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Binary Search Tree "stack" explanation

I have a very simple implemention of BST in C#. The code:
class Node
{
public int? value;
public Node parent;
public Node left;
public Node right;
public Node(int? value, Node parent = null)
{
this.value = value;
this.parent = parent;
}
}
class BST
{
public Node root;
public List<Node> tree = new List<Node>();
public BST(int? value = null)
{
if (value != null)
{
this.root = new Node(value);
this.tree.Add(this.root);
}
}
public Node insert(int value)
{
Node node = this.root;
if (node == null)
{
this.root = new Node(value);
this.tree.Add(this.root);
return this.root;
}
while (true)
{
if (value > node.value)
{
if (node.right != null)
{
node = node.right;
}
else
{
node.right = new Node(value, node);
node = node.right;
break;
}
}
else if (value < node.value)
{
if (node.left != null)
{
node = node.left;
}
else
{
node.left = new Node(value, node);
node = node.left;
break;
}
}
else
{
break;
}
}
return node;
}
}
class Program
{
static void Main()
{
BST superTree = new BST(15);
superTree.insert(14);
superTree.insert(25);
superTree.insert(2);
}
}
My Question is regarding the "Insert" method of the BST class.
How exactly its "return" work when I just call it in the main method?
How does it know to put that "node" on the "left"? I am not referencing "root.left" anywhere but somehow it gets properly inserted.
I realized at some point that some kind of recursion occurs there, but its been like 6 hours and I still can't understand how this method properly works.
I appreaciate any explanation of that "insert" method.Thanks.

Node node = this.root;
Your code always starts with the root, because of this line. It's only after node is no longer null that node be re-assigned to something other than root. The rest of the code works on node.left, but because your code begins with root as above, node.left is actually referencing root at the start.

Recursive implementation of "append if not present" for linked list

public bool add(int e)
{
if(head == null)
{
Node n = new Node
{
element = e
};
head = n;
return true;
}
Node t = head;
if(t.next == null)
{
if(t.element == e)
{ return false; }
Node n = new Node
{
element = e
};
t.next = n;
return true;
}
t = t.next;
this.add(e);
return true;
}
This is a code to add a new node in set. No duplicated values allowed. There is Main Class called Sets and one inner class called Nodes.
I know Node t = head; is creating a problem is there anyway to make this recursive? Even passing extra optional parameters doesn't help.

If I understood your question correctly, to make it recursive you would need to split it into two functions, a public one for handling the head == null case, and a private one for handling n.next == null and is recursive.
public bool add(int e)
{
if (head == null)
{
head = new Node { element = e };
return true;
}
return add(head, e);
}
private bool add(Node n, int e) {
if (n.element == e)
return false;
if (n.next == null) {
n.next = new Node { element = e };
return true;
}
return add(n.next, e);
}
However, I would suggest instead doing something akin to the following which does everything in one function:
public bool add(int e)
{
if (head == null)
{
head = new Node { element = e };
return true;
}
if (head.element == e)
return false;
Node n = head;
while (n.next != null) {
if (n.element == e)
return false;
n = n.next;
}
n.next = new Node { element = e };
return true;
}

reverse a linked list in a recursive function c#

I'm having problems trying to write a reverse recursive method for a LinkedList class I created in C#.
The LinkedList has 2 pointers in it one for the head and the other for the tail:
public class Node
{
public object data;
public Node next;
public Node(object Data)
{
this.data = Data;
}
}
public class LinkedList
{
Node head;
Node tail;
public void Add(Node n)
{
if (head == null)
{
head = n;
tail = head;
}
else
{
tail.next = n;
tail = tail.next;
}
}
Now, the recursive reverse function goes like this:
public void reverse_recursive()
{
Node temp_head = head;
if (temp_head == tail)
{
return;
}
while (temp_head != null)
{
if (temp_head.next == tail)
{
tail.next = temp_head;
tail = temp_head;
reverse_recursive();
}
temp_head = temp_head.next;
}
}
I'm having 2 troubles with it: first, a logic problem, I know that head doesn't point to the first node after the reverse. The second problem is that i probably do something wrong with the null pointer so the program crashes.
I also give you the main program:
class Program
{
static void Main(string[] args)
{
LinkedList L = new LinkedList();
L.Add(new Node("first"));
L.Add(new Node("second"));
L.Add(new Node("third"));
L.Add(new Node("forth"));
L.PrintNodes();
L.reverse_recursive();
L.PrintNodes();
Console.ReadLine();
}
}
Thank you for helping!!

