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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 ...
The following is the skeleton of a generic branch and bound algorithm for minimizing an arbitrary objective function f. [3] To obtain an actual algorithm from this, one requires a bounding function bound, that computes lower bounds of f on nodes of the search tree, as well as a problem-specific branching rule.
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]
In fact all bounds (lower and upper) currently known for the average case are precisely matched by this lower bound. For example, this gives the new result that the Janson-Knuth upper bound is matched by the resulting lower bound for the used increment sequence, showing that three pass Shellsort for this increment sequence uses Θ ( N 23 / 15 ...
The Edwards-Erdős gives a lower bound on b(G) for every connected signed graph G. Bound (a) was improved for special classes of graphs: triangle-free graphs, graphs of given maximum degree, H-free graphs, etc., see e.g. [5] [6] [7] Poljak and Turzik [8] extended the Edwards-Erdős bound to weighted Max-Cut:
The cost of the solution produced by the algorithm is within 3/2 of the optimum. To prove this, let C be the optimal traveling salesman tour. Removing an edge from C produces a spanning tree, which must have weight at least that of the minimum spanning tree, implying that w(T) ≤ w(C) - lower bound to the cost of the optimal solution.
A multiplication algorithm is an algorithm ... (akin to languages such as Java and C) for compactness. ... Lower bounds for multiplication are also known for some ...
In computer science, best, worst, and average cases of a given algorithm express what the resource usage is at least, at most and on average, respectively.Usually the resource being considered is running time, i.e. time complexity, but could also be memory or some other resource.