proxpero

// Swift 2.1

extension Array where Element : Comparable {
    
    private func merge(var left: Array<Element>, var _ right: Array<Element>) -> Array<Element> {
        
        var result: Array<Element> = []
        
        while !left.isEmpty && !right.isEmpty {
            

proxpero

// Swift 2.1

extension MutableCollectionType where Self.Generator.Element : Comparable, Self.Index == Int {
    
    /// Return a new sorted collection of the elements in `source`
    /// using [Shell Sort](https://en.wikipedia.org/wiki/Shellsort).
    ///
    /// Complexity O(n^(3/2)).
    @warn_unused_result(mutable_variant="shellSortInPlace")

proxpero

// Swift 2.1

extension MutableCollectionType where Self.Generator.Element : Comparable {
    
    /// Return a new sorted collection of the elements in `source`
    /// using [Insertion Sort](https://en.wikipedia.org/wiki/Insertion_sort).
    ///
    /// Complexity O(n^2).
    @warn_unused_result(mutable_variant="insertionSortInPlace")
    public func insertionSort() -> Self {

proxpero

// Swift 2.1

extension MutableCollectionType where Self.Generator.Element : Comparable {
    
    /// Return a new sorted collection of the elements in `source` 
    /// using [Selection Sort](https://en.wikipedia.org/wiki/Selection_sort).
    ///
    /// Complexity O(n^2).
    @warn_unused_result(mutable_variant="selectionSortInPlace")
    public func selectionSort() -> Self {

proxpero

// Swift 2.2

extension NSColor {
    
    convenience init(rgb: String) {
        
        guard rgb.characters.count == 6 else { fatalError("Invalid rgb value: \(rgb)") }
        
        let scanner = NSScanner(string: rgb)
        var hexValue: UInt32 = 0

proxpero

//: [Sub-string Divisibility](https://projecteuler.net/problem=43)
/*:
The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property.

Let d[1] be the 1st digit, d[2] be the 2nd digit, and so on. In this way, we note the following:

* d[2]d[3]d[4] = 406  is divisible by 2
* d[3]d[4]d[5] = 063  is divisible by 3
* d[4]d[5]d[6] = 635  is divisible by 5
* d[5]d[6]d[7] = 357  is divisible by 7

proxpero

//: [Pentagonal Numbers](https://projecteuler.net/problem=44)
/*:
Pentagonal numbers are generated by the formula, P[n]=n[3n−1]/2. The first ten pentagonal numbers are:

1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...

It can be seen that P[4] + P[7] = 22 + 70 = 92 = P[8]. However, their difference, 70 − 22 = 48, is not pentagonal.

Find the pair of pentagonal numbers, P[j] and P[k], for which their sum and difference are pentagonal and D = |P[k] − P[j]| is minimised; what is the value of D?
*/

proxpero

//: Cube digit pairs
//: [Problem 90](https://projecteuler.net/problem=90)
//: Xcode 7.0, Swift 2.0
/*:
Each of the six faces on a cube has a different digit (0 to 9) written on it; the same is done to a second cube. By placing the two cubes side-by-side in different positions we can form a variety of 2-digit numbers.

For example, the square number 64 could be formed:
![Two cubes showing 64](https://projecteuler.net/project/images/p090.gif)

In fact, by carefully choosing the digits on both cubes it is possible to display all of the square numbers below one-hundred: 01, 04, 09, 16, 25, 36, 49, 64, and 81.

proxpero

//: Coded Triangle Numbers
//: [Problem 42](https://projecteuler.net/problem=42)
//: Xcode 7.0, Swift 2.0
/*:
The nth term of the sequence of triangle numbers is given by, t[n] = ½n(n+1); so the first ten triangle numbers are:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form a word value. For example, the word value for SKY is 19 + 11 + 25 = 55 = t[10]. If the word value is a triangle number then we shall call the word a triangle word.
Using [words.txt](https://projecteuler.net/project/resources/p042_words.txt), a 16K text file containing nearly two-thousand common English words, how many are triangle words?
*/
//: Note: I found and replaced the double quotes directly in the text file rather than in code since escaping the double quotes in a string kept crashing the playground. I named the file "words.txt" in the "Resources" folder of the playground.

proxpero

//: SICP Exercise 1.12
//: //: Xcode 7.0, Swift 2.0
/* The following pattern of numbers is called Pascal’s triangle.

                     1
                   1   1
                 1   2   1
               1   3   3   1
             1   4   6   4   1
                   . . .