Announcements – HW2 available, due 02/05, 11:59p. MT1 2/4, 7-9p. Perfect Binary tree: Perfect tree of height h, P h : • P -1 is an empty tree • if h > -1, then P h is {r, T L , T R }, where T L and T R are P h-1 . P 0 : P 2 : P 1 : Check for understanding: How many nodes in a perfect tree of height h?
Complete Binary tree: for any level k in [0,h-1], level k has 2 k nodes, and on level h, all nodes are "pushed to the left." Complete tree of height h, C h : • if h= -1, then C h is {} B • if h > -1, then C h is {r, T L , T R }, and either: U I T L is _______ and T R is ________ L D H E OR A P N O W T L is _______ and T R is ________ http://xlinux.nist.gov/dads//HTML/completeBinaryTree.html Check for understanding: Is every full tree complete? Is every complete tree full?
Rooted, directed, ordered, binary trees 1 template<class T> 2 class tree { 3 public: 4 … 5 private: Tree ADT: 6 struct Node { 7 T data; 8 Node * left; insert 9 Node * left; 10 }; remove 11 Node * root; 12 … traverse 13 };
Theorem: Our implementation of an n item binary tree has ______ null pointers.
Traversal…
Traversals: A few discussion points… template<class T> 1 void tree<T>::preOrder(Node * croot){ 2 3 if (croot != NULL){ yell(croot->data); 4 preOrder(croot->left); 5 preOrder(croot->right); 6 7 } } 8 Is preOrder public or private?
Traversal shortcuts…
Traversal summary (applications next time)… A traversal must visit every node Running time is O(n), where n is # of nodes in tree.
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