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The divide-and-conquer technique is the basis of efficient algorithms for many problems, such as sorting (e.g., quicksort, merge sort), multiplying large numbers (e.g., the Karatsuba algorithm), finding the closest pair of points, syntactic analysis (e.g., top-down parsers), and computing the discrete Fourier transform .
The Karatsuba algorithm is a fast multiplication algorithm. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. [ 1 ] [ 2 ] [ 3 ] It is a divide-and-conquer algorithm that reduces the multiplication of two n -digit numbers to three multiplications of n /2-digit numbers and, by repeating this reduction, to at most n log 2 3 ...
Download as PDF; Printable version; In other projects Wikimedia Commons; Wikidata item; Appearance. ... Divide-and-conquer algorithm; C. Closest pair of points problem;
This technique can be used to improve the efficiency of many eigenvalue algorithms, but it has special significance to divide-and-conquer. For the rest of this article, we will assume the input to the divide-and-conquer algorithm is an real symmetric tridiagonal matrix . The algorithm can be modified for Hermitian matrices.
In computer science, a dichotomic search is a search algorithm that operates by selecting between two distinct alternatives (dichotomies [1] or polychotomies [2] when they are more than two) at each step. It is a specific type of divide and conquer algorithm. A well-known example is binary search. [3]
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 divide and conquer technique decomposes complex problems recursively into smaller sub-problems. Each sub-problem is then solved and these partial solutions are recombined to determine the overall solution. This technique is often used for searching and sorting. [5]
Divide and conquer, a.k.a. merge hull — O(n log n) Another O(n log n) algorithm, published in 1977 by Preparata and Hong. This algorithm is also applicable to the three dimensional case. Chan calls this "one of the best illustrations of the power of the divide-and-conquer paradigm". [2] Monotone chain, a.k.a. Andrew's algorithm — O(n log n)