CSS 343: Notes from Lecture 6 (DRAFT)

Red Black Trees Again

• Standard template libary std::map container is typically implemented using a red-black tree
• SGI STL implementation is available for download
  • reading the code may hurt your brain

B Trees Again

• Some confusion about putting the overflow key into the parent node: it doesn't really work this way
  • it's an idea for exposition, but it appears to be hindering rather than helping understanding
  • the algorithm is recursive and does not require a parent pointer
• Sample B Tree animation: btree-animation.zip

Hashing

Coming RSN...

Priority Queues

• a binary search tree is geared toward random insert and removal
• a special case is random insert, remove minimum element
• a binary heap is a complete binary tree with the minimum element at the root
  • a heap is not a binary search tree
• the heap invariant is that each node is less than its children
  • by "less than", we could easily mean "greater than"
  • in fact, any ordering predicate will work:
    • sort strings by ASCII value
    • sort lexically
    • convert string to number and sort numerically
    • sort points in plane by distance from origin
    • etc.
• new entries are inserted at bottom-most left-most leaf position, breaking the invariant
  • the invariant is restored by sifting up (iteratively swaping with parent)
• removing minimum element: remove root and replace with bottom-most rightmost leaf.
  • heap invariant is restored by sifting down (swaping with the smaller of the child nodes)
• animation (click for larger image):