Top 10 Programming Language to learn in 2023

Are you a programming enthusiast looking to stay ahead of the curve in 2023? With the ever-evolving tech landscape, keeping up with the Best Programming Language to learn can be a daunting task. Fear not, as we have compiled a list of the top 10 Programming Languages that you should consider learning in 2023. Python: This versatile language continues to dominate in 2023, with its ease of use, readability, and a vast library of modules. JavaScript: As web development grows increasingly popular, JavaScript remains a crucial player, with its ability to create dynamic and interactive web pages. Java: This language has stood the test of time and remains a popular choice for enterprise software development. C++: A staple in the gaming and systems development industries, C++ offers exceptional performance and memory management. Swift: Apple's preferred language for iOS app development, Swift continues to grow in popularity with its simplicity and reliability. R: As data science and machin

Approximation Algorithms | DAA

Approximation Algorithms

An approximate algorithm is a way of dealing with NP—completeness for optimization problem. This technique does not guarantee the best solution. The goal of an approximation algorithm is to come as close as possible to the optimum value in a reasonable amount of time which is at most polynomial time. If we are dealing with optimization problem {maximization or minimization}
with feasible solution having positive cost then it is worthy to look at approximate algorithm for near optimal solution.


Vertex Cover Problem

A vertex cover of an undirected graph G =(V.E) is a subset V‘ I V such that for all edges (u.v) EE either usV’ or vsV’ or u and v 2 V’. The problem here is to find the vertex cover of minimum size in a given graph G. Optimal vertex—cover is the optimization version of an NP—complete problem but it is not too hard to find a vertex-cover that is near optimal.


Algorithm

ApproxVertexCover {G}
{
C ={ } ;
E’ = E
while E' is not empty
do Let (u, v} be an arbitrary edge of E‘
C = C U {u, v}
Remove from E' every edge incident on either u or v
return C
}

Example: (vertex cover running example for graph below)



Approximation Algorithms | DAA



Approximation Algorithms | DAA


Analysis: 

If E' is represented using the adjacency lists the above algorithm takes O (V+E) since each edge is processed only once and every vertex is processed only once throughout the whole operation.

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