fastutil` includes an {@linkplain it.unimi.dsi.fastutil.io I/O package} that provides, for instance, {@linkplain it.unimi.dsi.fastutil.io.FastBufferedInputStream fast, unsynchronized buffered input streams}, {@linkplain it.unimi.dsi.fastutil.io.FastBufferedOutputStream fast, unsynchronized buffered output streams}, and a wealth of static methods to store and retrieve data in {@linkplain it.unimi.dsi.fastutil.io.TextIO textual} and {@linkplain it.unimi.dsi.fastutil.io.BinIO binary} form. The latter, in particular, contain methods that load and store big arrays.

## Performance

The main reason behind `fastutil` is performance, both in time and in space. The relevant methods of type-specific hash maps and sets are something like 2 to 10 times faster than those of the standard classes. Note that performance of hash-based classes on object keys is usually slightly worse than that of {@link java.util}, because `fastutil` classes do not cache hash codes (albeit it will not be that bad if keys cache internally hash codes, as in the case of {@link java.lang.String}). Of course, you can try to get more speed from hash tables using a small load factor: to this purpose, alternative load factors are proposed in {@link it.unimi.dsi.fastutil.Hash#FAST_LOAD_FACTOR} and {@link it.unimi.dsi.fastutil.Hash#VERY_FAST_LOAD_FACTOR}.

For tree-based classes you have two choices: AVL and red-black trees. The essential difference is that AVL trees are more balanced (their height is at most 1.44 log n), whereas red-black trees have faster deletions (but their height is at most 2 log n). So on small trees red-black trees could be faster, but on very large sets AVL trees will shine. In general, AVL trees have slightly slower updates but faster searches; however, on very large collections the smaller height may lead in fact to faster updates, too.

`fastutil` reduces enormously the creation and collection of objects. First of all, if you use the polymorphic methods and iterators no wrapper objects have to be created. Moreover, since `fastutil` uses open-addressing hashing techniques, creation and garbage collection of hash-table entries are avoided (but tables have to be rehashed whenever they are filled beyond the load factor). The major reduction of the number of objects around has a definite (but very difficult to measure) impact on the whole application (as garbage collection runs proportionally to the number of alive objects).

Maps whose iteration is very expensive in terms of object creation (e.g., hash-based classes) usually return a type-specific {@link it.unimi.dsi.fastutil.ints.Int2IntMap.FastEntrySet FastEntrySet} whose {@link it.unimi.dsi.fastutil.ints.Int2IntMap.FastEntrySet#fastIterator() fastIterator()} method significantly reduces object creation by returning always the same entry object, suitably mutated.

### Memory Usage

The absence of wrappers makes data structures in `fastutil` much smaller: even in the case of objects, however, data structures in `fastutil` try to be space-efficient.

#### Hash Tables

To avoid memory waste, (unlinked) hash tables in `fastutil` keep no additional information about elements (such as a list of keys). In particular, this means that enumerations are always linear in the size of the table (rather than in the number of keys). Usually, this would imply slower iterators. Nonetheless, the iterator code includes a single, tight loop; moreover, it is possible to avoid the creation of wrappers. These two facts make in practice `fastutil` iterators faster than {@link java.util}'s.

The memory footprint for a table of length ℓ is exactly the memory required for the related types times ℓ. The absence of wrappers around primitive types can reduce space occupancy by several times (this applies even more to serialized data, e.g., when you save such a data structure in a file). These figures can greatly vary with your virtual machine, JVM versions, CPU etc.

More precisely, when you ask for a map that will hold n elements with load factor 0 < f ≤ 1, 2⌈log n / f⌉ entries are allocated. When the table is filled up beyond the load factor, it is rehashed doubling its size. When it is emptied below one fourth of the load factor, it is rehashed halving its size; however, a map is never reduced to a size smaller than that at creation time: this approach makes it possible to create maps with a large capacity in which insertions and deletions do not cause immediately rehashing.

In the case of linked hash tables, there is an additional vector of 2⌈log n / f⌉ longs that is used to store link information. Each element records the next and previous element (packed together so to be more cache friendly).

#### Balanced Trees

The balanced trees implementation is also very parsimonious. `fastutil` is based on the excellent (and unbelievably well documented) code contained in Ben Pfaff's GNU libavl, which describes in detail how to handle balanced trees with threads. Thus, the overhead per entry is two pointers and one integer, which compares well to three pointers plus one boolean of the standard tree maps. The trick is that we use the integer bit by bit, so we consume two bits to store thread information, plus one or two bits to handle balancing. As a result, we get bidirectional iterators in constant space and amortized constant time without having to store references to parent nodes.

It should be mentioned that all tree-based classes have a fixed overhead for some arrays that are used as stacks to simulate recursion; in particular, we need 48 booleans for AVL trees and 64 pointers plus 64 booleans for red-black trees.

