Search results
Results from the WOW.Com Content Network
In computer science, divide and conquer is an algorithm design paradigm. A divide-and-conquer algorithm recursively breaks down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem.
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 ...
The basic concept behind these algorithms is the divide-and-conquer approach from computer science. An eigenvalue problem is divided into two problems of roughly half the size, each of these are solved recursively, and the eigenvalues of the original problem are computed from the results of these smaller problems.
The basic principle of Karatsuba's algorithm is divide-and-conquer, using a formula that allows one to compute the product of two large numbers and using three multiplications of smaller numbers, each with about half as many digits as or , plus some additions and digit shifts.
Otherwise, provided the problem exhibits overlapping subproblems as well, divide-and-conquer methods or dynamic programming may be used. If there are no appropriate greedy algorithms and the problem fails to exhibit overlapping subproblems, often a lengthy but straightforward search of the solution space is the best alternative.
The Akra–Bazzi method is more useful than most other techniques for determining asymptotic behavior because it covers such a wide variety of cases. Its primary application is the approximation of the running time of many divide-and-conquer algorithms.
Quicksort is a type of divide-and-conquer algorithm for sorting an array, based on a partitioning routine; the details of this partitioning can vary somewhat, so that quicksort is really a family of closely related algorithms. Applied to a range of at least two elements, partitioning produces a division into two consecutive non empty sub-ranges ...
The FWHT h is a divide-and-conquer algorithm that recursively breaks down a WHT of size into two smaller WHTs of size /. [ 1 ] This implementation follows the recursive definition of the 2 m × 2 m {\displaystyle 2^{m}\times 2^{m}} Hadamard matrix H m {\displaystyle H_{m}} :