Finish threaded bin. tree images

Threaded Binary Tree/README.markdown

@@ -73,6 +73,26 @@ need to keep track of both.  For example, in a double threaded tree, if a node
 has a right child but no left child, it will track its predecessor in place of
 its left child.
 
+Here is a valid "full" threaded binary tree:
+
+![Full](/Images/Full.png)
+
+While the following threaded binary tree is not "full," it is still valid.  The
+structure of the tree does not matter as long as it follows the definition of a
+binary search tree:
+
+![Partial](/Images/Partial.png)
+
+The solid lines denote the links between parents and children, while the dotted
+lines denote the "threads."  The important thing to note here is how the
+children and thread edges interact with each other.  Every node besides the
+root has one entering edge (from its parent), and two leaving edges: one to the
+left and one to the right.  The left leaving edge goes to the node's left child
+if it exists, and to its in-order predecessor if it does not.  The right
+leaving edge goes to the node's right child if it exists, and to its in-order
+successor if it does not.  The exceptions are the left-most node and the
+right-most node, which do not have a predecessor or successor, respectively.
+
 
 ## Representation
 
@@ -175,6 +195,39 @@ to explain this with an example.  Please note that this requires knowledge of
 binary search trees, so make sure you have
 [read this first](../Binary Search Tree/).
 
+Base:
+
+![Base](/Images/Base.png)
+
+Insert1:
+
+![Insert1](/Images/Insert1.png)
+
+Insert2:
+
+![Insert2](/Images/Insert2.png)
+
+Insert3:
+
+![Insert3](/Images/Insert3.png)
+
+Remove1:
+
+![Remove1](/Images/Remove1.png)
+
+Remove2:
+
+![Remove2](/Images/Remove2.png)
+
+Remove3:
+
+![Remove3](/Images/Remove3.png)
+
+Remove4:
+
+![Remove4](/Images/Remove4.png)
+
+
 
 ### Still under construction.
 

Threaded Binary Tree/ThreadedBinaryTree.swift

@@ -485,20 +485,24 @@ extension ThreadedBinaryTree: CustomDebugStringConvertible {
 */
 
 // Simple little debug function to make testing output pretty
-private func check(tree: ThreadedBinaryTree<Int>) {
-  print("\(tree.count) Total Nodes:");
-  print(tree)
-  print("Debug Info:")
-  print(tree.debugDescription)
-  print("In-Order Traversal:")
-  let myArray = tree.toArray()
-  for node in myArray {
-    print(node)
-  }
-  if tree.isThreaded() {
-    print("This threaded binary tree is VALID.")
+private func check(tree: ThreadedBinaryTree<Int>?) {
+  if let tree = tree {
+    print("\(tree.count) Total Nodes:");
+    print(tree)
+    print("Debug Info:")
+    print(tree.debugDescription)
+    print("In-Order Traversal:")
+    let myArray = tree.toArray()
+    for node in myArray {
+      print(node)
+    }
+    if tree.isThreaded() {
+      print("This threaded binary tree is VALID.")
+    } else {
+      print("This threaded binary tree is INVALID.")
+    }
   } else {
-    print("This threaded binary tree is INVALID.")
+    print("This tree is nil.")
   }
 }
 
@@ -530,20 +534,28 @@ print("\nInsert 4")
 tree.insert(4)
 check(tree)
 
-print("\nRemove 13 (Not in the Tree)")
-tree.remove(13)
+print("\nInsert 15")
+tree.insert(15)
 check(tree)
 
-print("\nRemove 5")
-tree.remove(5)
+print("\nRemove 13 (Not in the Tree)")
+tree.remove(13)
 check(tree)
 
 print("\nRemove 7")
 tree.remove(7)
 check(tree)
 
-print("\nRemove 10")
-tree.remove(10)
+print("\nRemove 5")
+tree.remove(5)
 check(tree)
 
+print("\nRemove 9 (root)")
+let newRoot = tree.remove(9)
+check(newRoot)
+
+print("\nRemove 12")
+newRoot?.remove(12)
+check(newRoot)
+
 print("\n\nDone with Tests!\n")