Access makes use of splaying, which we know has an O log n amortized upper.

The more leaf nodes that the tree contains the higher complexity of the tree because we have more flexibility in partitioning the space into smaller pieces, and therefore more possibilities for fitting the training data. There's also the issue of how much importance to put on the size of the tree. The complexity parameter α adjusts that. Recently I have been trying to learn link cut trees (and splay trees, for that matter).

I have tried to polish an implementation that is short (for our ICPC notebooks), and also easy to use and extend.

Mo's algorithm sqrt-decomposition for answering queries.

I might be extending this blog post towards a tutorial on how link cut trees are used and, more so, how this template can be used. A link/cut tree is a data structure for representing a forest, a set of rooted trees, and offers the following operations: Add a tree consisting of a single node to the forest. Given a node in one of the trees, disconnect it from the tree of which it is part.

Attach a node to another node as its child. Given a node, find the root of the tree to which it belongs.

By doing this operation on two distinct nodes, one can check whether they belong to the same tree. Invented by: Daniel Dominic Sleator, Robert Endre Tarjan. LinkCut tree - dynamic tree with path queries.

Tree Centers.

// LinkCut tree with path queries. Query complexity is O (log (n)) amortized. // Modify the following 5 methods to implement your custom operations on the tree. // This example implements Add/Sum operations. Operations like Add/Max, Set/Max can also be.