github.com/mymmsc/gox@v1.3.33/util/README-gods.md

# GoDS (Go Data Structures)

Implementation of various data structures and algorithms in Go.

## Data Structures

- [Containers](#containers)
    - [Lists](#lists)
        - [ArrayList](#arraylist)
        - [SinglyLinkedList](#singlylinkedlist)
        - [DoublyLinkedList](#doublylinkedlist)
    - [Sets](#sets)
        - [HashSet](#hashset)
        - [TreeSet](#treeset)
        - [LinkedHashSet](#linkedhashset)
    - [Stacks](#stacks)
        - [LinkedListStack](#linkedliststack)
        - [ArrayStack](#arraystack)
    - [Maps](#maps)
        - [HashMap](#hashmap)
        - [TreeMap](#treemap)
        - [LinkedHashMap](#linkedhashmap)
        - [HashBidiMap](#hashbidimap)
        - [TreeBidiMap](#treebidimap)
    - [Trees](#trees)
        - [RedBlackTree](#redblacktree)
        - [AVLTree](#avltree)
        - [BTree](#btree)
        - [BinaryHeap](#binaryheap)
- [Functions](#functions)
    - [Comparator](#comparator)
    - [Iterator](#iterator)
        - [IteratorWithIndex](#iteratorwithindex)
        - [IteratorWithKey](#iteratorwithkey)
        - [ReverseIteratorWithIndex](#reverseiteratorwithindex)
        - [ReverseIteratorWithKey](#reverseiteratorwithkey)
    - [Enumerable](#enumerable)
        - [EnumerableWithIndex](#enumerablewithindex)
        - [EnumerableWithKey](#enumerablewithkey)
    - [Serialization](#serialization)
        - [JSONSerializer](#jsonserializer)
        - [JSONDeserializer](#jsondeserializer)
    - [Sort](#sort)
    - [Container](#container)
- [Appendix](#appendix)

## Containers

All data structures implement the container interface with the following methods:

```go
type Container interface {
	Empty() bool
	Size() int
	Clear()
	Values() []interface{}
}
```

Containers are either ordered or unordered. All ordered containers provide [stateful iterators](#iterator) and some of
them allow [enumerable functions](#enumerable).

| **Data** | **Structure** | **Ordered** | **[Iterator](#iterator)** | **[Enumerable](#enumerable)** | **Referenced
by** |
| :--- | :--- | :---: | :---: | :---: | :---: |
| [Lists](#lists) |
|   | [ArrayList](#arraylist) | yes | yes* | yes | index |
|   | [SinglyLinkedList](#singlylinkedlist) | yes | yes | yes | index |
|   | [DoublyLinkedList](#doublylinkedlist) | yes | yes* | yes | index |
| [Sets](#sets) |
|   | [HashSet](#hashset) | no | no | no | index |
|   | [TreeSet](#treeset) | yes | yes* | yes | index |
|   | [LinkedHashSet](#linkedhashset) | yes | yes* | yes | index |
| [Stacks](#stacks) |
|   | [LinkedListStack](#linkedliststack) | yes | yes | no | index |
|   | [ArrayStack](#arraystack) | yes | yes* | no | index |
| [Maps](#maps) |
|   | [HashMap](#hashmap) | no | no | no | key |
|   | [TreeMap](#treemap) | yes | yes* | yes | key |
|   | [LinkedHashMap](#linkedhashmap) | yes | yes* | yes | key |
|   | [HashBidiMap](#hashbidimap) | no | no | no | key* |
|   | [TreeBidiMap](#treebidimap) | yes | yes* | yes | key* |
| [Trees](#trees) |
|   | [RedBlackTree](#redblacktree) | yes | yes* | no | key |
|   | [AVLTree](#avltree) | yes | yes* | no | key |
|   | [BTree](#btree) | yes | yes* | no | key |
|   | [BinaryHeap](#binaryheap) | yes | yes* | no | index |
|   |  |  | <sub><sup>*reversible</sup></sub> |  | <sub><sup>*bidirectional</sup></sub> |

### Lists

A list is a data structure that stores values and may have repeated values.

Implements [Container](#containers) interface.

```go
type List interface {
	Get(index int) (interface{}, bool)
	Remove(index int)
	Add(values ...interface{})
	Contains(values ...interface{}) bool
	Sort(comparator utils.Comparator)
	Swap(index1, index2 int)
	Insert(index int, values ...interface{})
	Set(index int, value interface{})

	containers.Container
	// Empty() bool
	// Size() int
	// Clear()
	// Values() []interface{}
}
```

#### ArrayList

A [list](#lists) backed by a dynamic array that grows and shrinks implicitly.

Implements [List](#lists), [IteratorWithIndex](#iteratorwithindex), [EnumerableWithIndex](#enumerablewithindex)
, [JSONSerializer](#jsonserializer) and [JSONDeserializer](#jsondeserializer) interfaces.

```go
package main

import (
	"github.com/mymmsc/gox/util/lists/arraylist"
	"github.com/mymmsc/gox/util/utils"
)

func main() {
	list := arraylist.New()
	list.Add("a")                         // ["a"]
	list.Add("c", "b")                    // ["a","c","b"]
	list.Sort(utils.StringComparator)     // ["a","b","c"]
	_, _ = list.Get(0)                    // "a",true
	_, _ = list.Get(100)                  // nil,false
	_ = list.Contains("a", "b", "c")      // true
	_ = list.Contains("a", "b", "c", "d") // false
	list.Swap(0, 1)                       // ["b","a",c"]
	list.Remove(2)                        // ["b","a"]
	list.Remove(1)                        // ["b"]
	list.Remove(0)                        // []
	list.Remove(0)                        // [] (ignored)
	_ = list.Empty()                      // true
	_ = list.Size()                       // 0
	list.Add("a")                         // ["a"]
	list.Clear()                          // []
	list.Insert(0, "b")                   // ["b"]
	list.Insert(0, "a")                   // ["a","b"]
}
```

#### SinglyLinkedList

A [list](#lists) where each element points to the next element in the list.

