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best data structure for storing large number of numeric fields

I am working with a class, say Widget, that has a large number of numeric real world attributes (eg, height, length, weight, cost, etc.). There are different types of widgets (sprockets, cogs, etc.), but each widget shares the exact same attributes (the values will be different by widget, of course, but they all have a weight, weight, etc.). I have 1,000s of each type of widget (1,000 cogs, 1,000 sprockets, etc.)
I need to perform a lot of calculations on these attributes (say calculating the weighted average of the attributes for 1000s of different widgets). For the weighted averages, I have different weights for each widget type (ie, I may care more about length for sprockets than for cogs).
Right now, I am storing all the attributes in a Dictionary< string, double> within each widget (the widgets have an enum that specifies their type: cog, sprocket, etc.). I then have some calculator classes that store weights for each attribute as a Dictionary< WidgetType, Dictionary< string, double >>. To calculate the weighted average for each widget, I simply iterate through its attribute dictionary keys like:
double weightedAvg = 0.0;
foreach (string attibuteName in widget.Attributes.Keys)
{
double attributeValue = widget.Attributes[attributeName];
double attributeWeight = calculator.Weights[widget.Type][attributeName];
weightedAvg += (attributeValue * attributeWeight);
}
So this works fine and is pretty readable and easy to maintain, but is very slow for 1000s of widgets based on some profiling. My universe of attribute names is known and will not change during the life of the application, so I am wondering what some better options are. The few I can think of:
1) Store attribute values and weights in double []s. I think this is probably the most efficient option, but then I need to make sure the arrays are always stored in the correct order between widgets and calculators. This also decouples the data from the metadata so I will need to store an array (?) somewhere that maps between the attribute names and the index into double [] of attribute values and weights.
2) Store attribute values and weights in immutable structs. I like this option because I don't have to worry about the ordering and the data is "self documenting". But is there an easy way to loop over these attributes in code? I have almost 100 attributes, so I don't want to hardcode all those in the code. I can use reflection, but I worry that this will cause even a larger penalty hit since I am looping over so many widgets and will have to use reflection on each one.
Any other alternatives?

Three possibilities come immediately to mind. The first, which I think you rejected too readily, is to have individual fields in your class. That is, individual double values named height, length, weight, cost, etc. You're right that it would be more code to do the calculations, but you wouldn't have the indirection of dictionary lookup.
Second is to ditch the dictionary in favor of an array. So rather than a Dictionary<string, double>, you'd just have a double[]. Again, I think you rejected this too quickly. You can easily replace the string dictionary keys with an enumeration. So you'd have:
enum WidgetProperty
{
First = 0,
Height = 0,
Length = 1,
Weight = 2,
Cost = 3,
...
Last = 100
}
Given that and an array of double, you can easily go through all of the values for each instance:
for (int i = (int)WidgetProperty.First; i < (int)WidgetProperty.Last; ++i)
{
double attributeValue = widget.Attributes[i];
double attributeWeight = calculator.Weights[widget.Type][i];
weightedAvg += (attributeValue * attributeWeight);
}
Direct array access is going to be significantly faster than accessing a dictionary by string.
Finally, you can optimize your dictionary access a little bit. Rather than doing a foreach on the keys and then doing a dictionary lookup, do a foreach on the dictionary itself:
foreach (KeyValuePair<string, double> kvp in widget.Attributes)
{
double attributeValue = kvp.Value;
double attributeWeight = calculator.Weights[widget.Type][kvp.Key];
weightedAvg += (attributeValue * attributeWeight);
}

To calculate weighted averages without looping or reflection, one way would be to calculate the weighted average of the individual attributes and store them in some place. This should happen while you are creating instance of the widget. Following is a sample code which needs to be modified to your needs.
Also, for further processing of the the widgets themselves, you can use data parallelism. see my other response in this thread.
public enum WidgetType { }
public class Claculator { }
public class WeightStore
{
static Dictionary<int, double> widgetWeightedAvg = new Dictionary<int, double>();
public static void AttWeightedAvgAvailable(double attwightedAvg, int widgetid)
{
if (widgetWeightedAvg.Keys.Contains(widgetid))
widgetWeightedAvg[widgetid] += attwightedAvg;
else
widgetWeightedAvg[widgetid] = attwightedAvg;
}
}
public class WidgetAttribute
{
public string Name { get; }
public double Value { get; }
public WidgetAttribute(string name, double value, WidgetType type, int widgetId)
{
Name = name;
Value = value;
double attWeight = Calculator.Weights[type][name];
WeightStore.AttWeightedAvgAvailable(Value*attWeight, widgetId);
}
}
public class CogWdiget
{
public int Id { get; }
public WidgetAttribute height { get; set; }
public WidgetAttribute wight { get; set; }
}
public class Client
{
public void BuildCogWidgets()
{
CogWdiget widget = new CogWdiget();
widget.Id = 1;
widget.height = new WidgetAttribute("height", 12.22, 1);
}
}

