Search results
Results from the WOW.Com Content Network
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 mathematics, a recurrence relation is an equation according to which the th term of a sequence of numbers is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation.
This equation can be successively substituted into itself and expanded to obtain an expression for the total amount of work done. [2] The master theorem allows many recurrence relations of this form to be converted to Θ-notation directly, without doing an expansion of the recursive relation.
Recurrence relations are equations which define one or more sequences recursively. Some specific kinds of recurrence relation can be "solved" to obtain a non-recursive definition (e.g., a closed-form expression). Use of recursion in an algorithm has both advantages and disadvantages. The main advantage is usually the simplicity of instructions.
In computer science, the Akra–Bazzi method, or Akra–Bazzi theorem, is used to analyze the asymptotic behavior of the mathematical recurrences that appear in the analysis of divide and conquer algorithms where the sub-problems have substantially different sizes.
The reason that the dyadic transformation is also called the bit-shift map is that when y is written in binary notation, the map moves the binary point one place to the right (and if the bit to the left of the binary point has become a "1", this "1" is changed to a "0"). A cycle of length 3, for example, occurs if an iterate has a 3-bit ...
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.
However, they were not binary search trees. Bayer called them a "symmetric binary B-tree" in his paper and later they became popular as 2–3–4 trees or even 2–3 trees. [5] In a 1978 paper, "A Dichromatic Framework for Balanced Trees", [6] Leonidas J. Guibas and Robert Sedgewick derived the red–black tree from the symmetric binary B-tree. [7]