Why it matters

Link-cut trees enable dynamic tree algorithms. Understanding shapes advanced structures.

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The architecture

Preferred paths + splay trees.

Access + link + cut + expose ops.

Path queries + updates.

Link-cut tree structurePreferred pathsof treeSplay treesof preferred pathsAmortized log noperationsSleator + Tarjan 1983; enable dynamic MST, max flow, more
Link-cut trees.
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How it works end to end

Preferred child = last accessed.

Splay operations maintain.

Applications: dynamic connectivity, MST, flow.