Lecture 4: Recursive Data Structures

Background Material

• Lecture 2
• Recursion and induction
• Pointers and linked lists

Reading

• Chapter 5 (material on binary trees and binary search trees) of the text.

Topics

• Recursive Definition of a binary tree
  1. Height
  2. Maximum number of nodes
  3. Path length
• Recursive algorithms for binary trees
  1. Number of nodes
  2. Height
  3. Path length
• External representation of binary trees
  1. reading
  2. printing
  3. pretty printing
• Recursive Definition of a binary search tree
• Recursive algorithms for binary search trees
  1. search
  2. insert
  3. max
  4. delete
  5. traversal
• Runtime analysis of binary search trees
  1. maximum runtime (height)
  2. average runtime (internal path length)

Lecture Notes

• lec4.ppt

Programs

• tree.c, tree.h - algorithms for binary and binary search trees.
• treeinsert.c - main program to test tree algorithms.
• randbst.c - main program to analyze performance of tree algorithms. This requires the files perm.h and perm.c.

Resources

• None posted

Assignments

• Studyguide for first midterm