实用数字算法太慢了

Question

我正在尝试编写一个程序来查找实际数字，从1到n的输入。

实用数字：https://en.wikipedia.org/wiki/Practical_number

我的代码运行正常，但速度极慢 - 需要10秒才需要20分钟。计算50左右的数字时会发生这种情况 - 它会停留在44位。

用Swift写的

import Foundation

func getInteger() -> Int {
    var firstNum:Int = 0
    while true {
        // get value from user. Using optional input since readLine returns an optional string.
        let input = readLine()
        // ensure string is not nil
        if let unwrappedInput = input {
            if let unwrappedInt = Int(unwrappedInput) {
                firstNum = unwrappedInt
                break
            }
            else { // the input doesn't convert into an int
                print("`\(unwrappedInput)` is not an integer. Please enter an integer")
            }
        }
        else { // did not enter anything
            print("Please enter an integer")
        }
    }

    return firstNum
}
func addOne(signArray: [Int]) -> [Int] { // finds the combinations
    var signArray2 = [Int]()
    for i in 0...signArray.count-1 {
        signArray2.append (signArray[i])
    }

    for i in 0...signArray2.count-1 {
        if signArray2[i] == 1 {
            signArray2[i] = 0
        }
        else {
            signArray2[i] = 1
            break
        }
    }
    return signArray2
}
func signEval (signArray: [Int], divArray: [Int], inNum: Int) -> Bool  {// changes 2nd
  var counts = 0
    for i in 0...divArray.count-1 {
        if signArray[i] == 0 {
counts = divArray[i] + counts        }
        if counts == inNum {
            return true
        }
    }
        return false
}
print("Please enter a number to find the summable numbers up to that number:")
var input2 = getInteger()// if num = 1 print 1 if num = 2 print 1 and 2 else print >2 1, 2
var inNum = 0
var numHalf = 0.0
var numRound = 0.0
var numCheck = false
var numCheck2 = false
var numQuarter = 0.0
var numSixth = 0.0
var divArray:[Int] = []
var theirArray = [Int]()
var signArray = [Int]()// array of 0s and 1s
var summableArray:[Int] = [1,2] // need to check if num is bigger than 2!
for input in 1...input2 {
        numHalf = Double (input) / 2.0
        numRound = round(numHalf)
        if numRound == numHalf {
            numCheck = true }
        if input > 2 && numCheck == false { // odd numbers greater than one are not summable
        }
        else { // these are possible summable nums
            numQuarter = Double (input) / 4.0
            numRound = round(numQuarter)
            if numRound == numQuarter {
                numCheck = true
            }
            else {
                numCheck = false
            }
            numSixth = Double(input) / 6.0
            numRound = round(numSixth)
            if numRound == numSixth {
                numCheck2 = true }
            else { numCheck2 = false}
            if numCheck == true || numCheck2 == true {
        theirArray = []
        divArray = []
        signArray = []
        summableArray = []
for i in 1...input {
    theirArray.append (i)
    }
for i in 1...input { // creates an array of all the diviors of inputted number
    if input%i == 0 {
        divArray.append (i)
    }
}
        for j in 1...divArray.count {//
            signArray.append(0)
        }

for i in 1...input{
let x: Int = Int(pow(Double(2),Double(input-1)))// int 2 to the power of input -1
    var Boolcheck = false

    for q in 1...x-1 { // i to 2^n -1 (sequence to check)
    Boolcheck = (signEval(signArray: signArray, divArray: divArray, inNum: i))// checks
        signArray = addOne(signArray: signArray)// adding the ones to the array
        if Boolcheck == true {
        summableArray.append(i)// creates array of mini summable numbers
        break
    }
        }
   if summableArray.count == input {
      print ("\(input)")
    }
}
    }
}
}