proxpero

//: Problem 4
//  "Write a function that given a list of non-negative integers, arranges them such that they form the largest possible number. For example, given [50, 2, 1, 9], the largest formed number is 95021."
//  https://www.shiftedup.com/2015/05/07/five-programming-problems-every-software-engineer-should-be-able-to-solve-in-less-than-1-hour

//  This solution first finds the permutations of the integers in the given array. A string is made out of the digits of each permutation, the string is converted to an integer, and the maximum of all these integers is returned.
//  It is expensive! but it's short and guaranteed to work every time. 

//  I updated objc.io's permutation snippet to Swift 2.0 and used it in my solution
//  https://www.objc.io/blog/2014/12/08/functional-snippet-10-permutations/

proxpero

//: Problem 2
//  "Write a function that combines two lists by alternatingly taking elements. For example: given the two lists [a, b, c] and [1, 2, 3], the function should return [a, 1, b, 2, c, 3]."
//  https://www.shiftedup.com/2015/05/07/five-programming-problems-every-software-engineer-should-be-able-to-solve-in-less-than-1-hour

//  Xcode 7.0, Swift 2.0

//  Assumption: homogeneous arrays, same length


let first = ["a", "b", "c"]

proxpero

//: Problem 1
//  "Write three functions that compute the sum of the numbers in a given list using a for-loop, a while-loop, and recursion."
//  https://www.shiftedup.com/2015/05/07/five-programming-problems-every-software-engineer-should-be-able-to-solve-in-less-than-1-hour

//  Xcode 7.0, Swift 2.0

let series = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
let realSum = series.reduce(0, combine: +)

proxpero

//: Problem 3
//  "Write a function that computes the list of the first 100 Fibonacci numbers. By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two. As an example, here are the first 10 Fibonnaci numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, and 34."
//  https://www.shiftedup.com/2015/05/07/five-programming-problems-every-software-engineer-should-be-able-to-solve-in-less-than-1-hour

//  Xcode 7.0, Swift 2.0

func fibonacci(count: Int) -> [Double] {

    var n1: Double = 0
    var n2: Double = 1

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
                   . . .

proxpero

//: SICP Exercise 1.11
//: Xcode 7.0, Swift 2.0
//: A function f is defined by the rule that f(n)=n if n<3 and f(n)=f(n−1)+2f(n−2)+3f(n−3) if n≥3. Write a procedure that computes f by means of a recursive process. Write a procedure that computes f by means of an iterative process.

func recursive(n: Int) -> Int {
    if n < 3 { return n }
    else { return recursive(n-1) + 2 * recursive(n-2) + 3 * recursive(n-3) }
}

for n in (0...10) {

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

//: [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