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Here we will see how to use substitution method to solve recurrence relations. We will take two examples to understand it in better way.Suppose we are using the binary search technique. In this technique, we check whether the element is present at the end or not. If that is present at middle, then the algorithm terminates, otherwise we take either the left and right subarray from the actual array again and again. So in each step the size of the array decreases by n / 2. Suppose the binary search algorithm takes T(n) amount of time to execute. The base ... Read More
During analysis of algorithms, we find some recurrence relations. These recurrence relations are basically using the same function in the expression. In most of the cases for recursive algorithm analysis, and divide and conquer algorithm we get the recurrence relations.Here we will see one example of recurrence equation by the help of some examples. Suppose we are using the binary search technique. In this technique, we check whether the element is present at the end or not. If that is present at middle, then the algorithm terminates, otherwise we take either the left and right subarray from the actual array ... Read More
In algorithm analysis we count the operations and steps. This is basically justified when computer takes more time to perform an operation than they took to fetch the data needed for that operation. Nowadays the cost of performing an operation is significantly lower than the cost of fetching data from memory.The run time of many algorithms is dominated by the number of memory references (number of cache misses) rather than by the number of operations. So, when we will try to desing some algorithms, we have to focus on reducing not only the number of operations but also the number ... Read More
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
As we know that the queue data structure is First in First Out data structure. The queue has some variations also. These are the Dequeue and the Priority Queue.The Dequeue is basically double ended queue. So there are two front and two rear pairs. One pair of front and rear pointer is used to describe the queue from left side, and another one is used to describe it from the right side. We can insert or delete elements from both side in this structure. Here we will see some C++ code using dequeue STL to understand its functionality.Example (Dequeue) Live Demo#include ... Read More
A queue is an abstract data structure that contains a collection of elements. Queue implements the FIFO mechanism i.e the element that is inserted first is also deleted first.Queue cane be one linear data structure. But it may create some problem if we implement queue using array. Sometimes by using some consecutive insert and delete operation, the front and rear position will change. In that moment, it will look like the queue has no space to insert elements into it. Even if there are some free spaces, that will not be used due to some logical problems. To overcome this ... Read More
Both Last() and LastOrDefault() will fetch the last occurrence of a value. But the major difference between Last() and LastOrDefault() is that Last() will throw an exception if there is no result data for the supplied criteria whereas LastOrDefault() will return the default value (null) if there is no result data.Use Last() when we knew the sequence will have at least one element. Use LastOrDefault() when we are not sure about the data.Example Live Demousing System; using System.Collections.Generic; using System.Diagnostics; using System.Linq; namespace ConsoleApp { public class Student { public int Id { get; set; } ... Read More
Yield keyword helps to do custom stateful iteration over a collection. Meaning when we use yield keyword the control moves back and forth from the caller function to source and vice versa.Example Live Demousing System; using System.Collections.Generic; namespace DemoApplication { class Program { static List numbersList = new List { 1, 2, 3, 4, 5 }; public static void Main() { foreach(int i in RunningTotal()) { Console.WriteLine(i); } Console.ReadLine(); ... Read More
Generics allows us to define a class with placeholders for the type of its fields, methods, parameters, etc. Generics replace these placeholders with some specific type at compile time. A generic can be defined using angle brackets . A primary limitation of collections is the absence of effective type checking. This means that you can put any object in a collection because all classes in the C# programming language extend from the object base class.Also, we cannot simply return null from a generic method like in normal method. Below is the error that a generic method will throw if we ... Read More
While copying the entire contents of directory, it is more important that we have copy its sub directories and the related files.ExampleLet us consider demo source directory having sub directories and files like below. Below is the demo target directory which is empty initially.using System; using System.IO; namespace DemoApplication { class Program { public static void Main() { string sourceDirectory = @"d:\DemoSourceDirectory"; string targetDirectory = @"d:\DemoTargetDirectory"; DirectoryInfo sourceDircetory = new DirectoryInfo(sourceDirectory); DirectoryInfo targetDircetory = new DirectoryInfo(targetDirectory); CopyAll(sourceDircetory, ... Read More