CSOR W4231.002 Spring, 2016
Homework 1
Out: Monday, January 25, 2016
Due: 8pm, Monday, February 8, 2016
Please keep your answers clear and concise. Collaboration is limited to discussion of ideas
only
CSOR W4231.002 Spring, 2016
Homework 1
Out: Monday, January 25, 2015
Due: 8pm, Monday, February 8, 2015
Please keep your answers clear and concise. Collaboration is limited to discussion of ideas
only
CSOR 4231 Assignment 2 Solution
March 5, 2016
1
Problem 1
Number of inversions corrected by Bubble sort equals to number of adjacent inversions in
the input permutation.
n
1
n(n 1)
Expected number
CSOR W4231.002 Spring, 2016
Homework 2
Out: Monday, February 8, 2016
Due: 8pm, Monday, February 22, 2016
Please keep your answers clear and concise. For all algorithms you suggest, you must prove corr
Homework Assignment 1, Spring 2016
These problems are due at the beginning of class on Thursday, Feb. 4. They must be turned
in electronically on courseworks. Late submissions will be penalized at a r
Name, UNI:
CSOR W4231.002 | Midterm Exam Solutions
1.
i.
T
F
ii.
T
F
iii.
T
iv.
T
F
v.
T
F
F
2.
i. e)
ii. h)
3. (i) Let Xi be an indicator r.v. that takes on the value 1 if and only if (i) = i. Then
E
COMS 4231: Analysis of Algorithms I, Fall 2015
Problem Set 3, due Thursday October 22, 11:40am at on Courseworks.
Please follow the homework submission guidelines posted on courseworks.
Note: We plan
CSOR W4231.002 Spring, 2016
Homework 5
Out: Wednesday, March 30, 2016
Due: 8pm, Wednesday, April 13 , 2016
Please keep your answers clear and concise. For all algorithms you suggest, you must prove co
Analysis of Algorithms, I
CSOR W4231.002
Eleni Drinea
Computer Science Department
Columbia University
Thursday, February 25, 2016
Outline
1 Recap
2 Applications of BFS
Testing bipartiteness
3 Depth-rs
Analysis of Algorithms, I Hackathon 2016
CSOR W4231.002
Moderators: Bo Zhang, Devwrat More, Rajan Bhargava
Instructor: Eleni Drinea
Sponsored by: Eleni Drinea
Computer Science Department
Columbia Univ
Analysis of Algorithms, I
CSOR W4231.002
Eleni Drinea
Computer Science Department
Columbia University
Tuesday, February 16, 2016
Outline
1 Recap: matrix chain multiplication
Organizing DP computations
Analysis of Algorithms, I
CSOR W4231.002
Eleni Drinea
Computer Science Department
Columbia University
Thursday, February 18, 2016
Outline
1 Recap
2 Data segmentation
A Dynamic Programming solution
3 S
Analysis of Algorithms, I
CSOR W4231.002
Eleni Drinea
Computer Science Department
Columbia University
Tuesday, February 9, 2016
Outline
1 Recap
2 Cache maintenance (the oine problem)
3 A greedy optima
Lecture 10) Intrinsic Curvature
I) Definitions
Let g be a metric on a manifold M and D its Levi-Civita connection. The
curvature of the connection D is a tensor
R : TM x TM x TM TM
defined in the foll
Analysis of Algorithms, I
CSOR W4231.002
Eleni Drinea
Computer Science Department
Columbia University
Tuesday, January 20, 2015
Outline
1 Overview
2 A rst algorithm: Insertion Sort
3 Analysis of algor
CSOR W4231.002
Notes on the Master Theorem
29/1/2015
Often when analyzing a divide & conquer algorithm, we obtain a recurrence for its running time of
the following form
n
T (n) = aT ( ) + cnk
b
(1)
E
Analysis of Algorithms, I
CSOR W4246
Eleni Drinea
Computer Science Department
Columbia University
Thursday, January 21, 2016
Outline
1 Asymptotic notation
2 The divide & conquer principle; application
CSOR W4231: Analysis of Algorithms I
Class time: Tuesdays and Thursdays 7:10 - 8:25 PM
Class location: 309 Havemeyer Hall
Instructor: Allison Bishop
Oce hours for Instructor: Tuesday 10:00 AM - 12:00
1/19/2016
Analysis of Algorithms I,
CSOR W4231
Spring 2016, Lecture 1
Allison Bishop
TexPoint fonts used in EMF.
