Great series!!

Tree traversal can also be done without using stack. For example, http://vadmyst.blogspot.com/2007/09/non-recursive-binary-tree-traversal.html. But, this approach makes tree node more "heavy" as additional information has to be used.

You could make Visited an integer, incrementing it each time you visit a node.

Obviously, it also doesn't work for immutable trees :-)

I should say "incrementing it each time you TRAVERSE THE TREE"...

Dictionary approach seems to be better, in scenarios when traversing is done only with search purpose. In this case not all nodes will be visited and "visited" counter can be useless.

Perhaps a nice feature of a future C# would be to allow a function to delegate the yield ability to some deeper function. That would allow you to write InOrder like this maybe:

public static IEnumerable<T> InOrder<T>(this IBinaryTree<T> tree) { yield tree.left.InOrder(); yield return tree.value; yield tree.right.InOrder(); }

Of course that's not a trivial feature to implement, but maybe someday C# will have continuations.

The InOrder function should be checking against IsEmpty instead of null or Count > 0.

And speaking of null, it would be a nice feature to be able to specify that a variable of a class can not be set to null.  This would simplify code so that we would not have to check that a value passed into a method is null because it would not be allowed by the compiler.  This would require being able to identity a default value so that an array could be initialized.  In the case of these immutible data structues, the default would of course by Empty.

"I would very much like to add new syntax to a hypothetical future version of C# which would be a syntactic sugar for the code above."

It's called F#.

I've a small question unrelated to this immutables series, but I hope is still relevant for this blog:

Why did you not include generic properties/indexers in C#? Are you contemplating doing so in the "hypothetical future version of C#".

Why do we have to bother about "out-of-stack". Using the stack for recursion in trees are done in functional programming like F#, Lisp all the time.

The only datastructure too big to use the stack is lists and similar, which can be several thousand elements. Trees on the other seldom becomes deeper than 100 levels, especially if you use balanced trees like AVL or red-black trees.

Stackless in-order binary tree traversal with left, right and parent pointers only

Off the top of my head and untested

class Node {

 Node Parent;

 Node Left;

 Node Right;

 Object Value;

}

class InOrderTreeWalk {

 bool descendLeft;

 Node current;

 InOrderTreeWalk(Node start) {

   this.descendLeft = true;

   this.current = start;

 }

 bool moveNext() {

   if(this.current == null) {

     return false;

   }

   if(this.descendLeft) {

     this.descendLeft = false;

     while(this.current.left != null) {

       this.current = this.current.left;

     }

   }

   else {

     if(this.current.right != null) {

       this.current = this.current.right;

       while(this.current.left != null) {

         this.current = this.current.left;

       }

     }

     else {

       if(this.current.parent != null && this.current == this.current.parent.left) {

          this.current = this.current.parent;

       }

       else {

         while(this.current.parent != null && this.current == this.current.parent.right) {

           this.current = this.current.parent;

         }

         if(this.current.parent == null) {

           this.current = null;

         }

       }

     }

   }

   return this.current != null;

 }

 object getValue() {

   return (this.current != null) ? this.current.Value : null;

 }

}

Note that in Ifeanyi's code you are still using an additional O(n) memory for the parent pointers vs Eric's b-tree implementation. A binary tree already takes up O(n) memory for n nodes though, so you could just add it together and get back O(n) total memory usage. This doesn't sound so bad in theory.

On the other hand, if you are using a balanced binary search tree, with recursion or explicit stack a traversal will only use O(log n) for extra memory. In practice it will then use less memory, as you'd have to run O(n/logn) traversals concurrently for it to actually use more.

For some reason, there's been a lot of buzz lately around immutability in C#. If you're interested in

I didn't realize that b-tree was an acronym for another data structure. I meant to say binary tree there.

As for building immutable trees with parent pointers, I was not suggesting that, but pointing out that Ifeanyi's binary tree class has parent pointers, whereas Eric's binary tree class does not. The point was that including a parent pointer misleadingly looks like it uses less memory to traverse, when it actually grows at a faster rate than the stack usage.

why?

       current = stack.Peek();

       stack = stack.Pop();

why not?

       current = stack.Pop();