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  2. Master theorem (analysis of algorithms) - Wikipedia

    en.wikipedia.org/wiki/Master_theorem_(analysis...

    The master theorem always yields asymptotically tight bounds to recurrences from divide and conquer algorithms that partition an input into smaller subproblems of equal sizes, solve the subproblems recursively, and then combine the subproblem solutions to give a solution to the original problem. The time for such an algorithm can be expressed ...

  3. Analysis of algorithms - Wikipedia

    en.wikipedia.org/wiki/Analysis_of_algorithms

    For a worst-case evaluation, it should be assumed that step 3 will be run as well. Thus the total amount of time to run steps 1-3 and step 7 is: + + +. The loops in steps 4, 5 and 6 are trickier to evaluate. The outer loop test in step 4 will execute ( n + 1 ) times, [10] which will consume T 4 ( n + 1

  4. MacMahon's master theorem - Wikipedia

    en.wikipedia.org/wiki/MacMahon's_Master_theorem

    He explained the title as follows: "a Master Theorem from the masterly and rapid fashion in which it deals with various questions otherwise troublesome to solve." The result was re-derived (with attribution) a number of times, most notably by I. J. Good who derived it from his multilinear generalization of the Lagrange inversion theorem .

  5. Matrix multiplication algorithm - Wikipedia

    en.wikipedia.org/wiki/Matrix_multiplication...

    The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop:

  6. Master theorem - Wikipedia

    en.wikipedia.org/wiki/Master_theorem

    In mathematics, a theorem that covers a variety of cases is sometimes called a master theorem. Some theorems called master theorems in their fields include: Master theorem (analysis of algorithms), analyzing the asymptotic behavior of divide-and-conquer algorithms; Ramanujan's master theorem, providing an analytic expression for the Mellin ...

  7. Akra–Bazzi method - Wikipedia

    en.wikipedia.org/wiki/Akra–Bazzi_method

    It is a generalization of the master theorem for divide-and-conquer recurrences, which assumes that the sub-problems have equal size. It is named after mathematicians Mohamad Akra and Louay Bazzi. It is named after mathematicians Mohamad Akra and Louay Bazzi.

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  9. Quicksort - Wikipedia

    en.wikipedia.org/wiki/Quicksort

    The master theorem for divide-and-conquer recurrences tells us that T(n) = O(n log n). The outline of a formal proof of the O(n log n) expected time complexity follows. Assume that there are no duplicates as duplicates could be handled with linear time pre- and post-processing, or considered cases easier than the analyzed.