如何检测重复的小数

Question

我需要检测一个无限商.例如,当用户除以1/3时,我不会向他显示0.333333333333,我要告诉他结果是重复小数.

Answer 1

下面是一个可能的实现,如何计算分数的十进制扩展并检测重复小数(即十进制扩展中的句点).它是在Code Review到Swift 的有理数的十进制扩展中发布和审查的代码的翻译.

该算法只是Long Division,而array(remainders)用于检查周期性的十进制扩展.(为简单起见,假设分子是非负的,分母是正的.如果需要,这可以推广.)

struct DecimalFraction : Printable {
    let wholePart : Int         // Integer part
    let fractionDigits : [Int]  // Fractional digits
    let repeatingAt : Int?      // Position of first repeating digit, or `nil`

    // Create DecimalFraction from given fraction
    init(numerator : Int, denominator : Int) {
        precondition(numerator >= 0, "`numerator` must be non-negative")
        precondition(denominator > 0, "`denominator` must be positive")

        wholePart = numerator / denominator
        var fractionDigits : [Int] = []
        var repeatingAt : Int? = nil
        var rem = (abs(numerator) % denominator) * 10
        var remainders : [Int] = []
        while (rem > 0 && repeatingAt == nil) {
            remainders.append(rem)
            let digit = rem / denominator
            rem = (rem % denominator) * 10
            fractionDigits.append(digit)
            repeatingAt = find(remainders, rem)
        }
        self.fractionDigits = fractionDigits
        self.repeatingAt = repeatingAt
    }

    // Produce a string description, e.g. "12.3{45}"
    var description : String {
        var result = String(wholePart) + "."
        for (idx, digit) in enumerate(fractionDigits) {
            if idx == repeatingAt {
                result += "{"
            }
            result += String(digit)
        }
        if repeatingAt != nil {
            result += "}"
        }
        return result
    }
}

例子:

println(DecimalFraction(numerator: 3, denominator: 8))
// 0.375
println(DecimalFraction(numerator: 1, denominator: 3))
// 0.{3}
println(DecimalFraction(numerator: 20, denominator: 7))
// 2.{857142}
println(DecimalFraction(numerator: 12222, denominator: 990))
// 12.3{45}

句点简单地用花括号表示,但是应该很容易修改代码以产生一个NSAttributedString 表示句点的例子 - 例如 - 水平线.