Implements [List](#lists), [IteratorWithIndex](#iteratorwithindex), [EnumerableWithIndex](#enumerablewithindex)
, [JSONSerializer](#jsonserializer) and [JSONDeserializer](#jsondeserializer) interfaces.

```go
package main

import (
	sll "github.com/mymmsc/gox/util/lists/singlylinkedlist"
	"github.com/mymmsc/gox/util/utils"
)

func main() {
	list := sll.New()
	list.Add("a")                         // ["a"]
	list.Add("c", "b")                    // ["a","c","b"]
	list.Sort(utils.StringComparator)     // ["a","b","c"]
	_, _ = list.Get(0)                    // "a",true
	_, _ = list.Get(100)                  // nil,false
	_ = list.Contains("a", "b", "c")      // true
	_ = list.Contains("a", "b", "c", "d") // false
	list.Swap(0, 1)                       // ["b","a",c"]
	list.Remove(2)                        // ["b","a"]
	list.Remove(1)                        // ["b"]
	list.Remove(0)                        // []
	list.Remove(0)                        // [] (ignored)
	_ = list.Empty()                      // true
	_ = list.Size()                       // 0
	list.Add("a")                         // ["a"]
	list.Clear()                          // []
	list.Insert(0, "b")                   // ["b"]
	list.Insert(0, "a")                   // ["a","b"]
}
```

#### DoublyLinkedList

A [list](#lists) where each element points to the next and previous elements in the list.

Implements [List](#lists), [IteratorWithIndex](#iteratorwithindex), [EnumerableWithIndex](#enumerablewithindex)
, [JSONSerializer](#jsonserializer) and [JSONDeserializer](#jsondeserializer) interfaces.

```go
package main

import (
	dll "github.com/mymmsc/gox/util/lists/doublylinkedlist"
	"github.com/mymmsc/gox/util/utils"
)

func main() {
	list := dll.New()
	list.Add("a")                         // ["a"]
	list.Add("c", "b")                    // ["a","c","b"]
	list.Sort(utils.StringComparator)     // ["a","b","c"]
	_, _ = list.Get(0)                    // "a",true
	_, _ = list.Get(100)                  // nil,false
	_ = list.Contains("a", "b", "c")      // true
	_ = list.Contains("a", "b", "c", "d") // false
	list.Swap(0, 1)                       // ["b","a",c"]
	list.Remove(2)                        // ["b","a"]
	list.Remove(1)                        // ["b"]
	list.Remove(0)                        // []
	list.Remove(0)                        // [] (ignored)
	_ = list.Empty()                      // true
	_ = list.Size()                       // 0
	list.Add("a")                         // ["a"]
	list.Clear()                          // []
	list.Insert(0, "b")                   // ["b"]
	list.Insert(0, "a")                   // ["a","b"]
}
```

### Sets

A set is a data structure that can store elements and has no repeated values. It is a computer implementation of the
mathematical concept of a finite set. Unlike most other collection types, rather than retrieving a specific element from
a set, one typically tests an element for membership in a set. This structure is often used to ensure that no duplicates
are present in a container.

Implements [Container](#containers) interface.

```go
type Set interface {
	Add(elements ...interface{})
	Remove(elements ...interface{})
	Contains(elements ...interface{}) bool

	containers.Container
	// Empty() bool
	// Size() int
	// Clear()
	// Values() []interface{}
}
```

#### HashSet

A [set](#sets) backed by a hash table (actually a Go's map). It makes no guarantees as to the iteration order of the
set.

Implements [Set](#sets), [JSONSerializer](#jsonserializer) and [JSONDeserializer](#jsondeserializer) interfaces.

```go
package main

import "github.com/mymmsc/gox/util/sets/hashset"

func main() {
	set := hashset.New()   // empty
	set.Add(1)             // 1
	set.Add(2, 2, 3, 4, 5) // 3, 1, 2, 4, 5 (random order, duplicates ignored)
	set.Remove(4)          // 5, 3, 2, 1 (random order)
	set.Remove(2, 3)       // 1, 5 (random order)
	set.Contains(1)        // true
	set.Contains(1, 5)     // true
	set.Contains(1, 6)     // false
	_ = set.Values()       // []int{5,1} (random order)
	set.Clear()            // empty
	set.Empty()            // true
	set.Size()             // 0
}
```

#### TreeSet

A [set](#sets) backed by a [red-black tree](#redblacktree) to keep the elements ordered with respect to
the [comparator](#comparator).

Implements [Set](#sets), [IteratorWithIndex](#iteratorwithindex), [EnumerableWithIndex](#enumerablewithindex)
, [JSONSerializer](#jsonserializer) and [JSONDeserializer](#jsondeserializer) interfaces.

```go
package main

import "github.com/mymmsc/gox/util/sets/treeset"

func main() {
	set := treeset.NewWithIntComparator() // empty (keys are of type int)
	set.Add(1)                            // 1
	set.Add(2, 2, 3, 4, 5)                // 1, 2, 3, 4, 5 (in order, duplicates ignored)
	set.Remove(4)                         // 1, 2, 3, 5 (in order)
	set.Remove(2, 3)                      // 1, 5 (in order)
	set.Contains(1)                       // true
	set.Contains(1, 5)                    // true
	set.Contains(1, 6)                    // false
	_ = set.Values()                      // []int{1,5} (in order)
	set.Clear()                           // empty
	set.Empty()                           // true
	set.Size()                            // 0
}
```

#### LinkedHashSet

A [set](#sets) that preserves insertion-order. Data structure is backed by a hash table to store values
and [doubly-linked list](#doublylinkedlist) to store insertion ordering.

Implements [Set](#sets), [IteratorWithIndex](#iteratorwithindex), [EnumerableWithIndex](#enumerablewithindex)
, [JSONSerializer](#jsonserializer) and [JSONDeserializer](#jsondeserializer) interfaces.

```go
package main

import "github.com/mymmsc/gox/util/sets/linkedhashset"

func main() {
	set := linkedhashset.New() // empty
	set.Add(5)                 // 5
	set.Add(4, 4, 3, 2, 1)     // 5, 4, 3, 2, 1 (in insertion-order, duplicates ignored)
	set.Add(4)                 // 5, 4, 3, 2, 1 (duplicates ignored, insertion-order unchanged)
	set.Remove(4)              // 5, 3, 2, 1 (in insertion-order)
	set.Remove(2, 3)           // 5, 1 (in insertion-order)
	set.Contains(1)            // true
	set.Contains(1, 5)         // true
	set.Contains(1, 6)         // false
	_ = set.Values()           // []int{5, 1} (in insertion-order)
	set.Clear()                // empty
	set.Empty()                // true
	set.Size()                 // 0
}
```

### Stacks

A stack that represents a last-in-first-out (LIFO) data structure. The usual push and pop operations are provided, as
well as a method to peek at the top item on the stack.

