Questions tagged [splay-trees]

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Can every node of a link/cut tree be accessed in $O(n)$ time?

Per the Sequential Access Theorem we can access every node of a splay tree in $O(n)$ time, when accessing the nodes in a specific order. Given a link/cut tree, is it possible to access all of its ...
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Splay trees: why are depths of nodes on the access path halved?

The original paper describing splay trees Self-Adjusting Binary Search Trees by Sleator and Tarjan claims that: Splaying not only moves x to the root, but roughly halves the depth of every node ...
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Splay tree amortized analysis cost using Access Lemma

Currently studying for an algorithms exam and I came across this question and solution, but I can't understand the solution where it references nodes of depth less than $4\log n$ and not restructuring....
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70 views

Splay Tree - Insert Permutation

Let $T$ be a Splay Tree. For a given permutation $\sigma$ on a set $S = \{1,2,3,...n \}$ we defined the following function: ...
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24 views

Accounting value of Splay trees?

In Splay trees, by definition - the required element x - rises to the root of the tree, using the operations: zig, zig-zig, zig-zag. And the formula zig of the step is this: ...
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Why is maximum size of root is 2n + 1 in Splay trees?

In the amortized analysis of Splaying in Dynamic trees, let us consider a splay tree $T$ with $n$ keys and $v$ be a node of $T$. We define $size(v)$ as the number of nodes in the subtree rooted at $...
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29 views

(Searching + Splaying) in a Splay Tree

Given a tree To search for value 1, I do the following splay operations: i) Zag on 7 ii) Zag on 1 And hence obtain 1 in the root. But why would this be incorrect? i) Zag on 1 ii) Zag on 1 The ...
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25 views

How to reconstruct an existing splay tree by insertion?

I'm trying to figure out the same problem as stated in this question. In brief, I want to reconstruct an existing splay tree (printed on paper) on Splay Tree Visualization by inserting the values in ...
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28 views

Proof of Zig-Zig step

There was a question connected with one of the video lecture lessons that I'm currently watching. Let two trees be given - the original and the tree after the zig-zig step: Calculate the cost of ...
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320 views

Proof by induction for a splay tree?

I'm preparing for an exam about Trees. One of the questions that appear in Mark Allen Weiss' "Data Structures and Algorithms Analysis in C++" is: Prove by induction that if all nodes in a splay ...