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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 ...
On a sequential computer, all nearest smaller values may be found by using a stack data structure: one processes the values in sequence order, using the stack to maintain a subsequence of the values that have been processed so far and are smaller than any later value that has already been processed.
In the theory of optimal binary search trees, the interleave lower bound is a lower bound on the number of operations required by a Binary Search Tree (BST) to execute a given sequence of accesses. Several variants of this lower bound have been proven. [1] [2] [3] This article is based on a variation of the first Wilber's bound. [4]
A schematic picture of the skip list data structure. Each box with an arrow represents a pointer and a row is a linked list giving a sparse subsequence; the numbered boxes (in yellow) at the bottom represent the ordered data sequence.
An x-fast trie containing the integers 1 (001 2), 4 (100 2) and 5 (101 2), which can be used to efficiently solve the predecessor problem.. One simple solution to this problem is to use a balanced binary search tree, which achieves (in Big O notation) a running time of () for predecessor queries.
An augmented tree can be built from a simple ordered tree, for example a binary search tree or self-balancing binary search tree, ordered by the 'low' values of the intervals. An extra annotation is then added to every node, recording the maximum upper value among all the intervals from this node down.
The most common problem being solved is the 0-1 knapsack problem, which restricts the number of copies of each kind of item to zero or one. Given a set of items numbered from 1 up to , each with a weight and a value , along with a maximum weight capacity ,
While there is an upper bound on the amount of resources a certain user needs, most users use much less than the capacity. Therefore, the cloud manager may gain a lot by slight overcommitment . This induces a variant of bin packing with chance constraints : the probability that the sum of sizes in each bin is at most B should be at least p ...