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$ curl repovive.com/roadmaps/data-structures/advanced-trees/treap-operations-split

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$ curl repovive.com/roadmaps/data-structures/advanced-trees/treap-operations-split

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Treap Operations - Split - Advanced Trees | Data Structures | Repovive

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Data Structures19 sections · 729 units49h total

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Treap Operations - Split

Dividing by key

Split divides a treap into two treaps: one with keys $< x$ , one with keys $\geq x$ .

function split(node, x)
    if node is null then
        return (null, null)

    if node.key < x then
        (left, right) := split(node.right, x)
        node.right := left
        return (node, right)
    else
        (left, right) := split(node.left, x)
        node.left := right
        return (left, node)

Time: $O(\log n)$ expected. The recursion follows a path from root to leaf, and expected path length is $O(\log n)$ .