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reflection - Given a C# Type, Get its Base Classes and Implemented Interfaces

I'm working on a game engine in C#. The class I'm working on is called CEntityRegistry, and its job is to keep track of the many instances of CEntity in the game. My goal is to be able to query the CEntityRegistry with a given type, and get a list of each CEntity of that type.

What I'd like to do, therefore, is maintain a map:

private IDictionary<Type, HashSet<CEntity>> m_TypeToEntitySet;

And update the registry thusly:

private void m_UpdateEntityList()
        {
            foreach (CEntity theEntity in m_EntitiesToRemove.dequeueAll())
            {
                foreach (HashSet<CEntity> set in m_TypeToEntitySet.Values)
                {
                    if (set.Contains(theEntity))
                        set.Remove(theEntity);
                }
            }
            foreach (CEntity theEntity in m_EntitiesToAdd.dequeueAll())
            {
                Type entityType = theEntity.GetType();
                foreach (Type baseClass in entityType.GetAllBaseClassesAndInterfaces())
                  m_TypeToEntitySet[baseClass].Add(theEntity);

            }
        }

The problem I have is that there is no function Type.GetAllBaseClassesAndInterfaces- How would I go about writing it?

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You could write an extension method like this:

public static IEnumerable<Type> GetBaseTypes(this Type type) {
    if(type.BaseType == null) return type.GetInterfaces();

    return Enumerable.Repeat(type.BaseType, 1)
                     .Concat(type.GetInterfaces())
                     .Concat(type.GetInterfaces().SelectMany<Type, Type>(GetBaseTypes))
                     .Concat(type.BaseType.GetBaseTypes());
}

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