As it is always the case with data normalization, is that choosing your normalization level determines a good part of the performance. It looks like you would have to go from your current model to another model or a mix.
Better performance for your scenario is possible when you do not process this with the C# side, but with the database instead. You then get the benefit of indexes, no data transfer except the wanted result, plus 100000s of man hours already spent on performance optimization.

Use Data Parallelism supported by the .net 4 and above.
https://msdn.microsoft.com/en-us/library/dd537608(v=vs.110).aspx
An excerpt from the above link
When a parallel loop runs, the TPL partitions the data source so that the loop can operate on multiple parts concurrently. Behind the scenes, the Task Scheduler partitions the task based on system resources and workload. When possible, the scheduler redistributes work among multiple threads and processors if the workload becomes unbalanced

How to properly Clear a Queue containing structs?

I have declared a basic struct like this
private struct ValLine {
public string val;
public ulong linenum;
}
and declared a Queue like this
Queue<ValLine> check = new Queue<ValLine>();
Then in a using StreamReader setup where I'm reading through the lines of an input file using ReadLine in a while loop, among other things, I'm doing this to populate the Queue:
check.Enqueue(new ValLine { val = line, linenum = linenum });
("line" is a string containing the text of each line, "linenum" is just a counter that is initialized at 0 and is incremented each time through the loop.)
The purpose of the "check" Queue is that if a particular line meets some criteria, then I store that line in "check" along with the line number that it occurs on in the input file.
After I've finished reading through the input file, I use "check" for various things, but then when I'm finished using it I clear it out in the obvious manner:
check.Clear();
(Alternatively, in my final loop through "check" I could just use .Dequeue(), instead of foreach'ing it.)
But then I got to thinking - wait a minute, what about all those "new ValLine" I generated when populating the Queue in the first place??? Have I created a memory leak? I've pretty new to C#, so it's not coming clear to me how to deal with this - or even if it should be dealt with (perhaps .Clear() or .Dequeue() deals with the now obsoleted structs automatically?). I've spent over an hour with our dear friend Google, and just not finding any specific discussion of this kind of example in regard to the clearing of a collection of structs.
So... In C# do we need to deal with wiping out the individual structs before clearing the queue (or as we are dequeueing), or not? And if so, then what is the proper way to do this?
(Just in case it's relevant, I'm using .NET 4.5 in Visual Studio 2013.)
UPDATE: This is for future reference (you know, like if this page comes up in a Google search) in regard to proper coding. To make the struct immutable as per recommendation, this is what I've ended up with:
private struct ValLine {
private readonly string _val;
private readonly ulong _linenum;
public string val { get { return _val; } }
public ulong linenum { get { return _linenum; } }
public ValLine(string x, ulong n) { _val = x; _linenum = n; }
}
Corresponding to that change, the queue population line is now this:
check.Enqueue(new ValLine(line,linenum));
Also, though not strictly necessary, I did get rid of my foreach on the queue (and the check.Clear();, and changed it to this
while (check.Count > 0) {
ValLine ll = check.Dequeue();
writer.WriteLine("[{0}] {1}", ll.linenum, ll.val);
}
so that the queue is emptied out as the information is output.
UPDATE 2: Okay, yes, I'm still a C# newbie (less than a year). I learn a lot from the Internet, but of course, I'm often looking at examples from more than a year ago. I have changed my struct so now it looks like this:
private struct ValLine {
public string val { get; private set; }
public ulong linenum { get; private set; }
public ValLine(string x, ulong n): this()
{ this.val = x; this.linenum = n; }
}
Interestingly enough, I had actually tried exactly this off the top of my head before coming up with what's in the first update (above), but got a compile error (because I did not have the : this() with the constructor). Upon further suggestion, I checked further and found a recent example showing that : this() for making it work like I tried before, plugged that in, and - Wa La! - clean compile. I like the cleaner look of the code. What the private variables are called is irrelevant to me.