## An Example

Suppose you want to store a sorted map from longs to integers. The first step is to define a variable of the right interface, and assign it a new tree map (say, of the AVL type):

    Long2IntSortedMap m = new Long2IntAVLTreeMap();

Now we can easily modify and access its content:

    m.put(1, 5);
    m.put(2, 6);
    m.put(3, 7);
    m.put(1000000000L, 10);
    m.get(1); // This method call will return 5
    m.get(4); // This method call will return 0

We can also try to change the default return value:

    m.defaultReturnValue(-1);
    m.get(4); // This method call will return -1

We can obtain a type-specific iterator on the key set:

    LongBidirectionalIterator i = m.keySet().iterator();
    // Now we sum all keys
    long s = 0;
    while(i.hasNext()) s += i.nextLong();

We now generate a head map, and iterate bidirectionally over it starting from a given point:

    // This map contains only keys smaller than 4
    Long2IntSortedMap m1 = m.headMap(4);
    // This iterator is positioned between 2 and 3
    LongBidirectionalIterator t = m1.keySet().iterator(2);
    t.previous(); // This method call will return 2 (t.next() would return 3)

Should we need to access the map concurrently, we can wrap it:

    // This map can be safely accessed by many threads
    Long2IntSortedMap m2 = Long2IntSortedMaps.synchronize(m1);

Linked maps are very flexible data structures which can be used to implement, for instance, queues whose content can be probed efficiently:

    // This map remembers insertion order (note that we are using the array-based constructor)
    IntSortedSet s = new IntLinkedOpenHashSet(new int[] { 4, 3, 2, 1 });
    s.firstInt(); // This method call will return 4
    s.lastInt(); // This method call will return 1
    s.contains(5); // This method will return false
    IntBidirectionalIterator i = s.iterator(s.lastInt()); // We could even cast it to a list iterator
    i.previous(); // This method call will return 1
    i.previous(); // This method call will return 2
    s.remove(s.lastInt()); // This will remove the last element in constant time

Now, we play with iterators. It is easy to create iterators over intervals or over arrays, and combine them:

    IntIterator i = IntIterators.fromTo(0, 10); // This iterator will return 0, 1, ..., 9
    int[] a = new int[] { 5, 1, 9 };
    IntIterator j = IntIterators.wrap(a); // This iterator will return 5, 1, 9.
    IntIterator k = IntIterators.concat(new IntIterator[] { i , j }); // This iterator will return 0, 1, ..., 9, 5, 1, 9

It is easy to build sets and maps on the fly using the array-based constructors:

    IntSet s = new IntOpenHashSet(new int[] { 1, 2, 3 }); // This set will contain 1, 2, and 3
    Char2IntMap m = new Char2IntRBTreeMap(new char[] { '@', '-' }, new int[] { 0, 1 }); // This map will map '@' to 0 and '-' to 1

Whenever you have some data structure, it is easy to serialize it in an efficient (buffered) way, or to dump their content in textual form:

    BinIO.storeObject(s, "foo"); // This method call will save s in the file named "foo"
    TextIO.storeInts(s.intIterator(), "foo.txt"); // This method call will save the content of s in ASCII
    i = TextIO.asIntIterator("foo.txt"); // This iterator will parse the file and return the integers therein

You can sort arrays using type-specific comparators specified by lambda expressions (no boxing/unboxing here):

    IntArrays.quickSort(a, (x, y) -> y - x); // Sorts in reverse order

You can also easily specify complex generic sorting, like sorting indirectly on {@code a} while swapping elements in {@code a} and {@code b} in parallel:

    Arrays.quickSort(0, a.length, (i, j) -> Integer.compare(a[i], a[j]), (i, j) -> { IntArrays.swap(a, i, j); IntArrays.swap(b, i, j); }));

If you have several cores, you can do it in parallel:

    IntArrays.parallelQuickSort(a, (x, y) -> y - x); // Sorts in reverse order
    Arrays.parallelQuickSort(0, a.length, (i, j) -> Integer.compare(a[i], a[j]), (i, j) -> { IntArrays.swap(a, i, j); IntArrays.swap(b, i, j); }));

Some maps provide a fast iterator on their entry set: such iterators are allowed to reuse the {@link java.util.Map.Entry} instance they return, resulting is highly reduced garbage collection (e.g., for large hash maps). To easily access such iterators, we can use a helper static method:

    Int2IntOpenHashMap m = new Int2IntOpenHashMap();
    // Fill the map
    for (Int2IntMap.Entry e : Int2IntMaps.fastIterable(m)) {
        // do things with e.getIntKey() and e.getIntValue();
    }

The code above will not generate an object per enumerated item, as `for(Entry<Integer,Integer> e: m.entrySet())` (or even `for(Int2IntMap.Entry e: m.int2IntKeySet())`) would do.