如何从给定的数字中找到一个随机组合，这些组合在 Swift 中加起来是另一个数字？

Question

给定一组随机的正整数A，找出一个整数的随机组合，加起来等于N。

例如。

A = [4, 2, 10, 8, 13, 1, ...]  
N = 18  
The possibilities are [10, 8], [4, 13, 1], etc.

集合A 也可以是任意长度，并且只能容纳正整数。

N 可以是任何正整数。

我只需要一种数字组合，而不是全部。我也想随机选择，所以如果我得到相同的集合，我不会每次都得到相同的答案，我正在寻找可以在 Swift 中以编程方式执行此操作的最有效方法。

Answer 1

您首先需要创建一个方法来查找您的原始收藏的所有可能子集，正如我在此处发布的 Subset sum Swift。然后你只需要检查任何子集总和是否等于 n：

extension RangeReplaceableCollection  {
    var subSets: [SubSequence] {
        return isEmpty ? [SubSequence()] : dropFirst().subSets.lazy.flatMap { [$0, prefix(1) + $0] }
    }
}

---

let a = [4, 2, 10, 8, 13, 1]
let n = 18
let matches = a.subSets.lazy.filter { $0.reduce(0,+) == n }
print("Matches:", Array(matches.map{Array($0)}))  // Matches: [[10, 8], [4, 13, 1]]

您还可以使用非递归方法，正如您在我在这里发布的另一篇帖子 Find all combination of string array in swift 中看到的那样。请注意，我这样做的第二种方法是不将空集视为子集：

extension RangeReplaceableCollection {
    var subSetsNotRecursive : [SubSequence] {
        guard !isEmpty else { return [] }
        let count = self.count
        let n = 1 << count - 1
        var subSequences: [SubSequence] = .init(repeating: SubSequence(), count: n-1)
        (0 ..< n).map {
            var counter = 0
            for element in self {
                if $0 & 1 << counter > 0 {
                    subSequences[$0-1].append(element)
                }
                counter += 1
            }
        }
        return subSequences + [self[...]]
    }
}

---

let matches2 = a.subSetsNotRecursive.lazy.filter { $0.reduce(0,+) == n }
print("Matches2:", Array(matches2.map{Array($0)}))  // Matches2: [[10, 8], [4, 13, 1]]

或者进一步扩展它。如果您只对总和等于某个值的集合感兴趣，您可以在每次完成创建集合时检查附加元素的总和是否等于您想要的值：

extension RangeReplaceableCollection where Element: BinaryInteger {
    func subSetsThatSummedAre(equalTo value: Element) -> [SubSequence] {
        guard !isEmpty else { return [] }
        let count = self.count
        let n = 1 << count - 1
        var subSets: [SubSequence] = []
        (0 ..< n).map {
            var counter = 0
            var sum: Element = 0
            var subSequence = SubSequence()
            for element in self {
                if $0 & 1 << counter > 0 {
                    subSequence.append(element)
                    sum += element
                }
                counter += 1
            }
            if sum == value {
                subSets.append(subSequence)
            }
        }
        if reduce(0, +) == value {
            subSets.append(self[...])
        }
        return subSets
    }
}

---

let matches4 = a.subSetsThatSummedAre(equalTo: n)
print("Matches4:", Array(matches4.map{Array($0)}))  // Matches4: [[10, 8], [4, 13, 1]]