No, you won't have created a memory leak. Calling Clear or Dequeue will clear the memory appropriately - for example, if you had a List<T> then a clear operation might use:
for (int i = 0; i < capacity; i++)
{
array[i] = default(T);
}
I don't know offhand whether Queue<T> is implemented with a circular buffer built on an array, or a linked list - but either way, you'll be fine.
Having said that, I would strongly recommend against using mutable structs as you're doing here, along with mutable fields. While it's not causing the particular problem you're envisaging, they can behave in confusing ways.

How to implement a SearchByID?

Good afternoon all!
As a part of getting a better grip on some of the most aspects of object based programming, I've started to attempt something far larger than I have done in the past. Hereby I'm trying to learn about inheritance, code reuse, using classes far more extensively, and so on.
For this purpose I am trying to piece together all the parts required for a basic RPG/dungeon crawler.
I know this has been done a billion times before, but I find that actually trying to code something like it takes you through a lot more problems than you might think, which is a great way to learn (I think).
For now I have only loaded up a WPF application, since my interest is 95% on being able to piece together the working classes, routines, functions, etc. And not so much interested in how it will look. I am actually reading up on XNA, but since I am mostly trying to get a grip on the basic workings, I don't want to complicate those aspects with the graphical side of things just yet.
The problem I am now facing is that when I would a character to attack or defend, it should know from which other character it came, or to which one it should be pointed. I figured I could either use a GUID, or a manually appointed ID. But the problem is that I don't really know how I can implement such a thing.
The thing that I figured was that I could maybe add a reference to an array (Character[]), and have a SearchByID function loop through them to find the right one, and return it. Like so:
internal Character SearchByID(string _ID)
{
foreach(Character charToFind in Character[])
{
if(charToFind.ID == _ID)
return charToFind;
}
}
This of course has to be altered a bit due to the return at the moment, but just to give you an idea.
What I am stuck on is how to create the appropriate array outside of the "Character"-class? I can fill it up just fine, but how do I go about having it added above class level?
The way the "Character"-class is built up is that every new character instantiates from the Character class. The constructor then loads the appropriate values. But other than this, I see no possibility to initialize an array outside of this.
If it is preferable to post the entire code that I have, that will be no problem at all!
Thanks for any insights you may provide me with.

I think you can just use the Character-class and pass other Characters to it, for example:
public class Character
{
public string Name { get; private set; }
public int HitPoints { get; private set; }
public int Offense { get; private set; }
public int Defense { get; private set; }
public Character(string name, int hitPoints, int offense, int defense)
{
Name = name;
HitPoints = hitPoints;
Offense = offense;
Defense = defense;
}
public void Defend(Character source)
{
HitPoints = HitPoints - (source.Offense - Defense);
if (HitPoints <= 0)
{
Console.WriteLine("{0} died", Name);
}
}
public void Attack(Character target)
{
// Here you can call the other character's defend with this char as an attacker
target.Defend(this);
if (target.HitPoints <= 0)
{
Console.WriteLine("{0} killed {1}", Name, target.Name);
}
}
}
The thing with object oriented programming is that you have to start thinking in objects. Objects are like boxes when they're concrete. You can make new ones and give them some properties, like a name, height, width, hitpoints, whatever. You can also let these objects perform actions. Now a simple box won't do much itself, but a character can do various things, so it makes sense to put these actions in the Character-class.
Besides having Characters, you might have a Game-class which manages the game-state, characters, monsters, treasure chests etc...
Now this simple example may cause you to gain HitPoints when your defense is higher than the attacker's offense, but that's details, I'll leave the exact implementation up to you.

I guess you want a way to insert characters in an array when they are instantiated..
You can make a static array or list
So,your class in my opinion should be
class Character
{
static List<Character> characterList=new List<Character>();//all characters are here
public Character(string id,...)
{
//initialize your object
characterList.Add(this);//store them in the list as and when created
}
internal Character SearchByID(string _ID)
{
foreach(Character charToFind in characterList)
{
if(charToFind.ID == _ID)
return charToFind;
}
}
}
As you may be knowing static members are associated with the class not with the object.So,when you create a new character object it would be automatically added to the characterList

Unless you are dealing with seperate processes, e.g. client-server, you probably don't want to use "Id"s at all.
Whereever you are passing string _ID around, pass the actual Character instead. This saves you looking up in an array or whatever.
Post more code, and I can show you what I mean.

