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functional-red-black-tree
=========================
A [fully persistent](http://en.wikipedia.org/wiki/Persistent_data_structure) [red-black tree](http://en.wikipedia.org/wiki/Red%E2%80%93black_tree) written 100% in JavaScript.  Works both in node.js and in the browser via [browserify](http://browserify.org/).

Functional (or fully presistent) data structures allow for non-destructive updates.  So if you insert an element into the tree, it returns a new tree with the inserted element rather than destructively updating the existing tree in place.  Doing this requires using extra memory, and if one were naive it could cost as much as reallocating the entire tree.  Instead, this data structure saves some memory by recycling references to previously allocated subtrees.  This requires using only O(log(n)) additional memory per update instead of a full O(n) copy.

Some advantages of this is that it is possible to apply insertions and removals to the tree while still iterating over previous versions of the tree.  Functional and persistent data structures can also be useful in many geometric algorithms like point location within triangulations or ray queries, and can be used to analyze the history of executing various algorithms.  This added power though comes at a cost, since it is generally a bit slower to use a functional data structure than an imperative version.  However, if your application needs this behavior then you may consider using this module.

# Install

    npm install functional-red-black-tree

# Example

Here is an example of some basic usage:

```javascript
//Load the library
var createTree = require("functional-red-black-tree")

//Create a tree
var t1 = createTree()

//Insert some items into the tree
var t2 = t1.insert(1, "foo")
var t3 = t2.insert(2, "bar")

//Remove something
var t4 = t3.remove(1)
```


# API

```javascript
var createTree = require("functional-red-black-tree")
```

## Overview

- [Tree methods](#tree-methods)
  - [`var tree = createTree([compare])`](#var-tree-=-createtreecompare)
  - [`tree.keys`](#treekeys)
  - [`tree.values`](#treevalues)
  - [`tree.length`](#treelength)
  - [`tree.get(key)`](#treegetkey)
  - [`tree.insert(key, value)`](#treeinsertkey-value)
  - [`tree.remove(key)`](#treeremovekey)
  - [`tree.find(key)`](#treefindkey)
  - [`tree.ge(key)`](#treegekey)
  - [`tree.gt(key)`](#treegtkey)
  - [`tree.lt(key)`](#treeltkey)
  - [`tree.le(key)`](#treelekey)
  - [`tree.at(position)`](#treeatposition)
  - [`tree.begin`](#treebegin)
  - [`tree.end`](#treeend)
  - [`tree.forEach(visitor(key,value)[, lo[, hi]])`](#treeforEachvisitorkeyvalue-lo-hi)
  - [`tree.root`](#treeroot)
- [Node properties](#node-properties)
  - [`node.key`](#nodekey)
  - [`node.value`](#nodevalue)
  - [`node.left`](#nodeleft)
  - [`node.right`](#noderight)
- [Iterator methods](#iterator-methods)
  - [`iter.key`](#iterkey)
  - [`iter.value`](#itervalue)
  - [`iter.node`](#iternode)
  - [`iter.tree`](#itertree)
  - [`iter.index`](#iterindex)
  - [`iter.valid`](#itervalid)
  - [`iter.clone()`](#iterclone)
  - [`iter.remove()`](#iterremove)
  - [`iter.update(value)`](#iterupdatevalue)
  - [`iter.next()`](#iternext)
  - [`iter.prev()`](#iterprev)
  - [`iter.hasNext`](#iterhasnext)
  - [`iter.hasPrev`](#iterhasprev)

## Tree methods

### `var tree = createTree([compare])`
Creates an empty functional tree

* `compare` is an optional comparison function, same semantics as array.sort()

**Returns** An empty tree ordered by `compare`

### `tree.keys`
A sorted array of all the keys in the tree

### `tree.values`
An array array of all the values in the tree

### `tree.length`
The number of items in the tree

### `tree.get(key)`
Retrieves the value associated to the given key

* `key` is the key of the item to look up

**Returns** The value of the first node associated to `key`

### `tree.insert(key, value)`
Creates a new tree with the new pair inserted.

* `key` is the key of the item to insert
* `value` is the value of the item to insert

**Returns** A new tree with `key` and `value` inserted

### `tree.remove(key)`
Removes the first item with `key` in the tree

* `key` is the key of the item to remove

**Returns** A new tree with the given item removed if it exists

### `tree.find(key)`
Returns an iterator pointing to the first item in the tree with `key`, otherwise `null`.

### `tree.ge(key)`
Find the first item in the tree whose key is `>= key`

* `key` is the key to search for

**Returns** An iterator at the given element.

### `tree.gt(key)`
Finds the first item in the tree whose key is `> key`

* `key` is the key to search for

**Returns** An iterator at the given element

### `tree.lt(key)`
Finds the last item in the tree whose key is `< key`

* `key` is the key to search for

**Returns** An iterator at the given element

### `tree.le(key)`
Finds the last item in the tree whose key is `<= key`

* `key` is the key to search for

**Returns** An iterator at the given element

### `tree.at(position)`
Finds an iterator starting at the given element

* `position` is the index at which the iterator gets created

**Returns** An iterator starting at position

### `tree.begin`
An iterator pointing to the first element in the tree

### `tree.end`
An iterator pointing to the last element in the tree

### `tree.forEach(visitor(key,value)[, lo[, hi]])`
Walks a visitor function over the nodes of the tree in order.

* `visitor(key,value)` is a callback that gets executed on each node.  If a truthy value is returned from the visitor, then iteration is stopped.
* `lo` is an optional start of the range to visit (inclusive)
* `hi` is an optional end of the range to visit (non-inclusive)

**Returns** The last value returned by the callback

### `tree.root`
Returns the root node of the tree


## Node properties
Each node of the tree has the following properties:

### `node.key`
The key associated to the node

### `node.value`
The value associated to the node

### `node.left`
The left subtree of the node

### `node.right`
The right subtree of the node

## Iterator methods

### `iter.key`
The key of the item referenced by the iterator

### `iter.value`
The value of the item referenced by the iterator

### `iter.node`
The value of the node at the iterator's current position.  `null` is iterator is node valid.

### `iter.tree`
The tree associated to the iterator

### `iter.index`
Returns the position of this iterator in the sequence.

### `iter.valid`
Checks if the iterator is valid

### `iter.clone()`
Makes a copy of the iterator

### `iter.remove()`
Removes the item at the position of the iterator

**Returns** A new binary search tree with `iter`'s item removed

### `iter.update(value)`
Updates the value of the node in the tree at this iterator

**Returns** A new binary search tree with the corresponding node updated

### `iter.next()`
Advances the iterator to the next position

### `iter.prev()`
Moves the iterator backward one element

### `iter.hasNext`
If true, then the iterator is not at the end of the sequence

### `iter.hasPrev`
If true, then the iterator is not at the beginning of the sequence

# Credits
(c) 2013 Mikola Lysenko. MIT License

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