public void Reverse()
{
this.Reverse(this.head);
}
private void Reverse(Node node)
{
if (node != null && node.next != null)
{
// Create temporary references to the nodes,
// because we will be overwriting the lists references.
Node next = node.next;
Node afterNext = node.next.next;
Node currentHead = this.head;
// Set the head to whatever node is next from the current node.
this.head = next;
// Reset the next node for the new head to be the previous head.
this.head.next = currentHead;
// Set the current nodes next node to be the previous next nodes next node :)
node.next = afterNext;
// Keep on trucking.
this.Reverse(node);
}
else
{
this.tail = node;
}
}

public void reverse()
{
reverse_recursive(tail);
Node tmp = tail;
tail = head;
head = tmp;
}
public void reverse_recursive(Node endNode)
{
Node temp_head = head;
if (temp_head == endNode)
{
return;
}
while (temp_head != null)
{
if (temp_head.next == endNode)
{
break;
}
temp_head = temp_head.next;
}
endNode.next = temp_head;
temp_head.next = null;
reverse_recursive(temp_head);
}
See also this

Another option over here.
class Program{
static void Main(string[] args)
{
LinkedList L = new LinkedList();
L.Add(new Node("first"));
L.Add(new Node("second"));
L.Add(new Node("third"));
L.Add(new Node("forth"));
L.PrintNodes();
L.reverse_recursive();
Console.WriteLine("---------------------");
L.PrintNodes();
Console.ReadLine();
}
}
public class Node
{
public object data;
public Node next;
public Node(object Data)
{
this.data = Data;
}
}
public class LinkedList
{
Node head;
Node tail;
public void Add(Node n)
{
if (head == null)
{
head = n;
tail = head;
}
else
{
tail.next = n;
tail = tail.next;
}
}
public void PrintNodes()
{
Node temp = head;
while (temp != null)
{
Console.WriteLine(temp.data);
temp = temp.next;
}
}
private LinkedList p_reverse_recursive(Node first)
{
LinkedList ret;
if (first.next == null)
{
Node aux = createNode(first.data);
ret = new LinkedList();
ret.Add(aux);
return ret;
}
else
{
ret = p_reverse_recursive(first.next);
ret.Add(createNode(first.data));
return ret;
}
}
private Node createNode(Object data)
{
Node node = new Node(data);
return node;
}
public void reverse_recursive()
{
if (head != null)
{
LinkedList aux = p_reverse_recursive(head);
head = aux.head;
tail = aux.tail;
}
}
}
Hope it helps

A second variant
private void p_reverse_recursive2(Node node)
{
if (node != null)
{
Node aux = node.next;
node.next = null;
p_reverse_recursive2(aux);
if (aux != null)
aux.next = node;
}
}
public void reverse_recursive()
{
if (head != null)
{
Node aux = head;
head = tail;
tail = aux;
p_reverse_recursive2(tail);
}
}

Variation on a theme...
public Node Reverse(Node head)
{
if(head == null)
{
return null;
}
Node reversedHead = null;
ReverseHelper(head, out reversedHead);
return reversedHead;
}
public Node ReverseHelper(Node n, out Node reversedHead)
{
if(n.Next == null)
{
reversedHead = n;
return n;
}
var reversedTail = ReverseHelper(n.Next, out reversedHead);
reversedTail.Next = n;
n.Next = null;
return n;
}
}

