Added implmentation for the Karatsuba Algorithm

Author: richard-ash

Karatsuba Multiplication/KaratsubaMultiplication.playground/Contents.swift

@@ -0,0 +1,57 @@
+//: Playground - noun: a place where people can play
+
+import Foundation
+
+infix operator ^^ { associativity left precedence 160 }
+func ^^ (radix: Int, power: Int) -> Int {
+  return Int(pow(Double(radix), Double(power)))
+}
+
+// Long Multiplication - O(n^2)
+func multiply(num1: Int, _ num2: Int, base: Int = 10) -> Int {
+  let num1Array = String(num1).characters.reverse().map{ Int(String($0))! }
+  let num2Array = String(num2).characters.reverse().map{ Int(String($0))! }
+  
+  var product = Array(count: num1Array.count + num2Array.count, repeatedValue: 0)
+
+  for i in num1Array.indices {
+    var carry = 0
+    for j in num2Array.indices {
+      product[i + j] += carry + num1Array[i] * num2Array[j]
+      carry = product[i + j] / base
+      product[i + j] %= base
+    }
+    product[i + num2Array.count] += carry
+  }
+  
+  return Int(product.reverse().map{ String($0) }.reduce("", combine: +))!
+}
+
+// Karatsuba Multiplication - O(nlogn)
+func karatsuba(num1: Int, _ num2: Int) -> Int {
+  let num1Array = String(num1).characters
+  let num2Array = String(num2).characters
+  
+  guard num1Array.count > 1 && num2Array.count > 1 else {
+    return multiply(num1, num2)
+  }
+  
+  let n = max(num1Array.count, num2Array.count)
+  let nBy2 = n / 2
+  
+  let a = num1 / 10^^nBy2
+  let b = num1 % 10^^nBy2
+  let c = num2 / 10^^nBy2
+  let d = num2 % 10^^nBy2
+  
+  let ac = karatsuba(a, c)
+  let bd = karatsuba(b, d)
+  let adPluscd = karatsuba(a+b, c+d) - ac - bd
+  
+  let product = ac * 10^^(2 * nBy2) + adPluscd * 10^^nBy2 + bd
+  
+  return product
+}
+
+print(multiply(236742342, 1231234224))
+print(karatsuba(236742342, 1231234224))

Karatsuba Multiplication/KaratsubaMultiplication.playground/contents.xcplayground

@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
+<playground version='5.0' target-platform='ios' executeOnSourceChanges='false'>
+    <timeline fileName='timeline.xctimeline'/>
+</playground>

Karatsuba Multiplication/KaratsubaMultiplication.playground/playground.xcworkspace/contents.xcworkspacedata

@@ -7,3 +7,28 @@
 //
 
 import Foundation
+
+func karatsuba(num1: Int, _ num2: Int) -> Int {
+  let num1Array = String(num1).characters
+  let num2Array = String(num2).characters
+  
+  guard num1Array.count > 1 && num2Array.count > 1 else {
+    return num1 * num2
+  }
+  
+  let n = max(num1Array.count, num2Array.count)
+  let nBy2 = n / 2
+  
+  let a = num1 / 10^^nBy2
+  let b = num1 % 10^^nBy2
+  let c = num2 / 10^^nBy2
+  let d = num2 % 10^^nBy2
+  
+  let ac = karatsuba(a, c)
+  let bd = karatsuba(b, d)
+  let adPluscd = karatsuba(a+b, c+d) - ac - bd
+  
+  let product = ac * 10^^(2 * nBy2) + adPluscd * 10^^nBy2 + bd
+  
+  return product
+}