Define a splay tree and its properties.

A splay tree is a self-adjusting binary search tree with the additional property that recently accessed elements are quick to access again.

A splay tree is a type of binary search tree that reorganises itself every time an operation is performed, such as insertion, deletion, or search. This reorganisation is done to bring the element involved in the operation to the root of the tree, making it quicker to access in subsequent operations. This property makes splay trees particularly useful in applications where certain elements are accessed more frequently than others.

The reorganisation in a splay tree is done through a process called 'splaying'. When an element is accessed, it is 'splayed' to the root of the tree using a series of tree rotations. These rotations not only bring the accessed element to the root, but also partially rebalance the tree, which can improve the efficiency of future operations.

One of the key properties of a splay tree is that it is self-adjusting. This means that it automatically adjusts its structure based on the sequence of operations performed. This can lead to significant improvements in efficiency for certain sequences of operations. For example, if a particular element is accessed frequently, it will remain near the root of the tree, making future accesses to that element very fast.

Another important property of splay trees is that they do not need to store any additional information per node, unlike other types of self-adjusting trees such as AVL trees or red-black trees. This makes splay trees more space-efficient.

In terms of time complexity, the worst-case time complexity for search, insert, and delete operations in a splay tree is O(n). However, the amortised time complexity for these operations is O(log n), which means that over a sequence of n operations, the average time per operation is O(log n). This makes splay trees efficient for sequences of operations where certain elements are accessed more frequently than others.