You could use a dictionary, instantiated in your controller class:
Dictionary<Guid, Character> _characterList = new Dictionary<Guid, Character>();
Initialise:
var someCharacter = new Character() { stats = something };
var otherCharacter = new Character() { stats = anotherThing };
var char1Id = Guid.NewGuid();
var char2Id = Guid.NewGuid();
_characterList.Add(char1Id, someCharacter);
_characterList.Add(char2Id, otherCharacter);
then, to access characters:
var charToFind = _characterList[char1Id];
or
var charToFind = _characterList.Single(c => c.Name = "Fred The Killer");
or whatever else...

Check out keyed collection
KeyedCollection
It is like a dictionary where the key is a property of class.
You will be able to reference a Character with
Characters[id]
Syntax
On your Character class overrite GetHashCode and Equals for performance.
If you use Int32 for the ID then you will get a perfect hash.
Very fast and O(1).

C#: Enum anti-patterns [closed]

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There has been talk of Enums in general violating Clean Code-principles, so I'm looking for people's favorite Enum anti-patterns and alternative solutions for these.
For example I've seen code like this:
switch(enumValue) {
case myEnum.Value1:
// ...
break;
case myEnum.Value2:
// ...
break;
}
It's one step better than switch-statements with magic strings, but this probably could have been solved better with a factory, a container or other pattern.
Or even old-school code like this:
if(enumValue == myEnum.Value1) {
// ...
} else if (enumValue == myEnum.Value2) {
// ...
}
What other anti-patterns and better implementations have you experienced with enums?

I think Enums are quite useful. I've written a few extensions for Enum that have added even more value to its use
First, there's the Description extension method
public static class EnumExtensions
{
public static string Description(this Enum value)
{
var entries = value.ToString().Split(ENUM_SEPERATOR_CHARACTER);
var description = new string[entries.Length];
for (var i = 0; i < entries.Length; i++)
{
var fieldInfo = value.GetType().GetField(entries[i].Trim());
var attributes = (DescriptionAttribute[])fieldInfo.GetCustomAttributes(typeof(DescriptionAttribute), false);
description[i] = (attributes.Length > 0) ? attributes[0].Description : entries[i].Trim();
}
return String.Join(", ", description);
}
private const char ENUM_SEPERATOR_CHARACTER = ',';
}
This will allow me to define en enum like this:
public enum MeasurementUnitType
{
[Description("px")]
Pixels = 0,
[Description("em")]
Em = 1,
[Description("%")]
Percent = 2,
[Description("pt")]
Points = 3
}
And get the label by doing this: var myLabel = rectangle.widthunit.Description() (eliminating any need for a switch statement).
This will btw return "px" if rectangle.widthunit = MeasurementUnitType.Pixels or it will return "px,em" if rectangle.widthunit = MeasurementUnitType.Pixels | MeasurementUnitType.Em.
Then, there is a
public static IEnumerable<int> GetIntBasedEnumMembers(Type #enum)
{
foreach (FieldInfo fi in #enum.GetFields(BindingFlags.Public | BindingFlags.Static))
yield return (int)fi.GetRawConstantValue();
}
Which will let me traverse any enum with int based values and return the int values themselves.
I find these to be very useful in an allready useful concept.

