Probability Theory Review
Random variable: discrete versus continuous.
Expected value of a discrete RV:
E[V] i P[V i]
(assumes V is nonnegative)
i 0
Density and distribution functions.
For a discrete RV V, defined to be
P[V = i] and
P[V i], respecti
Skip Lists
Our text for this
topic is the handout
SkipLists.
Supports same operations as redblack tree.
Key Idea: Store keys in sorted linked list, with
the following twist:
Provide extra pointers so that portions of the list can
be skipped over whil
Comp 455
Models of Languages and Computation.
Usually taught each Fall and Spring.
Common Textbooks:
Introduction to Automata Theory, Languages, and
Computation, Hopcroft, Motwani, and Ullman,
AddisonWesley, 2001.
Introduction to the Theory of Compu
Chapter 19: Binomial Heaps
A way to implement mergeable heaps.
Useful in scheduling algorithms and graph algorithms.
Operations:
Jim Anderson
This is Chapter 19 from
an old edition of the book.
See the handout
BinomialHeaps.
MakeHeap().
Insert(H, x),
Chapter 21: Disjoint Sets
Want to maintain a collection S = cfw_S 1, , Sk of disjoint dynamic sets.
Each set has a representative member.
Operations:
MakeSet(x): Make new singleton set containing object x (x is
representative).
Union(x, y): Like bef
Chapter 18: BTrees
Example:
M
Note: Each leaf
has the same depth
BC
QTX
DH
FG
JKL
NP
RS
VW
YZ
Node x has the following fields:
n[x]  number of keys stored in x.
key1[x] key2[x] keyn[x][x]  the n[x] keys.
leaf[x]  Boolean.
if internal: n[x] + 1 pointe
Chapter 25: AllPairs Shortest Paths
Application: Computing distance table for a road atlas.
Atlanta
Atlanta Chicago 650
Detroit 520
Chicago
650
210
Detroit
520
210

One Approach: Run singlesource SP algorithm V times.
Nonnegative Edges: Use Dijkstra
Splay Trees
Our text for this
topic is the handout
SplayTrees.
Optional reading: SplayTreesJournalPaper.
In balanced tree schemes,
explicit rules are followed to ensure balance.
In splay trees, there are no such rules.
Search, insert, and delete ope
Chapter 24: SingleSource Shortest Paths
Given: A single source vertex in a weighted, directed
graph.
Want to compute a shortest path for each possible
destination.
Similar to BFS.
We will assume either
no negativeweight edges, or
no reachable nega