Lab 110, not hight count is funky (can be impossibly low) and seems to be incredibly unperformant. Im going to sleep on it.

Lab110-VenbergGE/src/AbstractBinaryTree.java

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+import java.util.ArrayList;
+import java.util.Iterator;
+import java.util.List;
+/*
+ *  * Data Structures & Algorithms 6th Edition 
+ * Goodrich, Tamassia, Goldwasser
+ * Code Fragments 8.7, 8.26, 8.22
+ *\
+
+/**
+ * an abstract base class providing some functionality of the binarytree interface
+ * @author Gabriel Venberg
+ */
+public abstract class AbstractBinaryTree<E> extends AbstractTree<E> implements BinaryTree<E> {
+	public Position<E> sibling(Position<E> p){
+		Position<E> parent = parent(p);
+		//p is root.
+		if (parent == null){return null;}
+		//p is left child, right child might be null.
+		if (p==left(parent)){return right(parent);}
+		//p is right child, left child might be null.
+		else {return left(parent);}
+	}
+	
+	/**returns the number of children of Position p*/
+	public int numChildren(Position<E> p){
+		int count=0;
+		if (left(p)!=null){count++;}
+		if(right(p)!=null){count++;}
+		return count;
+	}
+	
+	/**returns an iterable collection of Positions representing p's children.*/
+	public Iterable<Position<E>> children(Position<E> p){
+		//max capacity of 2
+		List <Position<E>> snapshot=new ArrayList<>(2);
+		//needed to modify this, as the arraylist we made in class needed an index
+		if(left(p)!=null){snapshot.add(left(p));}
+		if(right(p)!=null){snapshot.add(right(p));}
+		// and our arraylist 
+		return snapshot;
+	}
+	
+	/**adds positions of the subtree rooted at Position p to the given snapshot*/
+	private void inorderSubtree(Position<E> p, List<Position<E>> snapshot){
+		if(left(p)!=null){inorderSubtree(left(p), snapshot);}
+		snapshot.add(p);
+		if(right(p)!=null){inorderSubtree(right(p), snapshot);}
+	}
+	
+	/**returns an iterable collection of the positions of the tree, reported in inorder.*/
+	public Iterable<Position<E>> inorder(){
+		List<Position<E>> snapshot=new ArrayList<>();
+		//fill snapshot recursively
+		if(!isEmpty()){inorderSubtree(root(), snapshot);}
+		return snapshot;
+	}
+	
+	/**Overrides positions to make inorder the default order for binary trees*/
+	public Iterable<Position<E>> positions(){
+		return inorder();
+	}
+	
+			//nested ElementIterator class
+		/**this class adapts the iteration produced by positions() to returns elements*/
+		private class ElementIterator implements Iterator<E>{
+			Iterator<Position<E>> posIterator=positions().iterator();
+			public boolean hasNext(){return posIterator.hasNext();}
+			//return element
+			public E next(){return posIterator.next().getElement();}
+			public void remove(){posIterator.remove();}
+		}//end of nested ElementIterator class
+		
+		/**returns an iterator if the elements stored in the tree*/
+		public Iterator<E> iterator(){return new ElementIterator();}
+}