Google maps API compute shortest path using TSP

Question

Hi , 

i want to include google maps API into my ASP.NET page and allows users to input the locations(few places) they are going to visit.  When user input the location, the google maps API will mark these location.

After that, my application will need to know all the location information (eg, distances and the coordinates.). I want to use Travelling Salesman Problem (TSP) alogorithm to figure out the shortest path and then list out the sequence of the places . 

For example: 

1. city A
2. city C
3.city B
4. city D. 

Anyone know how to do this ? can help me ? i'm new to asp.net and C# .I will be using C# to write code behind  for TSP solver.  Anyone can help me ? you are welcome to give me any idea on how to implement this or you can just tell how to get the google maps API integrated to my ASP.NET. I dun understand how google maps API really works.   

Any related information im willing to know.

Waiting for reply . thank you very much.