Algorithms.2A

Randomized Algorithms

A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random bits.

Scheduling Algorithms

A scheduling algorithm is the algorithm which dictates how much CPU time is allocated to Processes and Threads. The goal of any scheduling algorithm is to fulfill a number of criteria: 1.) No task must be starved of resources - all tasks must get their chance at CPU time; 2.) If using priorities, a low-priority task must not hold up a high-priority task; 3.) The scheduler must scale well with a growing number of tasks, ideally being O(1). This has been done, for example, in the Linux kernel.

Searching Algorithms

A search algorithm is the step-by-step procedure used to locate specific data among a collection of data. It is considered a fundamental procedure in computing. In computer science, when searching for data, the difference between a fast application and a slower one often lies in the use of the proper search algorithm.

Mathematical Algorithms

An algorithm is a list of well-defined instructions or a step-by-step procedure to solve a problem

List Traversal Algorithms

Assume, that we have a list with some nodes. Traversal is the very basic operation, which presents as a part in almost every operation on a singly-linked list. For instance, algorithm may traverse a singly-linked list to find a value, find a position for insertion, etc. For a singly-linked list, only forward direction traversal is possible. ***Traversal algorithm*** *Beginning from the head,* 1.) check, if the end of a list hasn't been reached yet; 2.) do some actions with the current node, which is specific for particular algorithm; 3.) current node becomes previous and next node becomes current. Go to the step 1.

Bit Algorithms

Bit manipulation is the act of algorithmically manipulating bits or other pieces of data shorter than a word. Computer programming tasks that require bit manipulation include low-level device control, error detection and correction algorithms, data compression, encryption algorithms, and optimization.

Branch and Bound Algorithms

Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm for discrete and combinatoric optimization problems, as well as mathematical optimization. Branch and bound is a technique used in integer optimization problems - ie optimization problems for which the variables are integers. Often (though not always) the variables are constrained to have values of either 0 or 1.

Computability Theory (Recursion Theory)

Computability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The basic questions addressed by recursion theory are "What does it mean for a function on the natural numbers to be computable?" and "How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?". The answers to these questions have led to a rich theory that is still being actively researched.

Geometric Algorithms

Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. The main branches of computational geometry are: Combinatorial computational geometry, also called algorithmic geometry, which deals with geometric objects as discrete entities. Numerical computational geometry, also called machine geometry, computer-aided geometric design (CAGD), or geometric modeling, which deals primarily with representing real-world objects in forms suitable for computer computations in CAD/CAM systems.

Iteration

In computational mathematics, an iterative method is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.

Sorting Algorithms

In computer science a sorting algorithm is an algorithm that puts elements of a list in a certain order. The most-used orders are numerical order and lexicographical order.

Divide and Conquer Algorithms

In computer science, divide and conquer (D&C) is an algorithm design paradigm based on multi-branched recursion. A divide and conquer algorithm works by recursively breaking down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly.

Dynamic Programming

In computer science, mathematics, management science, economics and bioinformatics, dynamic programming (also known as dynamic optimization) is a method for solving a complex problem by breaking it down into a collection of simpler subproblems, solving each of those subproblems just once, and storing their solutions.

Tree Traversal Algorithms

In computer science, tree traversal (also known as tree search) is a form of graph traversal and refers to the process of visiting (checking and/or updating) each node in a tree data structure, exactly once. ... The following algorithms are described for a binary tree, but they may be generalized to other trees as well.

String Manipulation

Most programming languages that have a string datatype will have some string functions although there may be other low-level ways within each language to handle strings directly. In object-oriented languages, string functions are often implemented as properties and methods of string objects. In functional and list-based languages a string is represented as a list (of character codes), therefore all list-manipulation procedures could be considered string functions. However such languages may implement a subset of explicit string-specific functions as well.

Concrete vs. Abstract Data

To put it simple, ADT is a logical description and data structure is concrete. ADT is the logical picture of the data and the operations to manipulate the component elements of the data. Data structure is the actual representation of the data during the implementation and the algorithms to manipulate the data elements.