Implements [Container](#containers) interface.

```go
type Stack interface {
	Push(value interface{})
	Pop() (value interface{}, ok bool)
	Peek() (value interface{}, ok bool)

	containers.Container
	// Empty() bool
	// Size() int
	// Clear()
	// Values() []interface{}
}
```

#### LinkedListStack

A [stack](#stacks) based on a [linked list](#singlylinkedlist).

Implements [Stack](#stacks), [IteratorWithIndex](#iteratorwithindex), [JSONSerializer](#jsonserializer)
and [JSONDeserializer](#jsondeserializer) interfaces.

```go
package main

import lls "github.com/mymmsc/gox/util/stacks/linkedliststack"

func main() {
	stack := lls.New()  // empty
	stack.Push(1)       // 1
	stack.Push(2)       // 1, 2
	stack.Values()      // 2, 1 (LIFO order)
	_, _ = stack.Peek() // 2,true
	_, _ = stack.Pop()  // 2, true
	_, _ = stack.Pop()  // 1, true
	_, _ = stack.Pop()  // nil, false (nothing to pop)
	stack.Push(1)       // 1
	stack.Clear()       // empty
	stack.Empty()       // true
	stack.Size()        // 0
}
```

#### ArrayStack

A [stack](#stacks) based on a [array list](#arraylist).

Implements [Stack](#stacks), [IteratorWithIndex](#iteratorwithindex), [JSONSerializer](#jsonserializer)
and [JSONDeserializer](#jsondeserializer) interfaces.

```go
package main

import "github.com/mymmsc/gox/util/stacks/arraystack"

func main() {
	stack := arraystack.New() // empty
	stack.Push(1)             // 1
	stack.Push(2)             // 1, 2
	stack.Values()            // 2, 1 (LIFO order)
	_, _ = stack.Peek()       // 2,true
	_, _ = stack.Pop()        // 2, true
	_, _ = stack.Pop()        // 1, true
	_, _ = stack.Pop()        // nil, false (nothing to pop)
	stack.Push(1)             // 1
	stack.Clear()             // empty
	stack.Empty()             // true
	stack.Size()              // 0
}
```

### Maps

A Map is a data structure that maps keys to values. A map cannot contain duplicate keys and each key can map to at most
one value.

Implements [Container](#containers) interface.

```go
type Map interface {
	Put(key interface{}, value interface{})
	Get(key interface{}) (value interface{}, found bool)
	Remove(key interface{})
	Keys() []interface{}

	containers.Container
	// Empty() bool
	// Size() int
	// Clear()
	// Values() []interface{}
}
```

A BidiMap is an extension to the Map. A bidirectional map (BidiMap), also called a hash bag, is an associative data
structure in which the key-value pairs form a one-to-one relation. This relation works in both directions by allow the
value to also act as a key to key, e.g. a pair (a,b) thus provides a coupling between 'a' and 'b' so that 'b' can be
found when 'a' is used as a key and 'a' can be found when 'b' is used as a key.

```go
type BidiMap interface {
	GetKey(value interface{}) (key interface{}, found bool)

	Map
}
```

#### HashMap

A [map](#maps) based on hash tables. Keys are unordered.

Implements [Map](#maps), [JSONSerializer](#jsonserializer) and [JSONDeserializer](#jsondeserializer) interfaces.

```go
package main

import "github.com/mymmsc/gox/util/maps/hashmap"

func main() {
	m := hashmap.New() // empty
	m.Put(1, "x")      // 1->x
	m.Put(2, "b")      // 2->b, 1->x (random order)
	m.Put(1, "a")      // 2->b, 1->a (random order)
	_, _ = m.Get(2)    // b, true
	_, _ = m.Get(3)    // nil, false
	_ = m.Values()     // []interface {}{"b", "a"} (random order)
	_ = m.Keys()       // []interface {}{1, 2} (random order)
	m.Remove(1)        // 2->b
	m.Clear()          // empty
	m.Empty()          // true
	m.Size()           // 0
}
```

#### TreeMap

A [map](#maps) based on [red-black tree](#redblacktree). Keys are ordered ordered with respect to
the [comparator](#comparator).

Implements [Map](#maps), [IteratorWithKey](#iteratorwithkey), [EnumerableWithKey](#enumerablewithkey)
, [JSONSerializer](#jsonserializer) and [JSONDeserializer](#jsondeserializer) interfaces.

```go
package main

import "github.com/mymmsc/gox/util/maps/treemap"

func main() {
	m := treemap.NewWithIntComparator() // empty (keys are of type int)
	m.Put(1, "x")                       // 1->x
	m.Put(2, "b")                       // 1->x, 2->b (in order)
	m.Put(1, "a")                       // 1->a, 2->b (in order)
	_, _ = m.Get(2)                     // b, true
	_, _ = m.Get(3)                     // nil, false
	_ = m.Values()                      // []interface {}{"a", "b"} (in order)
	_ = m.Keys()                        // []interface {}{1, 2} (in order)
	m.Remove(1)                         // 2->b
	m.Clear()                           // empty
	m.Empty()                           // true
	m.Size()                            // 0

	// Other:
	m.Min() // Returns the minimum key and its value from map.
	m.Max() // Returns the maximum key and its value from map.
}
```

#### LinkedHashMap

A [map](#maps) that preserves insertion-order. It is backed by a hash table to store values
and [doubly-linked list](doublylinkedlist) to store ordering.

