没有动态的稀疏双重调度 - 没有O（n ^ 2）代码，有没有一种理智的方法呢？

Question

我有以下内容。有用。我希望以避免使用动态的方式来避免使用类型数量的代码增长为O（n ^ 2）。我所知道的标准双调度解决方案在A，B，C，D类型中都有O（n）代码，导致整体O（n ^ 2）。

有没有理智的方法呢？

  public class P {}
  public class A: P {}
  public class B: P {}
  public class C: P {}
  public class D: P {}
  public class DynamicDispatchLowPriorityMethods
  {
    // The superclass is to avoid a runtime error when calling Multi(b, a).
    // Without something like this, the call is ambiguous.
    protected string _Output {get;set;}
    public DynamicDispatchLowPriorityMethods()
    {
    }
    public void Multi(P x, P y) {
      _Output += "PP ";
    }
    public void Multi(B x, P y) {
      _Output += "bP ";
    }
  }
  [TestFixture()]
  public class DynamicDispatch: DynamicDispatchLowPriorityMethods
  {
    public void Multi(A x, A y) {
      _Output += "aa ";
    }
    public void Multi(A x, P y) {
      _Output += "aP ";
    }
    public void Multi(P x, A y) {
      _Output += "Pa ";
    }
    public void Multi(B x, B y) {
      _Output += "bb ";
    }
    public void Multi(C x, C y) {
      _Output += "cc ";
    }
    public void Multi(D x, D y) {
      _Output += "dd ";
    }
    public void Multi(B x, D y) {
      _Output += "bd ";
    }
    public void DynamicMulti(P x, P y) {
      this.Multi((dynamic)x, (dynamic)y);
    }
    [Test()]
    public void TestDynamicDispatch()
    {
      _Output = "";
      P a = new A ();
      P b = new B ();
      P c = new C ();
      P d = new D ();
      this.DynamicMulti(a, a);
      this.DynamicMulti(a, b);
      this.DynamicMulti(a, c);
      this.DynamicMulti(a, d);
      _Output += "\n";
      this.DynamicMulti(b, a);
      this.DynamicMulti(b, b);
      this.DynamicMulti(b, c);
      this.DynamicMulti(b, d);
      _Output += "\n";
      this.DynamicMulti(c, a);
      this.DynamicMulti(c, b);
      this.DynamicMulti(c, c);
      this.DynamicMulti(c, d);
      _Output += "\n";
      this.DynamicMulti(d, a);
      this.DynamicMulti(d, b);
      this.DynamicMulti(d, c);
      this.DynamicMulti(d, d);
      CommonDebug.WriteLine(_Output);
    }
  }

输出是：

  aa aP aP aP 
  Pa bb bP bd 
  Pa PP cc PP 
  Pa PP PP dd 

有关背景信息，请参阅this question有关双重调度的替代方法。