make the full circular path, shortest path exercise?

Question

I got this question in an interview and I was not able to solve it.

You have a circular road, with N number of gas stations. You know the ammount of gas that each station has. You know the ammount of gas you need to GO from one station to the next one. Your car starts with 0 gas. The question is: Create an algorithm, to know from which gas station you must start driving to COMPLETE the circular PATH. It does not specify that you must visit all stations. You can only drive clockwise.

I had to do it in c#

The only code I started is with a GasStation entity

class GasStation
  int gasAtStation;
  int gasToMoveToNextStationNeeded;
  string nameOfGasStation;


GasTation wheretoStart(List<GasStation> list)
{

}

I did it this way:

static void Main(string[] args)
        {
            int[] gasOnStation = {1, 2, 0, 4};
            int[] gasDrivingCostTonNextStation = {1, 1,2, 1};

            FindStartingPoint(gasOnStation, gasDrivingCostTonNextStation);

        }

        static void FindStartingPoint(int[] gasOnStation, int[] gasDrivingCosts)
        {
            // Assume gasOnStation.length == gasDrivingCosts.length
            int n = gasOnStation.Length;
            int[] gasEndValues = new int[n];
            int gasValue = 0;
            for (int i = 0; i < n; i++)
            {
                gasEndValues[i] = gasValue;
                gasValue += gasOnStation[i];
                gasValue -= gasDrivingCosts[i];
            }

            if (gasValue < 0)
            {
                Console.WriteLine("Instance does not have a solution");
                Console.ReadLine();
            }
            else
            {
                // Find the minimum in gasEndValues:
                int minI = 0;
                int minEndValue = gasEndValues[0];
                for (int i = 1; i < n; i++)
                {
                    if (gasEndValues[i] < minEndValue)
                    {
                        minI = i;
                        minEndValue = gasEndValues[i];
                    }
                }

                Console.WriteLine("Start at station: " + minI);
                Console.ReadLine();
            }
        }

Thanks

Answer 1

One easy way of solving this is using a brute force method. i.e. try every posibility and throw out ones that don't work.

i.e. Start at each gas station in turn (repeat below for each starting station).

• Have a varible that defines current gas level.
• Loop through each gas station, in a clockwise order.
  1. Fill up your gas (increment gas by gas station amount).
  2. Check you can move to the next station (gas >= gasToMoveToNextStationNeeded)
     • If not, this isn't a solution, so move to the next starting location.
     • If so, subtract that amount of gas used, then keep going until you reach the start again.
  3. If you get back to the starting gas station you have an answer.

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Edit As per @Vash's answer, As an improvement when deciding where to start, discount stations that don't have enough gas themselves to get to the next station and working through starting stations in order of amount of gas (descending).

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Note, this assumes we visit all gas stations. Will need refinement for skipping gas stations if you need an optimal solution (question doesn't specify this).