Binary Search on Keys of SortedList<K, V>

Question

I need to write some code for linear interpolation and I am trying to figure out the most efficient way to search the Keys of a SortedList<K, V> for the upper and lower keys that surround my target key.

SortedList<int, double> xyTable = new SortedList<int, double>()
{
    {1, 10}, {2, 20}, {3, 30}, {4,40}
};

double targetX = 3.5;

What is the most efficient way to search the list and determine that 3.5 is between 3 and 4? I have a method / cheat that works for integers (temporarily insert the target Key into the list then find the index) but I figured I'd ask the pros so I could produce quality code.

Thanks.

Answer 1

A binary search gives you decent performance on a list. However the Keys property on SortedList is of type IList, whereas BinarySearch is defined on List. Fortunately, you can find an implementation of binary search for IList in this related question:

How to perform a binary search on IList<T>?

Answer 2

In my case the source SortedList is not changing much, since its being used as a lookup table. So in this case it makes sense to convert the SortedList to a List<T> once. After that it is quite easy to use the built-in BinarySearch method of List<T>...

double targetX = 3.5;

// Assume keys are doubles, may need to convert to doubles if required here.
// The below line should only be performed sparingly as it is an O(n) operation.
// In my case I only do this once, as the list is unchanging.
List<double> keys = xyTable.Keys.ToList();

int ipos = keys.BinarySearch(targetX);

if (ipos >= 0)
{
    // exact target found at position "ipos"
}
else
{
    // Exact key not found: BinarySearch returns negative when the 
    // exact target is not found, which is the bitwise complement 
    // of the next index in the list larger than the target.
    ipos = ~ipos;
    if (ipos >= 0 && ipos < keys.Count)
    {
        if (ipos > 0)
        {
            // target is between positions "ipos-1" and "ipos"
        }
        else
        {
            // target is below position "ipos"
        }
    }
    else
    {
        // target is above position "ipos"
    }
}