Python Programming

  Graph Coloring A graph G(V, E) is given and some colors are given We have to color the vertices such that no two neighbours/adjacent vertices have the same color. This can be solved using Backtracking. There are two types of problem 1.  m-colorability decision problem If a graph G(V, E) is given and some colors are also given and just we want to know whether a graph can coloured using those colors or not. This is known as the m-coloring decision problem. 2.  m-colorability optimization problem If a graph G(V, E) is given and we want to know minimum how many colors required for coloring the graph. This problem is called the m-coloring optimization problem. Chromatic Number: The smallest number of colors needed to color a graph G is called its chromatic number.

Asymptotic  Notation Asymptotic notations are mathematical tools to represent time complexity of algorithms. Asymptotic notations are used to write fastest and slowest possible running time for an algorithm. These notations are important because  without expanding the cost of running the algorithm, we can estimate the complexity of the algorithm. Asymptotic notations is a way of comparing functions that ignores constant factors and small input size. Big Oh Notation(O) The notation O(n) is the formal way to express the upper bound of an algorithm’s running time. It measures the worst case time complexity or the longest amount of time an algorithm can possibly take to complete. Example - Insertion  Sort  f(n) = O(g(n)) If and only if exist positive constant C f(n) <= k.g(n) for n>n0 in all cases. Omega Notation(Ω) The notation Ω(n) is the formal way to express the lower bound of an algorithm’s running time. It measures the best case time complexity or the be...

  Graph: A graph is a non-linear data structure consisting of nodes and edges.The nodes are sometimes also referred to as vertices and the edges are lines and arcs that connect any two nodes in the graph. A graph consists of a finite set of vertices(or nodes) and a set of edges which connect a pair of nodes. Graphs are used to solve many real-life problems. Graphs are used to represent networks. The networks may include paths in a city or telephone network or circuit network. Graphs are also used in social networks like linkedIn, Facebook. A graph can be defined as a group of vertices and edges that are used to connect these vertices. A graph G can be defined as an ordered set of G(V,E) where V(G) represents the set of vertices and E(G) represents the set of edges which are used to connect these vertices. Directed and Undirected Graph  A graph can be directed or undirected. In an undirected graph, edges are not associated with the directions with them. If an edge exists betwee...

Divide and Conquer Divide and conquer is an algorithm pattern. In algorithm methods, the design is to take a dispute on a huge input, break the input into minor pieces,decide the problem on each of the small pieces, and then merge the piecewise solutions into a global solution. This mechanism of solving the problem is called the Divide & Conquer Strategy. Divide and Conquer algorithm consists of a dispute using the following three steps: Divide: The original problem into a set of subproblems. Conquer: Solve every sub problem individually recursively. Combine: Put together the solutions of the subproblem to get the solution to the whole problem. Some Examples of Divide & Conquer Algorithms are: Quick Sort  Merge Sort Binary Search Algorithm of Divide & Conquer  function DAndC(P){ if(small(p)then return S(p) else  divide the problem p into p1,p2,_ _ _ solve the problem p1,p2,_ _ pk ny recursive calling of DAndC }       ...

  Algorithm A finite set of instructions that specifies a sequence of operation is to be carried out in order to solve a specific problem or class of problems is called an Algorithm. An algorithm can be defined as a well-defined computational procedure that takes some values or the set of values, as an input and produces some value, or the set of values, as an output. An algorithm is thus a sequence of computational steps that transform the input into output. It describes the specific computational procedures for achieving the input-output relationship. An algorithm must have the following properties: Correctness: It should produce the output according to the requirement of the algorithm. Finiteness: Algorithm must complete after a finite number of instructions have been executed. An Absence of Ambiguity: Each step must be defined having only one interpretation. Definition of Sequence: Each step must have a unique defined preceding and succeeding step. The first step and the la...

A web framework is a code library that allows software creation quicker and simpler by offering standard templates for developing web applications that are stable, scalable and maintenable. We provide a majority of the best Python web frameworks in this blog that will be helpful on the path to becoming a professional backend developer and developing the current skills collection. An all-in-one system with libraries designed to operate together smoothly is a full-stack platform or an enterprise frame. It supports backend facilities, frontend interfaces, and database creation. A full-stack architecture includes everything needed by a developer to create an application. Python contains for one full-stack application Django With Django, you can take Web apps from idea to deployment within hours. Django takes care of much of the Web creation hassle so you can concentrate on developing the App without having to reinvent the wheel. It is open source and free. Django is one of the software dev...