Implements [Map](#maps), [IteratorWithKey](#iteratorwithkey), [EnumerableWithKey](#enumerablewithkey)
, [JSONSerializer](#jsonserializer) and [JSONDeserializer](#jsondeserializer) interfaces.

```go
package main

import "github.com/mymmsc/gox/util/maps/linkedhashmap"

func main() {
	m := linkedhashmap.New() // empty (keys are of type int)
	m.Put(2, "b")            // 2->b
	m.Put(1, "x")            // 2->b, 1->x (insertion-order)
	m.Put(1, "a")            // 2->b, 1->a (insertion-order)
	_, _ = m.Get(2)          // b, true
	_, _ = m.Get(3)          // nil, false
	_ = m.Values()           // []interface {}{"b", "a"} (insertion-order)
	_ = m.Keys()             // []interface {}{2, 1} (insertion-order)
	m.Remove(1)              // 2->b
	m.Clear()                // empty
	m.Empty()                // true
	m.Size()                 // 0
}

```

#### HashBidiMap

A [map](#maps) based on two hashmaps. Keys are unordered.

Implements [BidiMap](#maps), [JSONSerializer](#jsonserializer) and [JSONDeserializer](#jsondeserializer) interfaces.

```go
package main

import "github.com/mymmsc/gox/util/maps/hashbidimap"

func main() {
	m := hashbidimap.New() // empty
	m.Put(1, "x")          // 1->x
	m.Put(3, "b")          // 1->x, 3->b (random order)
	m.Put(1, "a")          // 1->a, 3->b (random order)
	m.Put(2, "b")          // 1->a, 2->b (random order)
	_, _ = m.GetKey("a")   // 1, true
	_, _ = m.Get(2)        // b, true
	_, _ = m.Get(3)        // nil, false
	_ = m.Values()         // []interface {}{"a", "b"} (random order)
	_ = m.Keys()           // []interface {}{1, 2} (random order)
	m.Remove(1)            // 2->b
	m.Clear()              // empty
	m.Empty()              // true
	m.Size()               // 0
}
```

#### TreeBidiMap

A [map](#maps) based on red-black tree. This map guarantees that the map will be in both ascending key and value order.
Other than key and value ordering, the goal with this structure is to avoid duplication of elements (unlike
in [HashBidiMap](#hashbidimap)), which can be significant if contained elements are large.

Implements [BidiMap](#maps), [IteratorWithKey](#iteratorwithkey), [EnumerableWithKey](#enumerablewithkey)
, [JSONSerializer](#jsonserializer) and [JSONDeserializer](#jsondeserializer) interfaces.

```go
package main

import (
	"github.com/mymmsc/gox/util/maps/treebidimap"
	"github.com/mymmsc/gox/util/utils"
)

func main() {
	m := treebidimap.NewWith(utils.IntComparator, utils.StringComparator)
	m.Put(1, "x")        // 1->x
	m.Put(3, "b")        // 1->x, 3->b (ordered)
	m.Put(1, "a")        // 1->a, 3->b (ordered)
	m.Put(2, "b")        // 1->a, 2->b (ordered)
	_, _ = m.GetKey("a") // 1, true
	_, _ = m.Get(2)      // b, true
	_, _ = m.Get(3)      // nil, false
	_ = m.Values()       // []interface {}{"a", "b"} (ordered)
	_ = m.Keys()         // []interface {}{1, 2} (ordered)
	m.Remove(1)          // 2->b
	m.Clear()            // empty
	m.Empty()            // true
	m.Size()             // 0
}
```

### Trees

A tree is a widely used data data structure that simulates a hierarchical tree structure, with a root value and subtrees
of children, represented as a set of linked nodes; thus no cyclic links.

Implements [Container](#containers) interface.

```go
type Tree interface {
	containers.Container
	// Empty() bool
	// Size() int
	// Clear()
	// Values() []interface{}
}
```

#### RedBlackTree

A red–black [tree](#trees) is a binary search tree with an extra bit of data per node, its color, which can be either
red or black. The extra bit of storage ensures an approximately balanced tree by constraining how nodes are colored from
any path from the root to the leaf. Thus, it is a data structure which is a type of self-balancing binary search tree.

The balancing of the tree is not perfect but it is good enough to allow it to guarantee searching in O(log n) time,
where n is the total number of elements in the tree. The insertion and deletion operations, along with the tree
rearrangement and recoloring, are also performed in O(log n)
time. <sub><sup>[Wikipedia](http://en.wikipedia.org/wiki/Red%E2%80%93black_tree)</sup></sub>

Implements [Tree](#trees), [ReverseIteratorWithKey](#reverseiteratorwithkey), [JSONSerializer](#jsonserializer)
and [JSONDeserializer](#jsondeserializer) interfaces.

<p align="center"><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/6/66/Red-black_tree_example.svg/500px-Red-black_tree_example.svg.png" width="400px" height="200px" /></p>

```go
package main

import (
	"fmt"
	rbt "github.com/mymmsc/gox/util/trees/redblacktree"
)

func main() {
	tree := rbt.NewWithIntComparator() // empty (keys are of type int)

	tree.Put(1, "x") // 1->x
	tree.Put(2, "b") // 1->x, 2->b (in order)
	tree.Put(1, "a") // 1->a, 2->b (in order, replacement)
	tree.Put(3, "c") // 1->a, 2->b, 3->c (in order)
	tree.Put(4, "d") // 1->a, 2->b, 3->c, 4->d (in order)
	tree.Put(5, "e") // 1->a, 2->b, 3->c, 4->d, 5->e (in order)
	tree.Put(6, "f") // 1->a, 2->b, 3->c, 4->d, 5->e, 6->f (in order)

	fmt.Println(tree)
	//
	//  RedBlackTree
	//  │           ┌── 6
	//	│       ┌── 5
	//	│   ┌── 4
	//	│   │   └── 3
	//	└── 2
	//		└── 1

	_ = tree.Values() // []interface {}{"a", "b", "c", "d", "e", "f"} (in order)
	_ = tree.Keys()   // []interface {}{1, 2, 3, 4, 5, 6} (in order)

	tree.Remove(2) // 1->a, 3->c, 4->d, 5->e, 6->f (in order)
	fmt.Println(tree)
	//
	//  RedBlackTree
	//  │       ┌── 6
	//  │   ┌── 5
	//  └── 4
	//      │   ┌── 3
	//      └── 1

	tree.Clear() // empty
	tree.Empty() // true
	tree.Size()  // 0

	// Other:
	tree.Left() // gets the left-most (min) node
	tree.Right() // get the right-most (max) node
	tree.Floor(1) // get the floor node
	tree.Ceiling(1) // get the ceiling node
}
```

Extending the red-black tree's functionality has been demonstrated in the
following [example](https://github.com/mymmsc/gox/util/blob/master/examples/redblacktreeextended/redblacktreeextended.go)
.

