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It has a O(n 2) time complexity, which makes it inefficient on large lists, and generally performs worse than the similar insertion sort. Selection sort is noted for its simplicity and has performance advantages over more complicated algorithms in certain situations, particularly where auxiliary memory is limited.
For typical serial sorting algorithms, good behavior is O(n log n), with parallel sort in O(log 2 n), and bad behavior is O(n 2). Ideal behavior for a serial sort is O(n), but this is not possible in the average case. Optimal parallel sorting is O(log n). Swaps for "in-place" algorithms. Memory usage (and use of other computer resources).
Karatsuba multiplication is an O(n log 2 3) ≈ O(n 1.585) divide and conquer algorithm, that uses recursion to merge together sub calculations. By rewriting the formula, one makes it possible to do sub calculations / recursion. By doing recursion, one can solve this in a fast manner.
The baby-step giant-step algorithm is a generic algorithm. It works for every finite cyclic group. It is not necessary to know the exact order of the group G in advance. The algorithm still works if n is merely an upper bound on the group order. Usually the baby-step giant-step algorithm is used for groups whose order is prime.
The naive implementation for generating a suffix tree going forward requires O(n 2) or even O(n 3) time complexity in big O notation, where n is the length of the string. By exploiting a number of algorithmic techniques, Ukkonen reduced this to O ( n ) (linear) time, for constant-size alphabets, and O ( n log n ) in general, matching the ...
As a baseline algorithm, selection of the th smallest value in a collection of values can be performed by the following two steps: Sort the collection; If the output of the sorting algorithm is an array, retrieve its th element; otherwise, scan the sorted sequence to find the th element.
The simplest algorithms are for addition and subtraction, where one simply adds or subtracts the digits in sequence, carrying as necessary, which yields an O(N) algorithm (see big O notation). Comparison is also very simple. Compare the high-order digits (or machine words) until a difference is found. Comparing the rest of the digits/words is ...
With n matrices in the multiplication chain there are n−1 binary operations and C n−1 ways of placing parentheses, where C n−1 is the (n−1)-th Catalan number. The algorithm exploits that there are also C n−1 possible triangulations of a polygon with n+1 sides. This image illustrates possible triangulations of a regular hexagon. These ...