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Binary insertion sort employs a binary search to determine the correct location to insert new elements, and therefore performs ⌈log 2 n⌉ comparisons in the worst case. When each element in the array is searched for and inserted this is O(n log n). [7]
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 ...
In computer science, a search data structure [citation needed] is any data structure that allows the efficient retrieval of specific items from a set of items, such as a specific record from a database. The simplest, most general, and least efficient search structure is merely an unordered sequential list of all the items.
A weight-balanced tree is a binary search tree that stores the sizes of subtrees in the nodes. That is, a node has fields key, of any ordered type; value (optional, only for mappings) left, right, pointer to node; size, of type integer. By definition, the size of a leaf (typically represented by a nil pointer) is zero.
A Fenwick tree or binary indexed tree (BIT) is a data structure that stores an array of values and can efficiently compute prefix sums of the values and update the values. It also supports an efficient rank-search operation for finding the longest prefix whose sum is no more than a specified value.
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.
To insert a new element, search the tree to find the leaf node where the new element should be added. Insert the new element into that node with the following steps: If the node contains fewer than the maximum allowed number of elements, then there is room for the new element. Insert the new element in the node, keeping the node's elements ordered.
insert: insert a new element at a given index. When the index is zero, this is called prepending; when the index is the last index in the list it is called appending. delete: remove the element at a given index.