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  2. Computational complexity of mathematical operations - Wikipedia

    en.wikipedia.org/wiki/Computational_complexity...

    Here, complexity refers to the time complexity of performing computations on a multitape Turing machine. [1] See big O notation for an explanation of the notation used. Note: Due to the variety of multiplication algorithms, () below stands in for the complexity of the chosen multiplication algorithm.

  3. Disjoint-set data structure - Wikipedia

    en.wikipedia.org/wiki/Disjoint-set_data_structure

    In 1975, Robert Tarjan was the first to prove the (()) (inverse Ackermann function) upper bound on the algorithm's time complexity,. [4] He also proved it to be tight. In 1979, he showed that this was the lower bound for a certain class of algorithms, that include the Galler-Fischer structure. [ 5 ]

  4. Time complexity - Wikipedia

    en.wikipedia.org/wiki/Time_complexity

    [1]: 226 Since this function is generally difficult to compute exactly, and the running time for small inputs is usually not consequential, one commonly focuses on the behavior of the complexity when the input size increases—that is, the asymptotic behavior of the complexity. Therefore, the time complexity is commonly expressed using big O ...

  5. Computational complexity - Wikipedia

    en.wikipedia.org/wiki/Computational_complexity

    Therefore, the time complexity, generally called bit complexity in this context, may be much larger than the arithmetic complexity. For example, the arithmetic complexity of the computation of the determinant of a n × n integer matrix is O ( n 3 ) {\displaystyle O(n^{3})} for the usual algorithms ( Gaussian elimination ).

  6. Association list - Wikipedia

    en.wikipedia.org/wiki/Association_list

    The disadvantage of association lists is that the time to search is O(), where n is the length of the list. [3] For large lists, this may be much slower than the times that can be obtained by representing an associative array as a binary search tree or as a hash table.

  7. k-way merge algorithm - Wikipedia

    en.wikipedia.org/wiki/K-way_merge_algorithm

    The running time can be improved by iteratively merging the first with the second, the third with the fourth, and so on. As the number of arrays is halved in each iteration, there are only Θ(log k) iterations. In each iteration every element is moved exactly once. The running time per iteration is therefore in Θ(n) as n is the number of elements.

  8. Comparison of data structures - Wikipedia

    en.wikipedia.org/wiki/Comparison_of_data_structures

    Here are time complexities [5] of various heap data structures. The abbreviation am. indicates that the given complexity is amortized, otherwise it is a worst-case complexity. For the meaning of "O(f)" and "Θ(f)" see Big O notation. Names of operations assume a max-heap.

  9. Skip list - Wikipedia

    en.wikipedia.org/wiki/Skip_list

    List of applications and frameworks that use skip lists: Apache Portable Runtime implements skip lists. [9] MemSQL uses lock-free skip lists as its prime indexing structure for its database technology. MuQSS, for the Linux kernel, is a cpu scheduler built on skip lists. [10] [11] Cyrus IMAP server offers a "skiplist" backend DB implementation [12]