using System;

using System.Xml.Linq;

using System.Xml.XPath;

public class Program

{

    public static void Main()

    {

        var yourString = "<p></p><p></p><p></p>";

        var x = XElement.Parse("<Root>" + yourString + "</Root>");

        var i = 0;

        foreach (var element in x.Elements("p"))

            element.Add(new XAttribute("id", i++));

        Console.WriteLine(String.Concat(x.Nodes()));

    }

}