CS241: Topics for the Week of November 5, 2007

• Reading: Chp 10, Chapter 11, Section 3
• Monday - go over Lab 8: Recursion and Divide-and-Conquer Sorting
• Discuss new lab: Lab 9: Trees
• Quicksort - divide and conquer (recursive algorithm)
  • sorts in place
  • can move elements long distance in single swap
  • Θ(n log n) on average, Θ(n²) worst case
  • See code in textbook on pp. 240 and 242.
  • Smart ways of picking the pivot can speed algorithm and reduce likelihood of worst case situation.
• Trees
  • The Tree Data Structure
  • Tree Abstract Data Type: defined by operations root(), children(), parent(). Other operations could be height(), find(), insert(), isLeaf(), isRoot(), isInternal(),...
  • Binary Tree Abstract Data Type: operations include above plus getLeft(), getRight();
  • Binary Search Tree Abstract Data Type: insert(), find(), contains(), remove(), successor(), getLargest(), getSmallest(), height(), traverse() - various kinds,
  • Terminology:
    root, children, leaf node, internal node, level, depth, degenerate tree, (proper) descendants, (proper) ancestors, siblings,height, full tree, perfect tree, binary tree, binary search tree, subtree.
  • Binary Trees and Binary Search Trees
  • Binary Tree Traversal:
    • pre-order, post-order, in-order
    • level order
    • depth-first vs breadth first
  • What is complexity of above operations for a tree? What if the tree is balanced?
  • Deleting items from a binary search tree
  • Given a complete binary tree of height h, how many nodes are there? How many nodes are in the last level (the leaf nodes)?
  • Balanced trees: Red Black Trees
    • Animation
    • Defined
  • Storing a set of comparable items. Compare the complexity of various operations (find, insert, remove) for the following data tpes:
    • unsorted list (array vs linked)
    • sorted list (array vs linked)
    • tree, balanced tree
    • hash table (to be covered later)
• Tree Applications
  • Solving Sudoku
  • Mazes
  • MiniMax Game Trees
    • Works for two player games with perfect information. Each level (or ply) corresponds to the choices of one of the players at a particular turn. Assumes player play to the best of their ability.
    • TicTacToe: see text, and Game tree
    • Game of Nim: Game Tree, MatchSticks, Coins