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$ curl repovive.com/roadmaps/data-structures/union-find/valid-tree-solution

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$ curl repovive.com/roadmaps/data-structures/union-find/valid-tree-solution

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Valid Tree Solution - Union-Find | Data Structures | Repovive

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Data Structures19 sections · 729 units49h total

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Valid Tree Solution

Check edges and connectivity

Two conditions to check:

$1.$ Exactly $n - 1$ edges (necessary for any tree)

$2.$ No cycles (every union should succeed)

def validTree(n, edges):
    if len(edges) != n - 1:
        return False

    uf = UnionFind(n)
    for u, v in edges:
        if not uf.union(u, v):
            return False  # cycle detected

    return True

if you have exactly $n-1$ edges and no cycles, the graph must be connected. Why? An acyclic graph with $n$ nodes and $n-1$ edges has exactly one component (any more components would require fewer edges).

Time: $O(n \cdot \alpha(n)) \approx O(n)$ . Space: $O(n)$ .