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A skip list is a probabilistic data structure that allows for efficient search, insertion, and removal operations.

A skip list is essentially a linked list that has been enhanced with additional forward pointers at various levels, which allow for faster traversal of the data. It is called a 'skip' list because these forward pointers allow us to skip over many nodes in the list, thereby speeding up the process of finding a particular element.

The structure of a skip list is made up of multiple sorted linked lists, each of which is a subset of the list below it. The bottom level list contains all the elements, while each higher level list contains a randomly selected subset of the elements from the list below it. The top level list contains the fewest elements, and the number of elements in each list decreases as we move up the levels. This structure allows for efficient search operations, as we can start at the top level and move down the levels until we find the desired element.

The efficiency of a skip list comes from the fact that it balances the benefits of a sorted array (quick search times) with the benefits of a linked list (quick insertion and removal times). The forward pointers allow us to skip over large sections of the list when searching for an element, similar to how we can quickly find an element in a sorted array by jumping to the middle of the array and eliminating half the elements from consideration. At the same time, because the skip list is still fundamentally a linked list, we can quickly insert or remove elements by simply updating a few pointers, without needing to shift large sections of data around.

In terms of complexity, search, insertion, and removal operations in a skip list all have an average and worst-case time complexity of O(log n), where n is the number of elements in the list. This makes skip lists an efficient option for many applications. However, they do require more space than a simple linked list, due to the additional forward pointers.

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