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Course Logistics
Instructor
1/26/2016
Analysis of Algorithms I,
CSOR W4231
Spring 2016, Lecture 3
Allison Bishop
Solving Recurrences
A Master Theorem:
- Applies to many recurrences of the form:
T(n) = a T(n/b) + f(n)
(Here, a a
1/21/2016
Analysis of Algorithms I,
CSOR W4231
Spring 2016, Lecture 2
Allison Bishop
TexPoint fonts used in EMF.
Read the TexPoint manual before you delete this box.: AAAAA
More Examples of Asymptotic
Analysis of Algorithms, I
CSOR W4231.002
Eleni Drinea
Computer Science Department
Columbia University
Thursday, February 11, 2016
Outline
1 Recap
2 Matrix chain multiplication
3 A rst attempt: brute-f
CSOR W4231.002 Spring, 2016
Homework 3
Out: 1pm, Tuesday, February 23, 2016
Due: 1pm, Tuesday, March 8, 2016
Please keep your answers clear and concise. For all algorithms you suggest, you must prove
Analysis of Algorithms, I
CSOR W4231.002
Eleni Drinea
Computer Science Department
Columbia University
Tuesday, March 22, 2016
Outline
1 Recap
2 Minimum Spanning Trees (MSTs)
Prims algorithm
Kruskals a
Lecture 11)The Schwarzschild Solution
We look for a solution to Einsteins equation for the geometry of empty space
Rc = 0
which is invariant under rotations and reflections of space, and translations
Vector Fields
I) Vector Notation
There are various notations for a vector, each useful in its own way. We
a
can write a vector V in terms of its x and y components V =
. Define the
b
1
0
basis vectors
Lecture 8) Euclidean Submanifolds
I) The Covariant Derivative on a Submanifold
A submanifold M of Euclidean space is a subset which can be written locally
near any point as the graph of a smooth funct
Lecture 2) Topology and Continuity
I) Open and Closed Sets
We can define a Topology on a set by specifying which sets are open. In
Euclidean space Rns, we say a set U is open if every point P in U lie
Lecture 7) Computing Connections
Suppose we are on a surface of two dimensions with coordinates cfw_u, v,
and let U = u
and V = v
. The metric g in these coordinates is given by
guu = gHU, UL guv = gH
Lecture 6) Connections
A connection is a rule which assigns to two vector fields X and Y on a manifold a third vector field Z = DX Y called the covariant derivative in the direction X
of Y, such that
Lecture 5) Metrics
I ) Distance Functions
On a given set M it is natural to want to define the distance between any
two points. If we write the distance between P and Q as d(P, Q) then d gives a
map
d
Lecture 5A) Maps of the World
1) Longitude and Latitude
In terms of the longitude q and latitude y, the map is given by
x = cos q cos y
y = sin q cos y .
z = sin y
On the globe the circles of longitud
Lecture 3) Vectors and Linearity
I) Vector Spaces
We can regard the points in Euclidean space as vectors; for example, in R3
x
take y as a vector. The sum of two vectors is the vector of sums of
z
com
CSOR W4231: Homework 3
TA Solutions
October 26, 2017
Points: 15, 15, 15, 15, 20, 20
Problem 1: Graded by Flora Park
Algorithm
HEAP-DELETE(A, i)
A[i] = A[n], where n=A.heap-size; i.e. take the last el
COMS 4111: Introduction to Databases
Lecture 14:
Midpoint Course Evaluation,
Database Systems Implementation (II):
Disks (continued)
Indexes
Dr. Donald F. Ferguson
[email protected]
Donald F. Ferguso