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What (who) is binary search - definition

SEARCH ALGORITHM IN SORTED LISTS THAT OPERATES BY DECREASING THE SEARCH SPACE BY HALF EACH PASS

Binary chop; Binary search; Bsearch; Binary Search; Half-interval search; Half-interval search method; Half interval search method

$In [[fractional cascading]], each array has pointers to every second element of another array, so only one binary search has to be performed to search all the arrays.$

binary search

<algorithm> A search algorithm which repeatedly divides an ordered search space in half according to how the required (key) value compares with the middle element. The following pseudo-C routine performs a binary search return the index of the element of vector "thing[first..last]" equal to "target": if (target < thing[first] || target > thing[last]) return NOT_FOUND; while (first < last) { mid = (first+last)/2; /* truncate to integer */ if (target == thing[mid]) return mid; if (target < thing[mid]) last = mid-1; else first = mid+1; } if (target == thing[last]) return last; return NOT_FOUND; (2003-01-14)

Binary search algorithm

In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position of a target value within a sorted array. Binary search compares the target value to the middle element of the array.

https://en.wikipedia.org/wiki/Binary_search_algorithm

Binary search tree

$The node <math>\text{D}</math> to be deleted has 2 children$

DATA STRUCTURE IN TREE FORM WITH 0, 1, OR 2 CHILDREN PER NODE, SORTED FOR FAST LOOKUP

Binary Search Tree; Binary search trees; Ordered binary tree

In computer science, a binary search tree (BST), also called an ordered or sorted binary tree, is a rooted binary tree data structure with the key of each internal node being greater than all the keys in the respective node's left subtree and less than the ones in its right subtree. The time complexity of operations on the binary search tree is directly proportional to the height of the tree.

Binary search trees allow binary search for fast lookup, addition, and removal of data items. Since the nodes in a BST are laid out so that each comparison skips about half of the remaining tree, the lookup performance is proportional to that of binary logarithm. BSTs were devised in the 1960s for the problem of efficient storage of labeled data and are attributed to Conway Berners-Lee and David Wheeler.

The performance of a binary search tree is dependent on the order of insertion of the nodes into the tree since arbitrary insertions may lead to degeneracy; several variations of the binary search tree can be built with guaranteed worst-case performance. The basic operations include: search, traversal, insert and delete. BSTs with guaranteed worst-case complexities perform better than an unsorted array, which would require linear search time.

The complexity analysis of BST shows that, on average, the insert, delete and search takes $O(\log n)$ for $n$ nodes. In the worst case, they degrade to that of a singly linked list: $O(n)$ . To address the boundless increase of the tree height with arbitrary insertions and deletions, self-balancing variants of BSTs are introduced to bound the worst lookup complexity to that of the binary logarithm. AVL trees were the first self-balancing binary search trees, invented in 1962 by Georgy Adelson-Velsky and Evgenii Landis.

Binary search trees can be used to implement abstract data types such as dynamic sets, lookup tables and priority queues, and used in sorting algorithms such as tree sort.

https://en.wikipedia.org/wiki/Binary_search_tree

Wikipedia

Binary search algorithm

In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position of a target value within a sorted array. Binary search compares the target value to the middle element of the array. If they are not equal, the half in which the target cannot lie is eliminated and the search continues on the remaining half, again taking the middle element to compare to the target value, and repeating this until the target value is found. If the search ends with the remaining half being empty, the target is not in the array.

Binary search runs in logarithmic time in the worst case, making $O(\log n)$ comparisons, where $n$ is the number of elements in the array. Binary search is faster than linear search except for small arrays. However, the array must be sorted first to be able to apply binary search. There are specialized data structures designed for fast searching, such as hash tables, that can be searched more efficiently than binary search. 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.

There are numerous variations of binary search. In particular, fractional cascading speeds up binary searches for the same value in multiple arrays. Fractional cascading efficiently solves a number of search problems in computational geometry and in numerous other fields. Exponential search extends binary search to unbounded lists. The binary search tree and B-tree data structures are based on binary search.

https://en.wikipedia.org/wiki/Binary search algorithm