he the post will be updated soon…

This post is a complete description about the video post on 15th May, 17 in AM; YourMove .

If you are a computer science student or if you have ever have looked various algorithms. Devising an algorithm can be really hard, but a well-optimized algorithm can always be appreciated. Classic algorithms never go out of fashion in fact In computer science most oof the systems are still working fine under those algorithms it self. Algorithms are answers or solutions to real world problem stated in the most interesting problem statement. I personally get excited when I see a great algorithm and always want to share the same knowledge and excitement.

But, Nowadays due boom of application development algorithm engineering is not really focused topic by engineering students. But we never know when a oldie-but-goodie algorithm might come in handy. This post focuses on a Google’s application Google Trips, Which used a 280-year-old algorithm!

If you do not know what is Google Trips where we can plan our vacation. One of the features, we can pre-plan which places we are interested in visiting and google creates a optimal route with minimum travel time. Google also takes care of your interests, timings and other important parameters. This is termed as **” itineraries”. **

The problem statement of the application is very similar to that of travelling salesmen problem. It states that,

Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?

But Travelling salesmen problem belongs to the class of NP-hard. NP-hard problems are those problems which cannot be solved in deterministic time. That means they cannot be solved in polynomial time. so, a TSP cannot be implemented and if so we cannot expect a great user experience! Which is, in fact, a real deal for a company like **Google.**

But TSP problem can be solved by making some assumptions and approximations. The rest of the post talks about how the problem of creating **itineraries **is solved by using the discoveries of some great scientists.

In 1736, Leonhard Euler, studied the following question: **is it possible to walk through the city crossing each bridge exactly once?**

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As it turns out, for the city of Königsberg, the answer is **no**.

Euler noticed that if all the nodes in the graph have an even number of edges (such graphs are called “Eulerian” in his honour) then, and only then, a cycle can be found that visits every edge exactly once. *Keep this in mind, as we’ll rely on this fact later!*

One of the approximation algorithms for TSP is an algorithm by **Christofides. The assumption is the distances form a metric space (they are symmetric and obey the triangle inequality). It is an approximation algorithm that guarantees that its solutions will be within a factor of 3/2 of the optimal solution length.**

**This is an important part of the solution and builds on Euler’s paper. here is a **quick four-step rundown of how it works here:

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