#### AVLTree

AVL [tree](#trees) is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any
node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property.
Lookup, insertion, and deletion all take O(log n) time in both the average and worst cases, where n is the number of
nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more
tree rotations.

AVL trees are often compared with red–black trees because both support the same set of operations and take O(log n) time
for the basic operations. For lookup-intensive applications, AVL trees are faster than red–black trees because they are
more strictly balanced. <sub><sup>[Wikipedia](https://en.wikipedia.org/wiki/AVL_tree)</sup></sub>

Implements [Tree](#trees), [ReverseIteratorWithKey](#reverseiteratorwithkey), [JSONSerializer](#jsonserializer)
and [JSONDeserializer](#jsondeserializer) interfaces.

<p align="center"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/a/ad/AVL-tree-wBalance_K.svg/262px-AVL-tree-wBalance_K.svg.png" width="300px" height="180px" /><br/><sub>AVL tree with balance factors (green)</sub></p>

```go
package main

import (
	"fmt"
	avl "github.com/mymmsc/gox/util/trees/avltree"
)

func main() {
	tree := avl.NewWithIntComparator() // empty(keys are of type int)

	tree.Put(1, "x") // 1->x
	tree.Put(2, "b") // 1->x, 2->b (in order)
	tree.Put(1, "a") // 1->a, 2->b (in order, replacement)
	tree.Put(3, "c") // 1->a, 2->b, 3->c (in order)
	tree.Put(4, "d") // 1->a, 2->b, 3->c, 4->d (in order)
	tree.Put(5, "e") // 1->a, 2->b, 3->c, 4->d, 5->e (in order)
	tree.Put(6, "f") // 1->a, 2->b, 3->c, 4->d, 5->e, 6->f (in order)

	fmt.Println(tree)
	//
	//  AVLTree
	//  │       ┌── 6
	//  │   ┌── 5
	//  └── 4
	//      │   ┌── 3
	//      └── 2
	//          └── 1


	_ = tree.Values() // []interface {}{"a", "b", "c", "d", "e", "f"} (in order)
	_ = tree.Keys()   // []interface {}{1, 2, 3, 4, 5, 6} (in order)

	tree.Remove(2) // 1->a, 3->c, 4->d, 5->e, 6->f (in order)
	fmt.Println(tree)
	//
	//  AVLTree
	//  │       ┌── 6
	//  │   ┌── 5
	//  └── 4
	//      └── 3
	//          └── 1

	tree.Clear() // empty
	tree.Empty() // true
	tree.Size()  // 0
}
```

#### BTree

B-tree is a self-balancing tree data structure that keeps data sorted and allows searches, sequential access,
insertions, and deletions in logarithmic time. The B-tree is a generalization of a binary search tree in that a node can
have more than two children.

According to Knuth's definition, a B-tree of order m is a tree which satisfies the following properties:

- Every node has at most m children.
- Every non-leaf node (except root) has at least ⌈m/2⌉ children.
- The root has at least two children if it is not a leaf node.
- A non-leaf node with k children contains k−1 keys.
- All leaves appear in the same level

Each internal node’s keys act as separation values which divide its subtrees. For example, if an internal node has 3
child nodes (or subtrees) then it must have 2 keys: a1 and a2. All values in the leftmost subtree will be less than a1,
all values in the middle subtree will be between a1 and a2, and all values in the rightmost subtree will be greater than
a2.<sub><sup>[Wikipedia](http://en.wikipedia.org/wiki/Red%E2%80%93black_tree)</sub></sup>

Implements [Tree](#trees), [ReverseIteratorWithKey](#reverseiteratorwithkey), [JSONSerializer](#jsonserializer)
and [JSONDeserializer](#jsondeserializer) interfaces.

<p align="center"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/65/B-tree.svg/831px-B-tree.svg.png" width="400px" height="111px" /></p>

```go
package main

import (
	"fmt"
	"github.com/mymmsc/gox/util/trees/btree"
)

func main() {
	tree := btree.NewWithIntComparator(3) // empty (keys are of type int)

	tree.Put(1, "x") // 1->x
	tree.Put(2, "b") // 1->x, 2->b (in order)
	tree.Put(1, "a") // 1->a, 2->b (in order, replacement)
	tree.Put(3, "c") // 1->a, 2->b, 3->c (in order)
	tree.Put(4, "d") // 1->a, 2->b, 3->c, 4->d (in order)
	tree.Put(5, "e") // 1->a, 2->b, 3->c, 4->d, 5->e (in order)
	tree.Put(6, "f") // 1->a, 2->b, 3->c, 4->d, 5->e, 6->f (in order)
	tree.Put(7, "g") // 1->a, 2->b, 3->c, 4->d, 5->e, 6->f, 7->g (in order)

	fmt.Println(tree)
	// BTree
	//         1
	//     2
	//         3
	// 4
	//         5
	//     6
	//         7

	_ = tree.Values() // []interface {}{"a", "b", "c", "d", "e", "f", "g"} (in order)
	_ = tree.Keys()   // []interface {}{1, 2, 3, 4, 5, 6, 7} (in order)

	tree.Remove(2) // 1->a, 3->c, 4->d, 5->e, 6->f (in order)
	fmt.Println(tree)
	// BTree
	//     1
	//     3
	// 4
	//     5
	//     6

	tree.Clear() // empty
	tree.Empty() // true
	tree.Size()  // 0

	// Other:
	tree.Height() // gets the height of the tree
	tree.Left() // gets the left-most (min) node
	tree.LeftKey() // get the left-most (min) node's key
	tree.LeftValue() // get the left-most (min) node's value
	tree.Right() // get the right-most (max) node
	tree.RightKey() // get the right-most (max) node's key
	tree.RightValue() // get the right-most (max) node's value
}
```

