我试图在Swift中实现Karatsuba乘法。我写了下面的代码,它对一些较小的数字工作正常,但随着数字变大,这段代码无法给予正确的答案。我已经尽可能地调试了我可以,但无法找到错误。算法明智,我认为我正确地写了代码。代码对较小的数字工作正常。但是最后的答案对于更大的数字是错误的。如果有人能纠正我犯的错误,请帮助我
func findMultiplication(x: String, y: String) -> String {
if isZero(str: x) || isZero(str: y) {
return "0"
}
var x = removeLeadingZeros(number: x)
var y = removeLeadingZeros(number: y)
if x.count < 2 || y.count < 2 {
let result = Int(x)!*Int(y)!
return String(result)
}
var middleIndexX: String.Index
var middleIndexY: String.Index
var middleIndex: Int
if x.count >= y.count {
y = addLeftPaddingZeros(numberOfZeros: x.count-y.count, for: y)
middleIndex = x.count / 2
if x.count % 2 != 0 {
middleIndex += 1
}
} else {
x = addLeftPaddingZeros(numberOfZeros: y.count-x.count, for: x)
middleIndex = y.count / 2
if y.count % 2 != 0 {
middleIndex += 1
}
}
middleIndexX = x.index(x.startIndex, offsetBy: middleIndex)
middleIndexY = y.index(y.startIndex, offsetBy: middleIndex)
let a = String(x[x.startIndex..<middleIndexX])
let b = String(x[middleIndexX..<x.endIndex])
let c = String(y[y.startIndex..<middleIndexY])
let d = String(y[middleIndexY..<y.endIndex])
let ac = findMultiplication(x: a, y: c)
let bd = findMultiplication(x: b, y: d)
let aPb = Int(a)! + Int(b)!
let cPd = Int(c)! + Int(d)!
let gauss = findMultiplication(x: String(aPb), y: String(cPd))
let thirdItem = String(Int(gauss)! - Int(ac)! - Int(bd)!)
var returnSum = 0
returnSum += Int(addLeftPaddingZeros(numberOfZeros: x.count, for: ac, isLeft: false)) ?? 0
returnSum += Int(addLeftPaddingZeros(numberOfZeros: middleIndex, for: thirdItem, isLeft: false)) ?? 0
returnSum += Int(bd) ?? 0
return String(returnSum)
}
print(findMultiplication(x: "123400", y: "123711"))
func removeLeadingZeros(number: String) -> String {
var number = number
while number.first == "0" {
number.removeFirst()
}
if number == "" {
return "0"
}
return number
}
//The function name is given like this only. BUt his will help to add padding zero in left and right also
func addLeftPaddingZeros(numberOfZeros: Int, for str: String, isLeft: Bool = true) -> String {
var padding = ""
for _ in 0 ..< numberOfZeros {
padding += "0"
}
if isLeft {
return padding+str
} else {
return str + padding
}
}
func isZero(str: String) -> Bool {
for char in str {
if char != "0" {
return false
}
}
return true
}
1条答案
按热度按时间yacmzcpb1#
这里有一个实现:
https://victorqi.gitbooks.io/swift-algorithm/content/karatsuba-multiplication.html
他们的代码如下: