31 Facts About Binary search

Binary search compares the target value to the middle element of the array.

Binary search is faster than linear search except for small arrays.

However, binary search can be used to solve a wider range of problems, such as finding the next-smallest or next-largest element in the array relative to the target even if it is absent from the array.

Binary search begins by comparing an element in the middle of the array with the target value.

However, it is trivial to extend binary search to perform approximate matches because binary search operates on sorted arrays.

Related searches

For example, binary search can be used to compute, for a given value, its rank, predecessor, successor, and nearest neighbor.

In terms of the number of comparisons, the performance of binary search can be analyzed by viewing the run of the procedure on a binary tree.

The comparison tree representing binary search has the fewest levels possible as every level above the lowest level of the tree is filled completely.

Average number of iterations performed by binary search depends on the probability of each element being searched.

The number of iterations performed by a Binary search, given that the corresponding path has length, is counting the initial iteration.

Since binary search is the optimal algorithm for searching with comparisons, this problem is reduced to calculating the minimum internal path length of all binary trees with nodes, which is equal to:.

Each iteration of the binary search procedure defined above makes one or two comparisons, checking if the middle element is equal to the target in each iteration.

However, it guarantees that the Binary search takes the maximum number of iterations, on average adding one iteration to the Binary search.

Binary search can be used to perform exact matching and set membership .

Linear Binary search is a simple Binary search algorithm that checks every record until it finds the target value.

Linear Binary search can be done on a linked list, which allows for faster insertion and deletion than an array.

Binary search is faster than linear search for sorted arrays except if the array is short, although the array needs to be sorted beforehand.

Binary search tree is a binary tree data structure that works based on the principle of binary search.

Binary search trees lend themselves to fast searching in external memory stored in hard disks, as binary search trees can be efficiently structured in filesystems.

Binary search is ideal for such matches, performing them in logarithmic time.

For example, searches, approximate matches, and the operations available to sorted arrays can be performed more efficiently than binary search on specialized data structures such as van Emde Boas trees, fusion trees, tries, and bit arrays.

In practice, interpolation search is slower than binary search for small arrays, as interpolation search requires extra computation.

Binary search has been generalized to work on certain types of graphs, where the target value is stored in a vertex instead of an array element.

The standard binary search algorithm is simply the case where the graph is a path.

Similarly, binary search trees are the case where the edges to the left or right subtrees are given when the queried vertex is unequal to the target.

Related searches

Noisy binary search algorithms solve the case where the algorithm cannot reliably compare elements of the array.

Noisy binary search can find the correct position of the target with a given probability that controls the reliability of the yielded position.

Quantum algorithms for binary search are still bounded to a proportion of queries, but the constant factor is less than one, providing for a lower time complexity on quantum computers.

Every published binary search algorithm worked only for arrays whose length is one less than a power of two until 1960, when Derrick Henry Lehmer published a binary search algorithm that worked on all arrays.

In 1962, Hermann Bottenbruch presented an ALGOL 60 implementation of binary search that placed the comparison for equality at the end, increasing the average number of iterations by one, but reducing to one the number of comparisons per iteration.

The Java programming language library implementation of binary search had the same overflow bug for more than nine years.