#### BinaryHeap

A binary heap is a [tree](#trees) created using a binary tree. It can be seen as a binary tree with two additional
constraints:

- Shape property:

  A binary heap is a complete binary tree; that is, all levels of the tree, except possibly the last one (deepest) are
  fully filled, and, if the last level of the tree is not complete, the nodes of that level are filled from left to
  right.
- Heap property:

  All nodes are either greater than or equal to or less than or equal to each of its children, according to a comparison
  predicate defined for the heap. <sub><sup>[Wikipedia](http://en.wikipedia.org/wiki/Binary_heap)</sub></sup>

Implements [Tree](#trees), [ReverseIteratorWithIndex](#reverseiteratorwithindex), [JSONSerializer](#jsonserializer)
and [JSONDeserializer](#jsondeserializer) interfaces.

<p align="center"><img src="http://upload.wikimedia.org/wikipedia/commons/thumb/3/38/Max-Heap.svg/501px-Max-Heap.svg.png" width="300px" height="200px" /></p>

```go
package main

import (
	"github.com/mymmsc/gox/util/trees/binaryheap"
	"github.com/mymmsc/gox/util/utils"
)

func main() {

	// Min-heap
	heap := binaryheap.NewWithIntComparator() // empty (min-heap)
	heap.Push(2)                              // 2
	heap.Push(3)                              // 2, 3
	heap.Push(1)                              // 1, 3, 2
	heap.Values()                             // 1, 3, 2
	_, _ = heap.Peek()                        // 1,true
	_, _ = heap.Pop()                         // 1, true
	_, _ = heap.Pop()                         // 2, true
	_, _ = heap.Pop()                         // 3, true
	_, _ = heap.Pop()                         // nil, false (nothing to pop)
	heap.Push(1)                              // 1
	heap.Clear()                              // empty
	heap.Empty()                              // true
	heap.Size()                               // 0

	// Max-heap
	inverseIntComparator := func(a, b interface{}) int {
		return -utils.IntComparator(a, b)
	}
	heap = binaryheap.NewWith(inverseIntComparator) // empty (min-heap)
	heap.Push(2, 3, 1)                              // 3, 2, 1 (bulk optimized)
	heap.Values()                                   // 3, 2, 1
}
```

## Functions

Various helper functions used throughout the library.

### Comparator

Some data structures (e.g. TreeMap, TreeSet) require a comparator function to automatically keep their elements sorted
upon insertion. This comparator is necessary during the initalization.

Comparator is defined as:

Return values (int):

```go
negative , if a < b
zero     , if a == b
positive , if a > b
```

Comparator signature:

```go
type Comparator func(a, b interface{}) int
```

All common comparators for builtin types are included in the library:

```go
func StringComparator(a, b interface{}) int

func IntComparator(a, b interface{}) int

func Int8Comparator(a, b interface{}) int

func Int16Comparator(a, b interface{}) int

func Int32Comparator(a, b interface{}) int

func Int64Comparator(a, b interface{}) int

func UIntComparator(a, b interface{}) int

func UInt8Comparator(a, b interface{}) int

func UInt16Comparator(a, b interface{}) int

func UInt32Comparator(a, b interface{}) int

func UInt64Comparator(a, b interface{}) int

func Float32Comparator(a, b interface{}) int

func Float64Comparator(a, b interface{}) int

func ByteComparator(a, b interface{}) int

func RuneComparator(a, b interface{}) int

func TimeComparator(a, b interface{}) int
```

Writing custom comparators is easy:

```go
package main

import (
	"fmt"
	"github.com/mymmsc/gox/util/sets/treeset"
)

type User struct {
	id   int
	name string
}

// Custom comparator (sort by IDs)
func byID(a, b interface{}) int {

	// Type assertion, program will panic if this is not respected
	c1 := a.(User)
	c2 := b.(User)

	switch {
	case c1.id > c2.id:
		return 1
	case c1.id < c2.id:
		return -1
	default:
		return 0
	}
}

func main() {
	set := treeset.NewWith(byID)

	set.Add(User{2, "Second"})
	set.Add(User{3, "Third"})
	set.Add(User{1, "First"})
	set.Add(User{4, "Fourth"})

	fmt.Println(set) // {1 First}, {2 Second}, {3 Third}, {4 Fourth}
}
```

### Iterator

All ordered containers have stateful iterators. Typically an iterator is obtained by _Iterator()_ function of an ordered
container. Once obtained, iterator's _Next()_ function moves the iterator to the next element and returns true if there
was a next element. If there was an element, then element's can be obtained by iterator's _Value()_ function. Depending
on the ordering type, it's position can be obtained by iterator's _Index()_ or _Key()_ functions. Some containers even
provide reversible iterators, essentially the same, but provide another extra _Prev()_ function that moves the iterator
to the previous element and returns true if there was a previous element.

Note: it is unsafe to remove elements from container while iterating.

#### IteratorWithIndex

An [iterator](#iterator) whose elements are referenced by an index.

Typical usage:

```go
it := list.Iterator()
for it.Next() {
	index, value := it.Index(), it.Value()
	...
}
```

Other usages:

```go
if it.First() {
	firstIndex, firstValue := it.Index(), it.Value()
	...
}
```

```go
for it.Begin(); it.Next(); {
	...
}
```

#### IteratorWithKey

An [iterator](#iterator) whose elements are referenced by a key.

Typical usage:

```go
it := tree.Iterator()
for it.Next() {
	key, value := it.Key(), it.Value()
	...
}
```

Other usages:

```go
if it.First() {
	firstKey, firstValue := it.Key(), it.Value()
	...
}
```

```go
for it.Begin(); it.Next(); {
	...
}
```

#### ReverseIteratorWithIndex

An [iterator](#iterator) whose elements are referenced by an index. Provides all functions
as [IteratorWithIndex](#iteratorwithindex), but can also be used for reverse iteration.

