Divide and Conquer Algorithms: Binary Tree Traversals

• Read section 5.3 (pages 182-185)
• Why is divide-and-conquer a natural approach to solving problems involving binary trees?
• Study the algorithm to compute the height of a binary tree.
  • What is the basic operation?
  • Why is -1 the correct value to return for an empty tree?
  • What nodes do we call external? What nodes do we call internal?
    • What is the relationship between the number of external nodes and the number of internal nodes?
  • What is the time efficiency class of the height algorithm? How is that related to the number of external and internal nodes?
  • Is the height algorithm’s running time affected by how balanced the tree is?
  • Can we perform a similar algorithm for a rooted ordered tree (i.e. allowing any number of children)?
    • Is the relation between external and internal nodes the same for such a tree?
    • Can you come up with at least an upper bound on how many external nodes a tree with \(n\) internal nodes can have?
• What are the three traversal orders for binary trees?
  • Write pseudocode for each traversal order.
  • Work out by hand the three orders in Figure 5.6
• Practice problems: 5.3.1, 5.5.5, 5.5.7