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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 ...
Fig. 1: A binary search tree of size 9 and depth 3, with 8 at the root. 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.
In computer science, an optimal binary search tree (Optimal BST), sometimes called a weight-balanced binary tree, [1] is a binary search tree which provides the smallest possible search time (or expected search time) for a given sequence of accesses (or access probabilities). Optimal BSTs are generally divided into two types: static and dynamic.
Algorithms that search for local structure in the input, for example finding a local minimum in a 1-D array (can be solved in ( ()) time using a variant of binary search). A closely related notion is that of Local Computation Algorithms (LCA) where the algorithm receives a large input and queries to local information about some valid large ...
Time complexity; Function: ... It is the first self-balancing binary search tree data structure to be invented. [3] ... The complexity of each of union, ...
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 all nodes, the left subtree's key must be less than the node's key, and the right subtree's key must be greater than the node's key. These subtrees must all qualify as binary search trees. The worst-case time complexity for searching a binary search tree is the height of the tree, which can be as small as O(log n) for a tree with n elements.
The auxiliary indices have turned the search problem from a binary search requiring roughly log 2 N disk reads to one requiring only log b N disk reads where b is the blocking factor (the number of entries per block: b = 100 entries per block in our example; log 100 1,000,000 = 3 reads).