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Binary search Visualization of the binary search algorithm where 7 is the target value Class Search algorithm Data structure Array Worst-case performance O (log n) Best-case performance O (1) Average performance O (log n) Worst-case space complexity O (1) Optimal Yes In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search ...
When using such algorithms to factor a large number n, it is necessary to search for smooth numbers (i.e. numbers with small prime factors) of order n 1/2. The size of these values is exponential in the size of n (see below). The general number field sieve, on the other hand, manages to search for smooth numbers that are subexponential in the ...
Sorted arrays are the most space-efficient data structure with the best locality of reference for sequentially stored data. [citation needed]Elements within a sorted array are found using a binary search, in O(log n); thus sorted arrays are suited for cases when one needs to be able to look up elements quickly, e.g. as a set or multiset data structure.
Algorithms are often evaluated by their computational complexity, or maximum theoretical run time. Binary search functions, for example, have a maximum complexity of O(log n), or logarithmic time. In simple terms, the maximum number of operations needed to find the search target is a logarithmic function of the size of the search space.
For example, O(2 log 2 n) is not the same as O(2 ln n) because the former is equal to O(n) and the latter to O(n 0.6931...). Algorithms with running time O(n log n) are sometimes called linearithmic. [37] Some examples of algorithms with running time O(log n) or O(n log n) are: Average time quicksort and other comparison sort algorithms [38]
Interpolation search resembles the method by which people search a telephone directory for a name (the key value by which the book's entries are ordered): in each step the algorithm calculates where in the remaining search space the sought item might be, based on the key values at the bounds of the search space and the value of the sought key ...
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).
For constant dimension query time, average complexity is O(log N) [6] in the case of randomly distributed points, worst case complexity is O(kN^(1-1/k)) [7] Alternatively the R-tree data structure was designed to support nearest neighbor search in dynamic context, as it has efficient algorithms for insertions and deletions such as the R* tree. [8]