Add prime generation

Author: tikipatel

Prime Numbers/PrimeSieve.swift

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+infix operator ^^ { associativity left precedence 160 }
+func ^^ (radix: Int, power: Int) -> Int {
+    return Int(pow(CGFloat(radix), CGFloat(power)))
+}
+
+infix operator .. {associativity left precedence 60 }
+
+func ..<T: Strideable>(left: T, right: T.Stride) -> (T, T.Stride) {
+    return (left, right)
+}
+
+func ..<T: Strideable>(left: (T, T.Stride), right: T) -> [T] {
+    return [T](left.0.stride(through: right, by: left.1))
+}
+
+
+func primesTo(max: Int) -> [Int] {
+    let m = Int(sqrt(ceil(Double(max))))
+    let set = NSMutableSet(array: 3..2..max)
+    set.addObject(2)
+    for i in (2..1..m) {
+        if (set.containsObject(i)) {
+            for j in i^^2..i..max {
+                set.removeObject(j)
+            }
+        }
+    }
+    return set.sortedArrayUsingDescriptors([NSSortDescriptor(key: "integerValue", ascending: true)]) as! [Int]
+}

Prime Numbers/README.md

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+# Sieve Primes
+
+Goal: To quickly get an array of prime numbers with a specified limit using the Sieve of Eratosthenes.
+
+The Sieve of Eratosthenes is an algorithm that finds all primes numbers up to any given limit.
+
+Here's an implementation in Swift that should be easy to understand:
+
+```
+func primesTo(max: Int) -> [Int] {
+    let m = Int(sqrt(ceil(Double(max))))
+    let set = NSMutableSet(array: 3..2..max)
+    set.addObject(2)
+    for i in (2..1..m) {
+        if (set.containsObject(i)) {
+            for j in i^^2..i..max {
+                set.removeObject(j)
+            }
+        }
+    }
+    return set.sortedArrayUsingDescriptors([NSSortDescriptor(key: "integerValue", ascending: true)]) as! [Int]
+}
+```
+
+Put this code in a playground and test it like so:
+
+```
+let primesArray = primesTo(50)
+print(primesArray)
+// prints [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
+```
+
+--*write some introduction to the Sieve of Eratosthenes*--
+
+## See also
+
+[Sieve of Eratosthenes on Wikipedia](https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes)
+
+*Written for Swift Algorithm Club by Pratikbhai Patel*

Prime Numbers/SievePrimes.playground/Contents.swift

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+//: Playground - noun: a place where people can play
+
+import Foundation
+import UIKit
+
+infix operator ^^ { associativity left precedence 160 }
+func ^^ (radix: Int, power: Int) -> Int {
+    return Int(pow(CGFloat(radix), CGFloat(power)))
+}
+
+infix operator .. {associativity left precedence 60 }
+
+func ..<T: Strideable>(left: T, right: T.Stride) -> (T, T.Stride) {
+    return (left, right)
+}
+
+func ..<T: Strideable>(left: (T, T.Stride), right: T) -> [T] {
+    return [T](left.0.stride(through: right, by: left.1))
+}
+
+func primesTo(max: Int) -> [Int] {
+    assert(max > 1, "Prime numbers can only be above 1")
+    print("Getting all primes under \(max)")
+    let m = Int(sqrt(ceil(Double(max))))
+    print("Need to remove all multiples of numbers through \(m)")
+    let set = NSMutableSet(array: 3..2..max)
+    set.addObject(2)
+    print(set)
+    for i in (2..1..m) {
+        if (set.containsObject(i)) {
+            print("Removing all multiples of \(i)")
+            for j in i^^2..i..max {
+                print("removing j: \(j)")
+                set.removeObject(j)
+            }
+        }
+    }
+    return set.sortedArrayUsingDescriptors([NSSortDescriptor(key: "integerValue", ascending: true)]) as! [Int]
+}
+
+let startDate = NSDate().timeIntervalSince1970 * 1000
+print(primesTo(50))
+let endDate = NSDate().timeIntervalSince1970 * 1000
+print("Prime generation time: \(endDate - startDate) ms.")

Prime Numbers/SievePrimes.playground/contents.xcplayground

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+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>