Yes, Splay Trees can become unbalanced in certain scenarios. While Splay Trees are designed to be self-adjusting and adapt to access patterns, there are cases where the tree may exhibit unbalanced structures, particularly in the worst-case scenario. The primary reason for potential unbalancing is the lack of strict balancing criteria in Splay Trees.
Here are a few scenarios that can lead to unbalanced Splay Trees:
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Sequential or Ordered Insertions/Deletions:
- If elements are inserted or deleted in a sequential or ordered manner, the tree may become skewed or unbalanced.
- For example, repeatedly inserting elements in ascending or descending order without interleaving other operations may lead to a tree resembling a linked list.
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Repeated Access to Extreme Nodes:
- If there is a sequence of repeated accesses to nodes near the extremes (either the smallest or largest elements), the tree may become unbalanced.
- Splaying the extreme nodes to the root in succession could result in a tree with a skewed structure.
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Long Sequences of Zig-Zig or Zig-Zag Operations:
- In certain access patterns, particularly those involving long sequences of zig-zig or zig-zag operations, the tree may exhibit unbalanced structures.
- These patterns can lead to elongated paths in the tree.
While Splay Trees are not guaranteed to maintain a strict balance, their amortized time complexity over a sequence of operations is often favorable, and they adapt well to various access patterns. It's important to note that the lack of strict balancing criteria in Splay Trees is a trade-off for their simplicity and adaptiveness.
In practice, the efficiency of Splay Trees is often measured by their average-case performance, where the adaptiveness to access patterns allows frequently accessed elements to be brought closer to the root, contributing to efficient average-case time complexity.
