## Welcome to Algorithm

Algorithm is a library of tools that is used to create intelligent applications.

## Features

- Probability Tools
- Expected Value
- Programmable Probability Blocks
- Array Extensions
- Set Extensions

## Data Structures

- DoublyLinkedList
- Stack
- Queue
- Deque
- RedBlackTree
- SortedSet
- SortedMultiSet
- SortedDictionary
- SortedMultiDictionary

## Requirements

- iOS 8.0+ / Mac OS X 10.9+
- Xcode 8.0+

## Communication

- If you
**need help**, use Stack Overflow. (Tag 'cosmicmind') - If you'd like to
**ask a general question**, use Stack Overflow. - If you
**found a bug**,*and can provide steps to reliably reproduce it*, open an issue. - If you
**have a feature request**, open an issue. - If you
**want to contribute**, submit a pull request.

## Installation

Embedded frameworks require a minimum deployment target of iOS 8.

## CocoaPods

CocoaPods is a dependency manager for Cocoa projects. You can install it with the following command:

`$ gem install cocoapods`

To integrate Algorithm's core features into your Xcode project using CocoaPods, specify it in your `Podfile`

:

```
source 'https://github.com/CocoaPods/Specs.git'
platform :ios, '8.0'
use_frameworks!
pod 'Algorithm', '~> 3.1.0'
```

Then, run the following command:

`$ pod install`

## Carthage

Carthage is a decentralized dependency manager that builds your dependencies and provides you with binary frameworks.

You can install Carthage with Homebrew using the following command:

```
$ brew update
$ brew install carthage
```

To integrate Algorithm into your Xcode project using Carthage, specify it in your Cartfile:

`github "CosmicMind/Algorithm"`

Run `carthage update`

to build the framework and drag the built `Algorithm.framework`

into your Xcode project.

## Changelog

Algorithm is a growing project and will encounter changes throughout its development. It is recommended that the Changelog be reviewed prior to updating versions.

# Samples

The following are samples to see how Algorithm may be used within your applications.

- Visit the Samples repo to see example projects using Algorithm.

## Probability

Each data structure within Algorithm is equipped with probability tools.

#### Basic Probability

For example, determining the probability of rolling a 3 using a die of 6 numbers.

```
let die = [Int](arrayLiteral: 1, 2, 3, 4, 5, 6)
if 0.1 < die.probability(of: 3)
// Do something ...
}
```

#### Conditional Probability

For conditional probabilities that require a more complex calculation, use block statements.

```
let die = [Int](arrayLiteral: 1, 2, 3, 4, 5, 6)
let pOfX = die.probability { (number) in
return 5 < number || 0 == number % 3
}
if 0.33 < pOfX {
// Do something ...
}
```

## Expected Value

The expected value of rolling a 3 or 6 with 100 trials using a die of 6 numbers.

```
let die = [Int](arrayLiteral: 1, 2, 3, 4, 5, 6)
if 20 < die.expectedValue(trials: 100, for: 3, 6) {
// Do something ...
}
```

## DoublyLinkedList

The DoublyLinkedList data structure is excellent for large growing collections of data. Below is an example of its usage.

```
var listA = DoublyLinkedList<Int>()
listA.insert(atFront: 3)
listA.insert(atFront: 2)
listA.insert(atFront: 1)
var listB = DoublyLinkedList<Int>()
listB.insert(atBack: 4)
listB.insert(atBack: 5)
listB.insert(atBack: 6)
var listC = listA + listB
listC.cursorToFront()
var value = listC.cursor
while nil != value {
// Do something ...
value = listC.next()
}
```

## Stack

The Stack data structure is a container of objects that are inserted and removed according to the last-in-first-out (LIFO) principle. Below is an example of its usage.

```
var stack = Stack<Int>()
stack.push(1)
stack.push(2)
stack.push(3)
while !stack.isEmpty {
let value = stack.pop()
// Do something ...
}
```

