[Swift]经典解题思路:联合查找Union Find

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➤微信公众号：山青咏芝（shanqingyongzhi）
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【结构】

public struct UnionFind<T: Hashable> {
    private var index: [T: Int] = [:]
    private var parent: [Int] = []
    private var size: [Int] = []
    public var numerOfSets: Int = 0 
    
    public mutating func addSet(_ element: T) {
        if index[element] == nil {
            index[element] = parent.count
            parent.append(parent.count)
            size.append(1)
            numerOfSets += 1
        }
    }
    
    public mutating func find(_ element: T) ->Int? {
        guard let index = index[element] else {
            return nil 
        }
        return setByIndex(index)
    }
    
    private mutating func setByIndex(_ index: Int) -> Int {
        if parent[index] == index {
            return index 
        } else {
            parent[index] = setByIndex(parent[index])
            return parent[index]
        }
    }
    
    public mutating func union(_ element1: T, _ element2: T) {
        guard let set1 = find(element1), let set2 = find(element2) else {
            return 
        }
        
        if set1 != set2 {
            numerOfSets -= 1 
            if size[set1] > size[set2] {
                parent[set2] = set1 
                size[set1] += size[set2]
            } else {
                parent[set1] = set2 
                size[set2] += size[set1]
            }
        }
    }
}

【类】

class UnionFind {
    private var connectivities: [Int]
    private var sizes: [Int]
    init(size: Int) {
        self.connectivities = [Int](repeating: 0, count: size)
        self.sizes = [Int](repeating: 1, count: size)
        for i in 0..<size {
            connectivities[i] = i
        }
    }
    func connect(n1: Int, n2: Int) {
        guard let root1 = root(of: n1),
            let root2 = root(of: n2),
            root1 != root2 else { return }
        let sz1 = sizes[root1]
        let sz2 = sizes[root2]
        if sz1 > sz2 {
            connectivities[root2] = root1
            sizes[root1] += sizes[root2]
        } else {
            connectivities[root1] = root2
            sizes[root2] += sizes[root1]
        }
    }
    func isConnected(n1: Int, n2: Int) -> Bool {
        return root(of: n1) == root(of: n2)
    }
    func root(of n: Int) -> Int? {
        guard n < connectivities.count else { return nil }
        let parent = connectivities[n]
        if parent == n {
            return n
        }
        guard let rt = root(of: parent) else { return nil }
        connectivities[n] = rt
        return rt
    }
    func snapshot() {
        print("c: \(connectivities)")
        print("s: \(sizes)")
    }
}