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$ curl repovive.com/roadmaps/data-structures/link-cut-trees/splay-with-push-down

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$ curl repovive.com/roadmaps/data-structures/link-cut-trees/splay-with-push-down

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Splay with Push Down - Link-Cut Trees | Data Structures | Repovive

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Data Structures19 sections · 729 units49h total

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Splay with Push Down

Handling lazy flags

Before splaying, push down lazy flags along the path:

function splay(x)
 // Push down from root to x
 pushDownPath(x)

 while not x.isRoot()
 p := x.parent
 if not p.isRoot()
 g := p.parent
 pushDown(g)
 pushDown(p)
 pushDown(x)

 if not p.isRoot()
 g := p.parent
 if (x = p.left) = (p = g.left) then
 rotate(p)
 else
 rotate(x)
 rotate(x)
 pushUp(x)

function pushDownPath(x)
 if not x.isRoot() then
 pushDownPath(x.parent)
 pushDown(x)

Push down ensures lazy values are applied before we rotate.