Found 216 Articles for Analysis of Algorithms

There are different methods to estimate the cost of some algorithm. One of them by using the operation count. We can estimate the time complexity of an algorithm by choosing one of different operations. These are like add, subtract etc. We have to check how many of these operations are done. The success of this method depends on our ability to identify the operations that contribute most of the time complexity.Suppose we have an array, of size n [0 to n - 1]. Our algorithm will find the index of largest element. We can estimate the cost by counting number ... Read More

Back Off Algorithm is an algorithm used for collision resolution. It works as, When this collision occurs, both the devices wait for a random amount of time before retransmitting the signal again, they keep on trying until the data is transferred successfully. This is called back off, since the nodes ‘back-off’ for a certain amount of time, before they try to re-access it again. This random amount of time is directly proportional to the number of attempts it has made to transmit the signal.AlgorithmBelow is a simple flowchart to explain the Back Off Algorithm in brief.As can be seen, that ... Read More

Both Block cipher and Stream cipher belong to the family of symmetric key ciphers which are the basically encryption methods primarily used for converting the plaintext into ciphertext directly.Go through this article to find out more about the features of block ciphers and stream ciphers and how they are different from each other.What is Block Cipher?A block cipher is a symmetric cryptographic technique that uses a shared, secret key to encrypt a fixed-size data block. During encryption, plaintext is used, and ciphertext is the resultant encrypted text. The plaintext and ciphertext are both encrypted using the same key.A block cipher ... Read More

In the context of programming, an Algorithm is a set of well-defined instructions in sequence to perform a particular task and achieve the desired output. Here we say "a set of defined instructions" which means that somewhere the user knows the outcome of those instructions if they get executed in the expected manner. On the basis of the knowledge about outcome of the instructions, there are two types of algorithms namely, Deterministic and Non-deterministic Algorithms. Read this article to learn more about deterministic and non-deterministic algorithms and how they are different from each other. What is Deterministic Algorithm? A deterministic ... Read More

Recurrence relations are equations that recursively defines a multidimensional array.Here we will solve so questions based on recurrence relations.Solve the recurrence reation:T(n) = 12T(n/2) + 9n2 + 2. T(n) = 12T(n/2) + 9n2 + 2. Here, a = 12 and b = 2 and f(n) = 9(n)2 + 2 It is of the form f(n) = O(n^c), where c = 2This form its in the master’s theorem condition, So, logb(a) = log2(12) = 3.58 Using case 1 of the masters theorm, T(n) = θ(n3.58).Solve the recurrence reation:T(n) = 5T(n/2 + 23) + 5n2 + 7n - 5/3. T(n) = 5T(n/2 ... Read More

DefinitionHuffman coding provides codes to characters such that the length of the code depends on the relative frequency or weight of the corresponding character. Huffman codes are of variable-length, and without any prefix (that means no code is a prefix of any other). Any prefix-free binary code can be displayed or visualized as a binary tree with the encoded characters stored at the leaves.Huffman tree or Huffman coding tree defines as a full binary tree in which each leaf of the tree corresponds to a letter in the given alphabet.The Huffman tree is treated as the binary tree associated with ... Read More

A dictionary is defined as a general-purpose data structure for storing a group of objects. A dictionary is associated with a set of keys and each key has a single associated value. When presented with a key, the dictionary will simply return the associated value.For example, the results of a classroom test could be represented as a dictionary with student's names as keys and their scores as the values:results = {'Anik' : 75, 'Aftab' :80, 'James' : 85, 'Manisha': 77, 'Suhana' :87, 'Margaret': 82}Main operations of dictionariesDictionaries typically support so many operations −retrieve a value (based on language, attempting to ... Read More

A way to update our beliefs depended on the arrival of new, relevant pieces of evidence are provided by Bayes rule. For example, if we were trying to provide the probability that a given person has cancer, we would initially just conclude it is whatever percent of the population has cancer. However, given extra evidence such as the fact that the person is a smoker, we can update our probability, since the probability of having cancer is greater given that the person is a smoker. This allows us to utilize prior knowledge to improve our probability estimations.The rule is explained ... Read More

In probability theory, according to Boole's inequality, also denoted as the union bound, for any finite or countable set of events, the probability that at least one of the events happens is no higher than the sum of the probabilities of the individual events.In mathematics, the probability theory is denoted as an important branch that studies about the probabilities of the random event. The probability is denoted as the measurement of chances of happening an event which is an outcome of an experiment.For Example − tossing a coin is denoted as an experiment and getting head or tail is denoted ... Read More

An overflow occurs at the time of the home bucket for a new pair (key, element) is full.We may tackle overflows bySearch the hash table in some systematic manner for a bucket that is not full.Linear probing (linear open addressing).Quadratic probing.Random probing.Eliminate overflows by allowing each bucket to keep a list of all pairs for which it is the home bucket.Array linear list.Chain.Open addressing is performed to ensure that all elements are stored directly into the hash table, thus it attempts to resolve collisions implementing various methods.Linear Probing is performed to resolve collisions by placing the data into the next ... Read More