一组（x，y）点的C＃数据结构

Question

I'm not familiar with all the collections available in C# but I'd like to implement a class to store a mathematical relation or function, ie a set of pairs (x,y). Presumably it would include a list of tuples or some other built collection from .NET, but I'm not sure what's best. Some potentially relevant facts:

1. up a million pairs
2. frequently would want to lookup which y goes with a particular x
3. x would be a double type for all cases I know of now
4. may want to interpolate y's to nonexistant x's
5. will want to extract a subset of the relation including all pairs with x in a certain range
6. will want to iterate through pairs in order of xs sometimes seems like it should be sorted by xs based on above things?

Answer 1

The SortedSet<T> seems like the right tool for this task.

We can define an IComparable element type as follows.

struct FunctionPoint : IComparable<FunctionPoint>
{
    public double X, Y;
    public FunctionPoint(double x)
    {
        this.X = x;
        this.Y = 0;
    }
    public FunctionPoint(double x, double y)
    {
        this.X = x;
        this.Y = y;
    }
    public int CompareTo(FunctionPoint other)
    {
        return X.CompareTo(other.X);
    }
}

And then use it in a SortedSet<FunctionPoint> as follows.

var function = new SortedSet<FunctionPoint>();

1. up a million pairs

for (int i = 0; i < 100000; i++)
{
    var x = 2 * Math.PI * i / 1000000;
    var y = Math.Sin(x);
    function.Add(new FunctionPoint { X = x, Y = y });
}

2. frequently would want to lookup which y goes with a particular x

var view = function.GetViewBetween(new FunctionPoint(x), new FunctionPoint(x));
if (view.Count > 0)
{
    var y = view.Min;
}

4. may want to interpolate y's to nonexistant x's

var left = function.GetViewBetween(new FunctionPoint(double.NegativeInfinity), new FunctionPoint(x)).Max;
var right = function.GetViewBetween(new FunctionPoint(x), new FunctionPoint(double.PositiveInfinity)).Min;
var y = LinearInterpolate(left, right, x);

5. will want to extract a subset of the relation including all pairs with x in a certain range

var view = function.GetViewBetween(new FunctionPoint(a), new FunctionPoint(b));

6. will want to iterate through pairs in order of xs sometimes seems like it should be sorted by xs based on above things?

foreach (var point in function)
{
}

Answer 2

Maybe a System.Collections.Generic.SortedList<double, double> is what you need?
SortedList

If you constantly remove and add items, a SortedDictionary might perform better.