Spanning tree using BFS

Spanning Trees with kruskal algorithm

Tree :   A tree is a connected graph without cycles.

Properties of Trees:  

• A graph is a tree if and only if there is one and only one path joining any two of its vertices.
• A connected graph is a tree if and only if every one of its edges is a bridge.
• A connected graph is a tree if and only if it has N vertices and N; 1 edges.

Definitions :

• A sub-graph that spans (reaches out to ) all vertices of a graph is called a spanning sub-graph.
• A sub-graph that is a tree and that spans (reaches out to ) all vertices of the original graph is called a spanning tree.
• Among all the spanning trees of a weighted and connected graph, the one (possibly more) with the least total weight is called a minimum spanning tree (MST).

Kruskal's Algorithm :

• Kruskal Algorithm finds the minimal cost of edges between two vertices and forms the tree.
• The total weight should be minimized
• Graph should not be looped.
• Minimal cost should be chosen initially.

Pseudocode :

KRUSKAL(G):
1 A = ∅
2 foreach v ∈ G.V:
3   MAKE-SET(v)
4 foreach (u, v) ordered by weight(u, v), increasing:
5    if FIND-SET(u) ≠ FIND-SET(v):
6       A = A ∪ {(u, v)}
7       UNION(u, v)
8 return A

New Features in ASP.NET 5

ASP.NET 5 is a lean .NET stack for building modern web apps. We built it from the ground up to provide an optimized development framework for apps that are either deployed to the cloud or run on-premises. It consists of modular components with minimal overhead, so you retain flexibility while constructing your solutions..


ASP.NET 5 includes the following features:

• New flexible and cross-platform runtime
• New modular HTTP request pipeline
• Cloud-ready environment configuration
• Unified programming model that combines MVC, Web API, and Web Pages
• Ability to see changes without re-building the project
• Side-by-side versioning of the .NET Framework
• Ability to self-host or host on IIS
• New tools in Visual Studio 2015
• Open source in GitHub

Visual Studio 2015 Extension for ASP.NET Project Templates

In Visual Studio 2013, there were a handful of templates that supported developing ASP.NET projects with various frameworks and data structures.Some templates from  VS 2012 is removed and added Visual Studio Extension for VS 2015

Can download from here Download.

What this includes ?

• ASP.NET Dynamic Data Entities Project (.NET 4 and above)
• ASP.NET Dynamic Data Linq Project (.NET 4)
• ASP.NET MVC Facebook Project (.NET 4.5 and above)
• ASP.NET Web Forms Project (.NET 4 only)

Note: This template was using Universal Providers. Starting Visual Studio 2013, all templates including Web Forms were updated to use ASP.NET Identity and you can create these templates in VS 2015.

Other templates

All the other templates from VS 2013 are still part of VS 2015. You can create ASP.NET Web Forms, MVC 5, Web API 2, SPA, Azure Mobile Service projects, using the One ASP.NET dialog. This is the same as Visual Studio 2013.

How to install ?

Verdict :  Web sites and technologies are evolving quickly. We want to be able to deliver to you project templates that use new technologies and techniques on a more timely basis, and to do this we have enabled the ASP.NET Project Template extension.  If you are looking to work with Facebook apps, Dynamic Data, or Web Forms with the Universal Providers, try out the extension and let us know what you think.

Build apps for iOS, Android, and Windows devices by using Visual Studio

Yes,
   What you have read is absolutely true, Microsoft's Valuable product Visual studio 2013 update 2 and later versions make possible of building universal platform apps using .Net Framework.

The Key challenge for developers today is to build the app in different platforms with different types of developers, so the Production cost for the development increases, Microsoft came up with the Latest update as You can build apps for iOS, Android, and Windows devices by using Visual Studio, and you can easily add connected services such as Office 365, Azure Mobile Services, and Application Insights to your apps. You can build your app by using the .NET Framework, or by using HTML.

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To build an app for Windows devices, install Visual Studio 2013 Update 2 or later, and then choose a Windows or Windows Phone project. You can target all Windows devices by using a universal app project template. To build an app for Android or iOS, install Xamarin, and then create an Android or iOS project. You can target Windows, Android, and iOS devices in the same solution if you want, and then share code between all your device projects by using a shared project or a Portable Class Library project.

You can share most of your code between device projects. This includes any business logic, cloud integration, database access, or any other code that targets the .NET Framework. You can share quite a bit more between Windows and Windows Phone projects, because so many aspects of the two platforms have converged. The only code that you can’t share is code that targets a specific platform.

The Visual Studio team has recently announced its tooling support for Apache Cordova. What possibilities does it give? Now developers can use Visual Studio to easily build hybrid apps that run on iOS, Android, Windows and Windows Phone using a single project based on HTML and JavaScript.

This News is recently released by Microsoft Visual Studio team in there blogs.