This week's book giveaway is in the OO, Patterns, UML and Refactoring forum. We're giving away four copies of Refactoring for Software Design Smells: Managing Technical Debt and have Girish Suryanarayana, Ganesh Samarthyam & Tushar Sharma on-line! See this thread for details.
There are N petrol bunks arranged in circle. Each bunk is separated from the rest by a certain distance. You choose some mode of travel which needs 1 litre of petrol to cover 1 km distance. You can't infinitely draw any amount of petrol from each bunk as each bunk has some limited petrol only. But you know that the sum of liters of petrol in all the bunks is equal to the distance to be covered. i.e let P1, P2, ... Pn be n bunks arranged circularly. d1 is distance between p1 and p2, d2 is distance between p2 and p3. dn is distance between pn and p1.Now find out the bunk from where the travel can be started such that your mode of travel never runs out of fuel.
Also, derive the time complexity and space complexity measures.
I think it may be a good deal simpler than the traveling salesman, if my guesses about the intent here are correct.
[mani]: But you know that the sum of liters of petrol in all the bunks is equal to the distance to be covered.
What distance to be covered? It seems like there are many possible distances that we might travel, depending on our objectives - and the problem hasn't even given us a goal. Perhaps we are supposed to visit each fuel station once? Perhaps the "distance to be covered" is the total d1 + d2 + d3 + ... + dn? In this case, we could simply travel the circle (or polygon as the case may be), visiting each station in order, never reversing direction. The only important choices would be (a) where to start, and (b) which direction to travel in, so as not to ever run out of fuel. There's a reasonably simple algorithm that can be used here, and there will always be at least two solutions - one in each direction. Maybe more.