It all depends what your trying to do with the enum.
If you are trying to stop your developers from passing magic numbers into your operations and you want to keep the data referential integrity intact with your DB then, YES! Use T4-Templates (using your ORM) to go to your MeasurementUnitTypes table and generate a enum with the ID, Name and Description columns matching the enum’ int, Enum_Name and Description Attribute (nice approach for additional field\data to enum #danijels) as suggested above. If you add a new Measurement Type to your MeasurementUnitTypes table you can just right click and run the T4-Template and the enum code is generated for that new row added in the table. I don’t like hard-coded data in my application that doesnt link to my DB hence the mention of the T4-Template approach. It is not extensible otherwise...what if some other external system wants to retrieve our Measurement Criteria used in our system, then it is hard-coded in the system and you can't expose it to the client via a service. That left there.
If the purpose is not data related and you have some logic assigned to a specific enum then NO! this violates the SOLID (Open close principle) as you would somewhere in your application apply a switch or bunch of Ifs to action the logic per enum, ALSO if you did it REALLY bad these switches or Ifs are all over the show....good luck adding a new enum... so it is not open for extension and closed for modification as you need to modify existing code, as per the SOLID principle.
If your choice is 2 then I suggest then to replace your enum with the following using the example from #danijels comment:
public interface IMeasurementUnitType
{
int ID { get; }
string Description { get; }
// Just added to simulate a action needed in the system
string GetPrintMessage(int size);
}
The above code defines the interface (code contract) that each measurement should adhere to. Now lets define Percentage and Pixel measurement :
public class PixelsMeasurementUnitType : IMeasurementUnitType
{
public int ID => 1;
public string Description => "Pixel";
public string GetPrintMessage(int size)
{
return $"This is a {Description} Measurement that is equal to {size} pixels of the total screen size";
}
}
public class PercentMeasurementUnitType : IMeasurementUnitType
{
public int ID => 2;
public string Description => "Persentage";
public string GetPrintMessage(int size)
{
return $"This is a {Description} Measurement that is equal to {size} persent of total screen size (100)";
}
}
So wee have defined two types, we would use them in code as follows:
var listOfMeasurmentTypes = AppDomain.CurrentDomain.GetAssemblies()
.SelectMany(s => s.GetTypes())
.Where(p => typeof(IMeasurementUnitType).IsAssignableFrom(p)
&& !p.IsInterface)
.ToList();
Here we grab all the TYPES that extends the IMeasurementUnitType interface and NOT the interface itself. Now we can use the Activator to create instances of the classes to populate our UI controls:
public IEnumerable<IMeasurementUnitType> GetInstantiatedClassesFromTypes(List<Type> types)
{
foreach (var type in types)
{
yield return (IMeasurementUnitType)Activator.CreateInstance(type);
}
}
You can change the code above to be generic for any type, AND NOW life happens and the client give a new measuring unit type called Point as a new requirement, I don't need to CHANGE ANY code, just add the new type (extend the code NOT modify). The new type will automatically be picked up in the application.
public class PointMeasurementUnitType : IMeasurementUnitType
{
public int ID => 3;
public string Description => "Point";
public string GetPrintMessage(int size)
{
return $"This is a {Description} Measurement that is equal to {size} points of total screen size";
}
}
a Good idea would be to cache your types for performance benefits upon starting your application or try and use a DI container of your choice.
Also, one can argue that somewhere in you application you would need to distinguish between types and I agree, however you want to keep apples with apples. So try as far as possible to apply the same principle used for this types. If this type is used in some sort of Graphics processor (for example) class then have a IGraphicsProcessor and have your concrete classes that differentiate between these types for example PersentageAndPixelGraphicsProcessor (that extends from IGraphicsProcessor) or if it distinguishes only one type call it PersentageGraphicsProcessor.
Sorry for the HUGE SA but I really like enum's however I feel when you trying to separate logic using a enums it is a STRONG anti-pattern.
comments welcome,

This isn't an answer, as much as contributing to a list of Enum anti-patterns.
During a code review this morning, I ran into a case similar to the following, all in the same class.
Two cases:
Before drinking
After drinking
..
public enum ListEnum
{
CategoryOne,
CategoryTwo,
CategoryThree,
CategoryFour
}
public class UIELementType
{
public const string FactoryDomain = "FactoryDomain";
public const string Attributes = "Attributes";
}

Using enums in not anti-pattern. In some books about refactoring this code is used to demonstrate how to replace it with polymorphism. It would be OK when you overuse enums in code.

I see having two switch statements as a symptom of non-OO design as explained further in this answer.

C#: Returning 'this' for method nesting?

