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skip_list

Probabilistic data structure that facilitates efficient search, insertion, and deletion operations within a sorted sequence of elements

INFO

can be thought of as an enhancement of a linked list, where multiple layers of linked lists are used to allow for faster traversal

Structure of a Skip List​

Bottom Layer​

  • Standard sorted linked list
  • Contains all elements

Upper Layers​

  • Each subsequent layer acts as an "express lane," where fewer elements are present
  • The probability of an element being included in a higher layer is typically set at p=1/2​ or p=1/4
INFO

on average, each element appears in (1 / (1-p))​ layers > logarithmic height relative to the number of elements nn in the list

Operations​

  1. Start at the top-left node
  2. Move right until reaching a node with a value >= target
  3. If such a node is found, drop down one level and repeat until reaching the bottom layer
  4. If the target value is found, return it; otherwise, indicate that it is not present

Time complexity: O(LogN)

Insertion​

  1. Searching for the appropriate position (as per Search)
  2. Determining level for the new node using coin flip method (random)
  3. Updating pointers in all relevant layers to include the new node

Time complexity: O(LogN)

Deletion​

  1. Locate the node to be deleted
  2. Update pointers from its predecessors to bypass the node being removed across all levels
  3. Adjust levels if necessary

Time complexity: O(LogN)

Advantages and Applications​

  • Allow concurrent access during insertions / deletions without global rebalancing
  • Suitable for parallel computing environments

References

  • Perplexity AI