I was just playing with similar brain teaser with the only difference that LinkedList class only has a definition for head and all the rest of the nodes are linked there. So here is my quick and dirty recursive solution:
public Node ReverseRecursive(Node root)
{
Node temp = root;
if (root.next == null)
return root;
else
root = ReverseRecursive(root.next);
temp.next = null;
Node tail = root.next;
if (tail == null)
root.next = temp;
else
while (tail != null)
{
if (tail.next == null)
{
tail.next = temp;
break;
}
else
tail = tail.next;
}
return root;
}

"Sorting" a Tree Data Structure

I made a Tree Data Structure and I want the Elements to sort like this:
10
/ \
5 12
/ \ / \
3 7 11 18
If the value of the added element is smaller than the value of the other element, it should be linked left, and if bigger, right. My problem is, that I just can't get the sorting method right.
class Tree
{
private class TElement
{
public int _value;
public TElement _left;
public TElement _right;
public TElement(int value)
{
_value = value;
}
}
private TElement RootElement;
public void Add(int value)
{
TElement newElement = new TElement(value);
TElement current = new TElement(value);
current = RootElement;
if (RootElement == null)
{
RootElement = newElement;
return;
}
SortNewElement(RootElement, RootElement, newElement, RootElement);
}
private void SortNewElement(TElement left, TElement right, TElement newElement, TElement RootElement)
{
if (newElement._value < RootElement._value && RootElement._left == null)
{
left._left = newElement;
return;
}
if (newElement._value > RootElement._value && RootElement._right == null)
{
right._right = newElement;
return;
}
if (newElement._value < left._value && left._left == null)
{
left._left = newElement;
return;
}
if (newElement._value > right._value && right._right == null)
{
right._right = newElement;
return;
}
SortNewElement(left._left, right._right, newElement, RootElement);
}
}
I know it doesn't work because it's trying to get the linked nodes of a null element.

From what i can understand from your question you are just trying to insert a new node in a binary search tree. Its inorder traversal will be a sorted array.
You can do so by the following simple pseudo code
insert_new( Node* node, value)
{
if(value > node->value)
{
if(node->right != null)
{
insert_new(node->right,value);
}
else
{
node->right = new Node(value);
return;
}
}
else
{
if(node->left != null)
{
insert_new(node->left,value)
}
else
{
node->left = new Node(value);
return;
}
}
}

class element{
public:
int value;
*element left;
*element right;
element(int value)
value = value;
public add(&element a)
if (a != null)
{
if (left!=null){
left = a;
}
else{
if (left.value > a.value){
right = left;
left= a;
}
else{
right=a;
}
}

Fundamental Data Structures in C#

I would like to know how people implement the following data structures in C# without using the base class library implementations:-
Linked List
Hash Table
Binary Search Tree
Red-Black Tree
B-Tree
Binomial Heap
Fibonacci Heap
and any other fundamental data structures people can think of!
I am curious as I want to improve my understanding of these data structures and it'd be nice to see C# versions rather than the typical C examples out there on the internet!

There's a series of MSDN articles on this subject. However, I haven't really read the text myself. I believe that the collections framework by .NET has a broken interface and cannot be extended very well.
There's also C5, a libray that I am investigating right now.
For the reason mentioned above, I've had the project to implement my own collections library for .NET but I've stopped this project after the first benchmark revealed that even a straightforward, non-thread-safe generic Vector implementation is slower than the native List<T>. Since I've taken care not to produce any inefficient IL code, this means that .NET is simply not suited (yet) for writing on-par replacements for intrinsic data structures, and that the .NET framework has to use some behind-the-scenes knowledge to optimize the builtin collection classes.

