Fall 2013
CS 513: #1 Math Fundamentals
Farach-Colton
Due by the beginning of class, Sept. 18.
1. Prove: A binary tree with n nodes has depth at least log n and at most n 1. (Hint:
Show that if a binar
Fall 2013
Farach-Colton
CS 513
Solutions to #1 Math Fundamentals
1. Prove: A binary tree with n nodes has depth at least log n and at most n 1. (Hint:
Show that if a binary tree has depth d and has n
Fall 2011
CS 513: #1 Math Fundamentals
Farach-Colton
Due by the beginning of class, Sept. 13.
1. Prove: A binary tree with n nodes has depth at least log n and at most n 1. (Hint:
Show that if a binar
Fall 2013
Farach-Colton
CS 513
Solutions to #2
1. Find a closed form for the recurrence:
T (1) = 1
T (n) = 2T (n/2) + log n (for n 2)
You may assume n is a power of 2. Give a tight big-oh bound on T .
Computer Science Department - Rutgers University
Fall 2017
CS 512: Comments on Vertex Ordering
16:198:512
The algorithms we are currently discussing (connectivity, strongly connected components, linea
Computer Science Department - Rutgers University
Fall 2017
CS 512: Comments on Graph Search
16:198:512
1
General Graph Search
In general terms, the generic graph search algorithm looks like the follow
Computer Science Department - Rutgers University
Fall 2017
CS 512: Commentary on Q2 - Proofs and Algorithms
16:198:512
On quiz two, you were given the following facts:
Fact 1: The multiplicative inver
Computer Science Department - Rutgers University
Fall 2017
CS 512: Independent Sets and Randomized Algorithms
16:198:512
Name:
RUID:
Consider an undirected graph G = (V, E). An independent set is a su
Computer Science Department - Rutgers University
Fall 2017
CS 512: Structured Graphs
16:198:512
Name:
RUID:
1) Let G be an undirected graph on n vertices, where every vertex v is of degree 2 (deg(v) =
Fall 2011
CS 513: #2
Farach-Colton
Due by the beginning of class, Sep. 20.
1. Find a closed form for the recurrence:
T (1) = 1
T (n) = 2T (n/2) + log n (for n 2)
You may assume n is a power of 2. Give
Fall 2013
CS 513: #2
Farach-Colton
Due by the beginning of class, Sep. 25.
1. Find a closed form for the recurrence:
T (1) = 1
T (n) = 2T (n/2) + log n (for n 2)
You may assume n is a power of 2. Give
Fall 2013
CS 513: #3
Farach-Colton
Due by the beginning of class, October 2.
1. Suppose that you are given an k -sorted array, in which no element is farther than
k positions away from its nal (sorted
Fall 2011
CS 513: #07
Farach-Colton
Due by the beginning of class, Dec. 6.
1. A boolean formula is in Disjunctive Normal Form if = 1 . . . k ,
where each i = i1 iji . That is, it is the disjunction of
Fall 2011
CS 513: #6
Farach-Colton
Due by the beginning of class, Nov. 8.
1. A palindrom is a string that reads the same forwards and backwards, like Able
was I ere I saw Elba or Lonenly Tylenol (in t
Fall 2011
CS 513: #5
Farach-Colton
Due by the beginning of class, Oct. 11.
1. Let A[1, n] be an array of numbers. Dene the cartesian tree, CA , of A recursively, as follows. If n = 1, then CA is a nod
Fall 2011
CS 513: #4
Farach-Colton
Due by the beginning of class, Oct. 4.
1. The Longest Common Prefix problem is dened as follows:
Preprocess: D = cfw_S1 , . . . , Sn , Si m , that is D is a set of n
Fall 2011
CS 513: #3
Farach-Colton
Due by the beginning of class, Sept. 27.
1. Suppose that you are given an k -sorted array, in which no element is farther than
k positions away from its nal (sorted)
Generalized Linear Models (GLM)
Ping Li
Department of Statistics and Biostatistics
Department of Computer Science
Rutgers University, the State University of New Jersey
Pisctaway, NJ 08854, USA
1
Crab