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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 ...
For example, the key may be a geographic position (latitude and longitude) on the Earth. In that case, common kinds of queries are "find the record with a key closest to a given point v ", or "find all items whose key lies at a given distance from v ", or "find all items within a specified region R of the space".
Array, a sequence of elements of the same type stored contiguously in memory; Record (also called a structure or struct), a collection of fields . Product type (also called a tuple), a record in which the fields are not named
Specific applications of search algorithms include: Problems in combinatorial optimization, such as: . The vehicle routing problem, a form of shortest path problem; The knapsack problem: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as ...
The most frequently used general-purpose implementation of an associative array is with a hash table: an array combined with a hash function that separates each key into a separate "bucket" of the array. The basic idea behind a hash table is that accessing an element of an array via its index is a simple, constant-time operation.
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.
The best case input is an array that is already sorted. In this case insertion sort has a linear running time (i.e., O(n)). During each iteration, the first remaining element of the input is only compared with the right-most element of the sorted subsection of the array. The simplest worst case input is an array sorted in reverse order.
It is the first self-balancing binary search tree data structure to be invented. [ 3 ] AVL trees are often compared with red–black trees because both support the same set of operations and take O ( log n ) {\displaystyle {\text{O}}(\log n)} time for the basic operations.