Merge branch 'master' of git://github.com/tikipatel/swift-algorithm-club into tikipatel-prime-numbers

Author: Chris Pilcher

Prime Numbers/Atkins_Sieve.swift

@@ -0,0 +1,54 @@
+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] {
+    var is_prime = [Bool](count: max + 1, repeatedValue: false)
+    is_prime[2] = true
+    is_prime[3] = true
+    let limit = Int(ceil(sqrt(Double(max))))
+    for x in 1...limit {
+        for y in 1...limit {
+            var num = 4 * x * x + y * y
+            if (num <= max && (num % 12 == 1 || num % 12 == 5)) {
+                is_prime[num] = true
+            }
+            num = 3 * x * x + y * y
+            if (num <= max && num % 12 == 7) {
+                is_prime[num] = true
+            }
+            if (x > y) {
+                num = 3 * x * x - y * y
+                if (num <= max && num % 12 == 11) {
+                    is_prime[num] = true
+                }
+            }
+        }
+    }
+    if limit > 5 {
+        for i in 5...limit {
+            if is_prime[i] {
+                for j in (i * i)..i..max {
+                    is_prime[j] = false
+                }
+            }
+        }
+    }
+    var primesArray = [Int]()
+    for (idx, val) in is_prime.enumerate() {
+        if val == true { primesArray.append(idx) }
+    }
+    return primesArray
+}

Prime Numbers/Eratosthenes_Sieve.swift

@@ -0,0 +1,29 @@
+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/PrimeGenerator.swift

@@ -0,0 +1,90 @@
+//
+//  Operators.swift
+//  Primes
+//
+//  Created by Pratikbhai Patel on 6/13/16.
+//  Copyright © 2016 Pratikbhai Patel. All rights reserved.
+//
+
+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](stride(from: left.0, through: right, by: left.1))
+}
+
+class PrimeGenerator {
+    
+    static let sharedInstance = PrimeGenerator()
+    private let eraQueue = DispatchQueue(label: "eraQueue")
+    private let atQueue = DispatchQueue(label: "atQueue")
+
+    func eratosthenesPrimes(_ max: Int, completion:([Int]) -> ()){
+        
+        eraQueue.async {
+            let m = Int(sqrt(ceil(Double(max))))
+            let set = NSMutableSet(array: 3..2..max)
+            set.add(2)
+            for i in (2..1..m) {
+                if (set.contains(i)) {
+                    for j in i^^2..i..max {
+                        set.remove(j)
+                    }
+                }
+            }
+            completion(set.sortedArray(using: [SortDescriptor(key: "integerValue", ascending: true)]) as! [Int])
+        }
+    }
+    
+    func atkinsPrimes(_ max: Int, completion:([Int]) -> ()) {
+        atQueue.async {
+            var is_prime = [Bool](repeating: false, count: max + 1)
+            is_prime[2] = true
+            is_prime[3] = true
+            let limit = Int(ceil(sqrt(Double(max))))
+            for x in 1...limit {
+                for y in 1...limit {
+                    var num = 4 * x * x + y * y
+                    if (num <= max && (num % 12 == 1 || num % 12 == 5)) {
+                        is_prime[num] = true
+                    }
+                    num = 3 * x * x + y * y
+                    if (num <= max && num % 12 == 7) {
+                        is_prime[num] = true
+                    }
+                    if (x > y) {
+                        num = 3 * x * x - y * y
+                        if (num <= max && num % 12 == 11) {
+                            is_prime[num] = true
+                        }
+                    }
+                }
+            }
+            
+            if limit > 5 {
+                for i in 5...limit {
+                    if is_prime[i] {
+                        for j in (i * i)..i..max {
+                            is_prime[j] = false
+                        }
+                    }
+                }
+            }
+            var primesArray = [Int]()
+            for (idx, val) in is_prime.enumerated() {
+                if val == true { primesArray.append(idx) }
+            }
+            completion(primesArray)
+        }
+    }
+}