## Queue

The Queue data structure is a container of objects that are inserted and removed according to the first-in-first-out (FIFO) principle. Below is an example of its usage.

```
var queue = Queue<Int>()
queue.enqueue(1)
queue.enqueue(2)
queue.enqueue(3)
while !queue.isEmpty {
let value = queue.dequeue()
// Do something ...
}
```

## Deque

The Deque data structure is a container of objects that are inserted and removed according to the first-in-first-out (FIFO) and last-in-first-out (LIFO) principle. Essentially, a Deque is a Stack and Queue combined. Below are examples of its usage.

```
var dequeA = Deque<Int>()
dequeA.insert(atBack: 1)
dequeA.insert(atBack: 2)
dequeA.insert(atBack: 3)
while !dequeA.isEmpty {
let value = dequeA.removeAtFront()
// Do something ...
}
var dequeB = Deque<Int>()
dequeB.insert(atBack: 4)
dequeB.insert(atBack: 5)
dequeB.insert(atBack: 6)
while !dequeB.isEmpty {
let value = dequeB.removeAtFront()
// Do something ...
}
```

## RedBlackTree

A RedBlackTree is a Balanced Binary Search Tree that maintains insert, remove, update, and search operations in a complexity of O(logn). The following implementation of a RedBlackTree also includes an order-statistic, which allows the data structure to be accessed using subscripts like an array or dictionary. RedBlackTrees may store unique keys or non-unique key values. Below is an example of its usage.

```
var ages = RedBlackTree<String, Int>(uniqueKeys: true)
ages.insert(value: 16, for: "Sarah")
ages.insert(value: 12, for: "Peter")
ages.insert(value: 23, for: "Alex")
let node = ages[1]
if "Peter" == node.key {
// Do something ...
}
```

## SortedSet

SortedSets are a powerful data structure for algorithm and analysis design. Elements within a SortedSet are unique and insert, remove, and search operations have a complexity of O(logn). The following implementation of a SortedSet also includes an order-statistic, which allows the data structure to be accessed using an index subscript like an array. Below are examples of its usage.

```
let setA = SortedSet<Int>(elements: 1, 2, 3)
let setB = SortedSet<Int>(elements: 4, 3, 6)
let setC = SortedSet<Int>(elements: 7, 1, 2)
let setD = SortedSet<Int>(elements: 1, 7)
let setE = SortedSet<Int>(elements: 1, 6, 7)
// Union.
setA + setB
setA.union(setB)
// Intersection.
setC.intersection(setD)
// Subset.
setD < setC
setD.isSubset(of: setC)
// Superset.
setD > setC
setD.isSuperset(of: setC)
// Contains.
setE.contains(setA.first!)
// Probability.
setE.probability(of: setA.first!, setA.last!)
```

## SortedMultiSet

A SortedMultiSet is identical to a SortedSet, except that a SortedMultiSet allows non-unique elements. Look at SortedSet for examples of its usage.

## SortedDictionary

A SortedDictionary is a powerful data structure that maintains a sorted set of keys with value pairs. Keys within a SortedDictionary are unique and insert, remove, update, and search operations have a complexity of O(logn).

## SortedMultiDictionary

A SortedMultiDictionary is identical to a SortedDictionary, except that a SortedMultiDictionary allows non-unique keys. Below is an example of its usage.

```
struct Student {
var name: String
}
let sarah = Student(name: "Sarah")
let peter = Student(name: "Peter")
let alex = Student(name: "Alex")
var students = SortedMultiDictionary<String, Student>()
students.insert(value: sarah, for: sarah.name)
students.insert(value: peter, for: peter.name)
students.insert(value: alex, for: alex.name)
for student in students {
// Do something ...
}
```

## License

The MIT License (MIT)

Copyright (C) 2019, CosmicMind, Inc. http://cosmicmind.com. All rights reserved.

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.