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Detailed explanations and implementations of some of my favorite specialized data structures and algorithms.

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Exotic Data Structures and Algorithms

A collection of some of my favorite rare and efficient data structures and algorithms written in Java.

The purpose of this project is not just to break down the exact mechanisms by which these data structures and algorithms per se function, but also to provide a deeper context for the rationale behind and the tradeoffs associated with the all data structures and algorithms that underlie different aspects of the software we program, test, and use today.

For example, the fact that Fibonacci Heaps are able to reduce their order of time-complexity when ???? by lazily defering clean-up until the next Extract Min operation helps us understand that (Binomial Heaps???).

Please note that, given the eductional purpose of this project, some Java best practices like using private access modifiers in conjunction with "getter" and "setter" methods are disregarded.

Concepts covered in this project include (but are not limited to) ?????>.

Built and tested using IntelliJ IDEA.

The Data Structures

  • Skip Lists: A Skip List is a type of linked list that is augmented with additional pointers so that each operation runs in average-case log n time. This is done by maintaining a linked hierarchy/levels of sub-sequences, with each successive sub-sequence skipping over fewer elements than the previous one; the selection of which elements exist in a given layer may be done randomly or deterministically (implemented randomly here, with a 50% chance an element added makes it up to the next tier), so that there are approximately log n layers. Skip List are sometimes considered as an alternative to balanced binary trees.

    • Advantages: Skip Lists have the best feature of a sorted array (namely, searching in log n time), while maintaining a linked list-like structure that allows insertion (not possible for a static array).
    • Disadvantages: Skip Lists suffer from two major problems: (1) Skip Lists are essentially keeping track of many linked lists at once, which negatively impacts its space-complexity (indeed, its worst-case space-complexity is O(n log n), which highlights this fact), and (2) Skip Lists have a deletion function which can be quite tricky to implement.
    • Visualization: Please find an example immediately below. For a fantastic animation of how Skip Lists are built and used, please click here.

  • Red-Black Trees: ???

    • ???
  • Binomial Heaps: A Binomial Heap is a type of mergable heap that acts as a priority queue; Binomial Heaps contain a collection of binomial trees linked at their roots, such that the roots form a linked list. Importantly, a Binomial Heap can only have 0 or 1 Binomial Tree of a given order. To that end, when calling EXTRACT-MIN1 on a Binomial Heap, the "orphaned" children of the obviated node are reversed in order (so to be in increasing order of order), placed in the linked list of binomial tree roots, and then UNION is continuously called until the Binomial Heap has no more than 1 Binomial Tree of a given order.

    • Review of Related Terms/Concepts:
      • Mergable Heap: A data structure containing several min- or max-heaps which themselves may be merged with one another.
      • Binomial Tree: An ordered tree that is defined recursively; the Binomial Tree B0 consists of a single node, and the Binomial Tree Bk consists of two binomial trees Bk-1 that are linked together so that the root of one is the leftmost child of the root of the other. Binomial Trees exhibit several interesting properties; for instance, a Binomial Tree of order k will have height k and 2k total nodes.
    • Advantages: ?
    • Disadvantages: ?
    • ???
  • Fibonacci Heaps: ???

    • ???

The Algorithms

  • Quick Select: ???
    • ???
  • Push-Relabel Network: ???
    • ???

Areas for Future Improvement

  • Modify code such that it follows Java best practices (e.g., using private access modifiers with getter and setter functions, utilizing Java interfaces, etc.).
  • asdf

Screenshots

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Acknowledgements

  • Professor Virgil Pavlu, my Algorithms professor.
  • The University of British Columbia, Okanagan Campus, for their fantastic Skip List visualization tool that I linked in my section on Skip Lists above.

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