Fastest way to search a number in a list of ranges

Question

I have the following code to find a match for a number in a list of ranges.

public class RangeGroup
{
    public uint RangeGroupId { get; set; }
    public uint Low { get; set; }
    public uint High { get; set; }
    // More properties related with the range here
}

public class RangeGroupFinder
{
    private static readonly List<RangeGroup> RangeGroups=new List<RangeGroup>();

    static RangeGroupFinder()
    {
        // Populating the list items here
        RangeGroups.Add(new RangeGroup { RangeGroupId = 0, Low = 1023238144, High = 1023246335 });
        RangeGroups.Add(new RangeGroup { RangeGroupId = 0, Low = 1023246336, High = 1023279103 });
        RangeGroups.Add(new RangeGroup { RangeGroupId = 0, Low = 1023279104, High = 1023311871 });
        RangeGroups.Add(new RangeGroup { RangeGroupId = 0, Low = 1023311872, High = 1023328255 });
        RangeGroups.Add(new RangeGroup { RangeGroupId = 0, Low = 1023328256, High = 1023344639 });
        RangeGroups.Add(new RangeGroup { RangeGroupId = 0, Low = 1023344640, High = 1023410175 });
        RangeGroups.Add(new RangeGroup { RangeGroupId = 0, Low = 1023410176, High = 1023672319 });
        RangeGroups.Add(new RangeGroup { RangeGroupId = 0, Low = 1023672320, High = 1023688703 });
        RangeGroups.Add(new RangeGroup { RangeGroupId = 0, Low = 1023692800, High = 1023696895 });
       // There are many more and the groups are not sequential as it can seen on last 2 groups
    }

    public static RangeGroup Find(uint number)
    {
        return RangeGroups.FirstOrDefault(rg => number >= rg.Low && number <= rg.High);
    }
}

The list of the RangeGroup consists about 5000000 items and the Find() method will be used a lot, so I'm looking for a faster way to make the search. It's no problem to change the structure of the data or split it in any way.

Edit:

All ranges are unique and added by in order of Low and they don't overlap.

Result:

Did a test using ikh's code and the result is approximately 7000 times faster than my code. The test code and results can be seen here.

Answer 1

Since you indicated that RangeGroups are added in order of RangeGroup.Low and that they do not overlap, you don't need to do any further pre-processing. You can do binary search on the RangeGroups list to find the range (warning: not fully tested, you'd need to check some edge conditions):

public static RangeGroup Find(uint number) {
    int position = RangeGroups.Count / 2;
    int stepSize = position / 2;

    while (true) {
        if (stepSize == 0) {
            // Couldn't find it.
            return null;
        }

        if (RangeGroups[position].High < number) {
            // Search down.
            position -= stepSize;

        } else if (RangeGroups[position].Low > number) {
            // Search up.
            position += stepSize;

        } else {
            // Found it!
            return RangeGroups[position];
        }

        stepSize /= 2;
    }
}

The worst-case run time should be around O(log(N)), where N is the number of RangeGroups.

Answer 2

Interval trees. were created exatcly for what you are asking for.

Answer 3

If you populate the list only once you can do a magic trick:

• Sort the List
• Use BinarySearch

Sort takes O(Nlog(N)) time and is only done once. Binary search takes O(log(N)), which takes at most 17 comparisons for 100.000 items.

Answer 4

May be use a sorted list and do a binary search. That way you reduce the number of comparisons to O(logN)