Algorithms Kruskals algorithm suggest change

Simple disjoint-set based implementation

The above forest methodology is actually a disjoint-set data structure, which involves three main operations:

subalgo makeSet(v: a node):
    v.parent = v    <- make a new tree rooted at v
    

subalgo findSet(v: a node):
    if v.parent == v:
        return v
    return findSet(v.parent)

subalgo unionSet(v, u: nodes):
    vRoot = findSet(v)
    uRoot = findSet(u)

    uRoot.parent = vRoot

algorithm kruskalMST''(G: a graph):
    sort G's edges by their value
    for each node n in G:
        makeSet(n)
    for each edge e in G:
        if findSet(e.first) != findSet(e.second):
            unionSet(e.first, e.second)

This naive implementation leads to O(n log n) time for managing the disjoint-set data structure, leading to O(m*n log n) time for the entire Kruskal’s algorithm.

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