create a disjoint set in swift

To create a disjoint set data structure in Swift, we can use the Union-Find algorithm. This algorithm represents each disjoint set as a tree, with one element as the root of each tree. Each set is identified by the root element, and elements in the set are connected to the root.

Here is an implementation of the Union-Find algorithm in Swift:

main.swift
class DisjointSet {
    var parent = [Int]()

    init(_ size: Int) {
        parent = Array(0..<size)
    }

    func find(_ x: Int) -> Int {
        if x != parent[x] {
            parent[x] = find(parent[x])
        }
        return parent[x]
    }

    func union(_ x: Int, _ y: Int) {
        parent[find(x)] = find(y)
    }
}
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To create a disjoint set of size n, we first instantiate a DisjointSet object with size n:

main.swift
let set = DisjointSet(n)
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To union two elements x and y, we call the union method:

main.swift
set.union(x, y)
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To find the root of an element x, we call the find method:

main.swift
let root = set.find(x)
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The find method uses path compression to optimize the search for the root element. It sets the parent of each element in the path to the root element, reducing the height of the tree and improving the time complexity of subsequent find operations.

With this implementation, we have an efficient way to manage disjoint sets in Swift.