Here is a generic Binary Search Tree. The only thing I didn't do was implement IEnumerable<T> so you could traverse the tree using a enumerator. However that should be fairly straight forward.
Special thanks to Scott Mitchel for his BSTTree article, I used it as a reference on the delete method.
The Node Class:
class BSTNode<T> where T : IComparable<T>
{
private BSTNode<T> _left = null;
private BSTNode<T> _right = null;
private T _value = default(T);
public T Value
{
get { return this._value; }
set { this._value = value; }
}
public BSTNode<T> Left
{
get { return _left; }
set { this._left = value; }
}
public BSTNode<T> Right
{
get { return _right; }
set { this._right = value; }
}
}
And the actual Tree class:
class BinarySearchTree<T> where T : IComparable<T>
{
private BSTNode<T> _root = null;
private int _count = 0;
public virtual void Clear()
{
_root = null;
_count = 0;
}
public virtual int Count
{
get { return _count; }
}
public virtual void Add(T value)
{
BSTNode<T> newNode = new BSTNode<T>();
int compareResult = 0;
newNode.Value = value;
if (_root == null)
{
this._count++;
_root = newNode;
}
else
{
BSTNode<T> current = _root;
BSTNode<T> parent = null;
while (current != null)
{
compareResult = current.Value.CompareTo(newNode.Value);
if (compareResult > 0)
{
parent = current;
current = current.Left;
}
else if (compareResult < 0)
{
parent = current;
current = current.Right;
}
else
{
// Node already exists
throw new ArgumentException("Duplicate nodes are not allowed.");
}
}
this._count++;
compareResult = parent.Value.CompareTo(newNode.Value);
if (compareResult > 0)
{
parent.Left = newNode;
}
else
{
parent.Right = newNode;
}
}
}
public virtual BSTNode<T> FindByValue(T value)
{
BSTNode<T> current = this._root;
if (current == null)
return null; // Tree is empty.
else
{
while (current != null)
{
int result = current.Value.CompareTo(value);
if (result == 0)
{
// Found the corrent Node.
return current;
}
else if (result > 0)
{
current = current.Left;
}
else
{
current = current.Right;
}
}
return null;
}
}
public virtual void Delete(T value)
{
BSTNode<T> current = this._root;
BSTNode<T> parent = null;
int result = current.Value.CompareTo(value);
while (result != 0 && current != null)
{
if (result > 0)
{
parent = current;
current = current.Left;
}
else if (result < 0)
{
parent = current;
current = current.Right;
}
result = current.Value.CompareTo(value);
}
if (current == null)
throw new ArgumentException("Cannot find item to delete.");
if (current.Right == null)
{
if (parent == null)
this._root = current.Left;
else
{
result = parent.Value.CompareTo(current.Value);
if (result > 0)
{
parent.Left = current.Left;
}
else if (result < 0)
{
parent.Right = current.Left;
}
}
}
else if (current.Right.Left == null)
{
if (parent == null)
this._root = current.Right;
else
{
result = parent.Value.CompareTo(current.Value);
if (result > 0)
{
parent.Left = current.Right;
}
else if (result < 0)
{
parent.Right = current.Right;
}
}
}
else
{
BSTNode<T> furthestLeft = current.Right.Left;
BSTNode<T> furthestLeftParent = current.Right;
while (furthestLeft.Left != null)
{
furthestLeftParent = furthestLeft;
furthestLeft = furthestLeft.Left;
}
furthestLeftParent.Left = furthestLeft.Right;
furthestLeft.Left = current.Left;
furthestLeft.Right = current.Right;
if (parent != null)
{
result = parent.Value.CompareTo(current.Value);
if (result > 0)
{
parent.Left = furthestLeft;
}
else if (result < 0)
{
parent.Right = furthestLeft;
}
}
else
{
this._root = furthestLeft;
}
}
this._count--;
}
}
}

I would recommend two resources for the data structures you mention:
First, there is the .NET Framework Source Code (information can be found on ScottGu's blog here).
Another useful resource is the Wintellect's Power Collections found on Codeplex here.
Hope this helps!

NGenerics
"A class library providing generic data structures and algorithms not implemented in the standard .NET framework."

Check out Rotor 2 or use reflector too see how Microsoft did it!!!
also you can check Microsoft reference source