Typical usage of iteration in reverse:

```go
it := list.Iterator()
for it.End(); it.Prev(); {
	index, value := it.Index(), it.Value()
	...
}
```

Other usages:

```go
if it.Last() {
	lastIndex, lastValue := it.Index(), it.Value()
	...
}
```

#### ReverseIteratorWithKey

An [iterator](#iterator) whose elements are referenced by a key. Provides all functions
as [IteratorWithKey](#iteratorwithkey), but can also be used for reverse iteration.

Typical usage of iteration in reverse:

```go
it := tree.Iterator()
for it.End(); it.Prev(); {
	key, value := it.Key(), it.Value()
	...
}
```

Other usages:

```go
if it.Last() {
	lastKey, lastValue := it.Key(), it.Value()
	...
}
```

### Enumerable

Enumerable functions for ordered containers that implement [EnumerableWithIndex](#enumerablewithindex)
or [EnumerableWithKey](#enumerablewithkey) interfaces.

#### EnumerableWithIndex

[Enumerable](#enumerable) functions for ordered containers whose values can be fetched by an index.

**Each**

Calls the given function once for each element, passing that element's index and value.

```go
Each(func(index int, value interface{}))
```

**Map**

Invokes the given function once for each element and returns a container containing the values returned by the given
function.

```go
Map(func(index int, value interface{}) interface{}) Container
```

**Select**

Returns a new container containing all elements for which the given function returns a true value.

```go
Select(func(index int, value interface{}) bool) Container
```

**Any**

Passes each element of the container to the given function and returns true if the function ever returns true for any
element.

```go
Any(func(index int, value interface{}) bool) bool
```

**All**

Passes each element of the container to the given function and returns true if the function returns true for all
elements.

```go
All(func(index int, value interface{}) bool) bool
```

**Find**

Passes each element of the container to the given function and returns the first (index,value) for which the function is
true or -1,nil otherwise if no element matches the criteria.

```go
Find(func(index int, value interface{}) bool) (int, interface{})}
```

**Example:**

```go
package main

import (
	"fmt"
	"github.com/mymmsc/gox/util/sets/treeset"
)

func printSet(txt string, set *treeset.Set) {
	fmt.Print(txt, "[ ")
	set.Each(func(index int, value interface{}) {
		fmt.Print(value, " ")
	})
	fmt.Println("]")
}

func main() {
	set := treeset.NewWithIntComparator()
	set.Add(2, 3, 4, 2, 5, 6, 7, 8)
	printSet("Initial", set) // [ 2 3 4 5 6 7 8 ]

	even := set.Select(func(index int, value interface{}) bool {
		return value.(int)%2 == 0
	})
	printSet("Even numbers", even) // [ 2 4 6 8 ]

	foundIndex, foundValue := set.Find(func(index int, value interface{}) bool {
		return value.(int)%2 == 0 && value.(int)%3 == 0
	})
	if foundIndex != -1 {
		fmt.Println("Number divisible by 2 and 3 found is", foundValue, "at index", foundIndex) // value: 6, index: 4
	}

	square := set.Map(func(index int, value interface{}) interface{} {
		return value.(int) * value.(int)
	})
	printSet("Numbers squared", square) // [ 4 9 16 25 36 49 64 ]

	bigger := set.Any(func(index int, value interface{}) bool {
		return value.(int) > 5
	})
	fmt.Println("Set contains a number bigger than 5 is ", bigger) // true

	positive := set.All(func(index int, value interface{}) bool {
		return value.(int) > 0
	})
	fmt.Println("All numbers are positive is", positive) // true

	evenNumbersSquared := set.Select(func(index int, value interface{}) bool {
		return value.(int)%2 == 0
	}).Map(func(index int, value interface{}) interface{} {
		return value.(int) * value.(int)
	})
	printSet("Chaining", evenNumbersSquared) // [ 4 16 36 64 ]
}
```

#### EnumerableWithKey

Enumerable functions for ordered containers whose values whose elements are key/value pairs.

**Each**

Calls the given function once for each element, passing that element's key and value.

```go
Each(func(key interface{}, value interface{}))
```

**Map**

Invokes the given function once for each element and returns a container containing the values returned by the given
function as key/value pairs.

```go
Map(func(key interface{}, value interface{}) (interface{}, interface{})) Container
```

**Select**

Returns a new container containing all elements for which the given function returns a true value.

```go
Select(func(key interface{}, value interface{}) bool) Container
```

**Any**

Passes each element of the container to the given function and returns true if the function ever returns true for any
element.

```go
Any(func(key interface{}, value interface{}) bool) bool
```

**All**

Passes each element of the container to the given function and returns true if the function returns true for all
elements.

```go
All(func(key interface{}, value interface{}) bool) bool
```

**Find**

Passes each element of the container to the given function and returns the first (key,value) for which the function is
true or nil,nil otherwise if no element matches the criteria.

```go
Find(func(key interface{}, value interface{}) bool) (interface{}, interface{})
```

**Example:**

```go
package main

import (
	"fmt"
	"github.com/mymmsc/gox/util/maps/treemap"
)

func printMap(txt string, m *treemap.Map) {
	fmt.Print(txt, " { ")
	m.Each(func(key interface{}, value interface{}) {
		fmt.Print(key, ":", value, " ")
	})
	fmt.Println("}")
}

func main() {
	m := treemap.NewWithStringComparator()
	m.Put("g", 7)
	m.Put("f", 6)
	m.Put("e", 5)
	m.Put("d", 4)
	m.Put("c", 3)
	m.Put("b", 2)
	m.Put("a", 1)
	printMap("Initial", m) // { a:1 b:2 c:3 d:4 e:5 f:6 g:7 }

	even := m.Select(func(key interface{}, value interface{}) bool {
		return value.(int) % 2 == 0
	})
	printMap("Elements with even values", even) // { b:2 d:4 f:6 }

	foundKey, foundValue := m.Find(func(key interface{}, value interface{}) bool {
		return value.(int) % 2 == 0 && value.(int) % 3 == 0
	})
	if foundKey != nil {
		fmt.Println("Element with value divisible by 2 and 3 found is", foundValue, "with key", foundKey) // value: 6, index: 4
	}

	square := m.Map(func(key interface{}, value interface{}) (interface{}, interface{}) {
		return key.(string) + key.(string), value.(int) * value.(int)
	})
	printMap("Elements' values squared and letters duplicated", square) // { aa:1 bb:4 cc:9 dd:16 ee:25 ff:36 gg:49 }

	bigger := m.Any(func(key interface{}, value interface{}) bool {
		return value.(int) > 5
	})
	fmt.Println("Map contains element whose value is bigger than 5 is", bigger) // true

	positive := m.All(func(key interface{}, value interface{}) bool {
		return value.(int) > 0
	})
	fmt.Println("All map's elements have positive values is", positive) // true

	evenNumbersSquared := m.Select(func(key interface{}, value interface{}) bool {
		return value.(int) % 2 == 0
	}).Map(func(key interface{}, value interface{}) (interface{}, interface{}) {
		return key, value.(int) * value.(int)
	})
	printMap("Chaining", evenNumbersSquared) // { b:4 d:16 f:36 }
}
```