I have a class that I have to call one or two methods a lot of times after each other. The methods currently return void. I was thinking, would it be better to have it return this, so that the methods could be nested? or is that considerd very very very bad? or if bad, would it be better if it returned a new object of the same type? Or what do you think? As an example I have created three versions of an adder class:
// Regular
class Adder
{
public Adder() { Number = 0; }
public int Number { get; private set; }
public void Add(int i) { Number += i; }
public void Remove(int i) { Number -= i; }
}
// Returning this
class Adder
{
public Adder() { Number = 0; }
public int Number { get; private set; }
public Adder Add(int i) { Number += i; return this; }
public Adder Remove(int i) { Number -= i; return this; }
}
// Returning new
class Adder
{
public Adder() : this(0) { }
private Adder(int i) { Number = i; }
public int Number { get; private set; }
public Adder Add(int i) { return new Adder(Number + i); }
public Adder Remove(int i) { return new Adder(Number - i); }
}
The first one can be used this way:
var a = new Adder();
a.Add(4);
a.Remove(1);
a.Add(7);
a.Remove(3);
The other two can be used this way:
var a = new Adder()
.Add(4)
.Remove(1)
.Add(7)
.Remove(3);
Where the only difference is that a in the first case is the new Adder() while in the latter it is the result of the last method.
The first I find that quickly become... annoying to write over and over again. So I would like to use one of the other versions.
The third works kind of like many other methods, like many String methods and IEnumerable extension methods. I guess that has its positive side in that you can do things like var a = new Adder(); var b = a.Add(5); and then have one that was 0 and one that was 5. But at the same time, isn't it a bit expensive to create new objects all the time? And when will the first object die? When the first method returns kind of? Or?
Anyways, I like the one that returns this and think I will use that, but I am very curious to know what others think about this case. And what is considered best practice.

The 'return this' style is sometimes called a fluent interface and is a common practice.

I like "fluent syntax" and would take the second one. After all, you could still use it as the first, for people who feel uncomfortable with fluent syntax.
another idea to make an interface like the adders one easier to use:
public Adder Add(params int[] i) { /* ... */ }
public Adder Remove(params int[] i) { /* ... */ }
Adder adder = new Adder()
.Add(1, 2, 3)
.Remove(3, 4);
I always try to make short and easy-to-read interfaces, but many people like to write the code as complicated as possible.

Chaining is a nice thing to have and is core in some frameworks (for instance Linq extensions and jQuery both use it heavily).
Whether you create a new object or return this depends on how you expect your initial object to behave:
var a = new Adder();
var b = a.Add(4)
.Remove(1)
.Add(7)
.Remove(3);
//now - should a==b ?
Chaining in jQuery will have changed your original object - it has returned this.
That's expected behaviour - do do otherwise would basically clone UI elements.
Chaining in Linq will have left your original collection unchanged. That too is expected behaviour - each chained function is a filter or transformation, and the original collection is often immutable.
Which pattern better suits what you're doing?

I think that for simple interfaces, the "fluent" interface is very useful, particularly because it is very simple to implement. The value of the fluent interface is that it eliminates a lot of the extraneous fluff that gets in the way of understanding. Developing such an interface can take a lot of time, especially when the interface starts to be involved. You should worry about how the usage of the interface "reads"; In my mind, the most compelling use for such an interface is how it communicates the intent of the programmer, not the amount of characters that it saves.
To answer your specific question, I like the "return this" style. My typical use of the fluent interface is to define a set of options. That is, I create an instance of the class and then use the fluent methods on the instance to define the desired behavior of the object. If I have a yes/no option (say for logging), I try not to have a "setLogging(bool state)" method but rather two methods "WithLogging" and "WithoutLogging". This is somewhat more work but the clarity of the final result is very useful.

Consider this: if you come back to this code in 5 years, is this going to make sense to you? If so, then I suppose you can go ahead.
For this specific example, though, it would seem that overloading the + and - operators would make things clearer and accomplish the same thing.

For your specific case, overloading the arithmetic operators would be probably the best solution.
Returning this (Fluent interface) is common practice to create expressions - unit testing and mocking frameworks use this a lot. Fluent Hibernate is another example.
Returning a new instance might be a good choice, too. It allows you to make your class immutable - in general a good thing and very handy in the case of multithreading. But think about the object creation overhead if immutability is of no use for you.

If you call it Adder, I'd go with returning this. However, it's kind of strange for an Adder class to contain an answer.
You might consider making it something like MyNumber and create an Add()-method.
Ideally (IMHO), that would not change the number that is stored inside your instance, but create a new instance with the new value, which you return:
class MyNumber
{
...
MyNumber Add( int i )
{
return new MyNumber( this.Value + i );
}
}

The main difference between the second and third solution is that by returning a new instance instead of this you are able to "catch" the object in a certain state and continue from that.
var a = new Adder()
.Add(4);
var b = a.Remove(1);
var c = a.Add(7)
.Remove(3);
In this case both b and c have the state captured in a as a starting point.
I came across this idiom while reading about a pattern for building test domain objects in Growing Object-Oriented Software, Guided by Tests by Steve Freeman; Nat Pryce.
On your question regarding the lifetime of your instances: I would exspect them to be elligible for garbage collection as soon as the invocation of Remove or Add are returning.