MA 240,  Instructor:  Jeffrey Horn

TREES

Rooted Trees

• Definitions:
  1. Be familiar with these.   I won't ask directly for definitions, but I will use the terms in asking you about the rest of the tree topics!   (E.g., How many leaf nodes are there in  full, balanced tree of depth d with branching factor k?)
  2. Node, leaf, internal node, branches, branching factor, parent, child, sibling (node), level, depth, subtree, root node, full tree, balanced tree, binary tree
• Counting Nodes:
  1. Number of nodes at level d in a full binary tree. 
  2. Number of nodes at level d in a full ternary tree. 
  3. Number of nodes at level d in a full k-ary tree.
     
  4. How deep is a balanced tree (branching factor k) that holds n nodes (total, leaves plus internal nodes)?
     
• Tree Traversals:
  1. Depth-first
     1. Pre-order
     2. In-order
     3. Post-order
  2. Breadth-first

Non-rooted Trees

• Spanning Tree
  1. Minimum cost Spanning Tree
  2. Prim and Kruskal's greedy algorithms