### Serialization

All data structures can be serialized (marshalled) and deserialized (unmarshalled). Currently only JSON support is
available.

#### JSONSerializer

Outputs the container into its JSON representation.

Typical usage for key-value structures:

```go
package main

import (
	"fmt"
	"github.com/mymmsc/gox/util/maps/hashmap"
)

func main() {
	m := hashmap.New()
	m.Put("a", "1")
	m.Put("b", "2")
	m.Put("c", "3")

	json, err := m.ToJSON()
	if err != nil {
		fmt.Println(err)
	}
	fmt.Println(string(json)) // {"a":"1","b":"2","c":"3"}
```

Typical usage for value-only structures:

```go
package main

import (
	"fmt"
	"github.com/mymmsc/gox/util/lists/arraylist"
)

func main() {
	list := arraylist.New()
	list.Add("a", "b", "c")

	json, err := list.ToJSON()
	if err != nil {
		fmt.Println(err)
	}
	fmt.Println(string(json)) // ["a","b","c"]
}
```

#### JSONDeserializer

Populates the container with elements from the input JSON representation.

Typical usage for key-value structures:

```go
package main

import (
	"fmt"
	"github.com/mymmsc/gox/util/maps/hashmap"
)

func main() {
	hm := hashmap.New()

	json := []byte(`{"a":"1","b":"2"}`)
	err := hm.FromJSON(json)
	if err != nil {
		fmt.Println(err)
	}
	fmt.Println(hm) // HashMap map[b:2 a:1]
}
```

Typical usage for value-only structures:

```go
package main

import (
	"fmt"
	"github.com/mymmsc/gox/util/lists/arraylist"
)

func main() {
	list := arraylist.New()

	json := []byte(`["a","b"]`)
	err := list.FromJSON(json)
	if err != nil {
		fmt.Println(err)
	}
	fmt.Println(list) // ArrayList ["a","b"]
}
```

### Sort

Sort is a general purpose sort function.

Lists have an in-place _Sort()_ function and all containers can return their sorted elements via _
containers.GetSortedValues()_ function.

Internally these all use the _utils.Sort()_ method:

```go
package main

import "github.com/mymmsc/gox/util/utils"

func main() {
	strings := []interface{}{}                  // []
	strings = append(strings, "d")              // ["d"]
	strings = append(strings, "a")              // ["d","a"]
	strings = append(strings, "b")              // ["d","a",b"
	strings = append(strings, "c")              // ["d","a",b","c"]
	utils.Sort(strings, utils.StringComparator) // ["a","b","c","d"]
}
```

### Container

Container specific operations:

```go
// Returns sorted container''s elements with respect to the passed comparator.
// Does not effect the ordering of elements within the container.
func GetSortedValues(container Container, comparator utils.Comparator) []interface{}
```

Usage:

```go
package main

import (
	"github.com/mymmsc/gox/util/lists/arraylist"
	"github.com/mymmsc/gox/util/utils"
)

func main() {
	list := arraylist.New()
	list.Add(2, 1, 3)
	values := GetSortedValues(container, utils.StringComparator) // [1, 2, 3]
}
```

## Appendix

### Motivation

Collections and data structures found in other languages: Java Collections, C++ Standard Template Library (STL)
containers, Qt Containers, Ruby Enumerable etc.

### Goals

**Fast algorithms**:

- Based on decades of knowledge and experiences of other libraries mentioned above.

**Memory efficient algorithms**:

- Avoiding to consume memory by using optimal algorithms and data structures for the given set of problems, e.g.
  red-black tree in case of TreeMap to avoid keeping redundant sorted array of keys in memory.

**Easy to use library**:

- Well-structured library with minimalistic set of atomic operations from which more complex operations can be crafted.

**Stable library**:

- Only additions are permitted keeping the library backward compatible.

**Solid documentation and examples**:

- Learning by example.

**Production ready**:

- Used in production.

**No dependencies**:

- No external imports.

There is often a tug of war between speed and memory when crafting algorithms. We choose to optimize for speed in most
cases within reasonable limits on memory consumption.

Thread safety is not a concern of this project, this should be handled at a higher level.

### Testing and Benchmarking

This takes a while, so test within sub-packages:

`go test -run=NO_TEST -bench . -benchmem -benchtime 1s ./...`

<p align="center"><img src="https://cloud.githubusercontent.com/assets/3115942/16892979/5e698d46-4b27-11e6-864b-cb2b865327b6.png" /></p>

### Contributing

Biggest contribution towards this library is to use it and give us feedback for further improvements and additions.

For direct contributions, _pull request_ into master branch or ask to become a contributor.

Coding style:

```shell
# Install tooling and set path:
go get github.com/golang/lint/golint
go get github.com/fzipp/gocyclo
go get github.com/kisielk/errcheck
export PATH=$PATH:$GOPATH/bin

# Fix errors and warnings:
go fmt ./... && gofmt -s -w . && go vet ./... && go get ./... && go test ./... && golint ./... && gocyclo -avg -over 15 . && errcheck ./...
```

### License

This library is distributed under the BSD-style license found in
the [LICENSE](https://github.com/mymmsc/gox/util/blob/master/LICENSE) file.

### Sponsors

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