Georgia Institute of Technology
College of Computing
April 2, 2015 Miracle
CS 3510 Test 3 Solutions
1. Run the strongly connected components algorithm given in class on the following directed
graph G. When doing DFS on GR : whenever there is a choice of v
CS 3510
Georgia Tech, Spring 2015
Homework 5
Instructor: Sarah Miracle
Student: YOUR NAME HERE
This homework is due by the start of class on Tuesday, February 24th. You can either submit
the homework via the course page on T-Square or hand it in at the be
CS 3510
Georgia Tech, Spring 2015
Homework 1
Instructor: Sarah Miracle
Student: YOUR NAME HERE
This homework is due by the start of class on Tuesday, January 20th. You can either
submit the homework via the course page on T-Square or hand it in at the beg
Last Name: . First Name: . Email: .
CS 3510 A, Spring 2015, Homework 7, 3/13/15 Due 3/25/15 in class Page 1/6
Problem 1, MST, 20 points
Let G(V, E) be an undirected connected graph with distinct costs on its edges. Let 66 be the cost
associated with every
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CS 3510 A, Spring 2015, Homework 8, 3/27/15 Due 4/03/15 in class
Page 1/5
Problem 1, ISP CLIQUE, 20 points
Recall that IS (Independet Set) is the following problem. On input an undirected graph G(V, E)
and an integer k
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CS 3510 A, Spring 2015, Homework 9, 4/8/15 Due 4/15/15 in class
Page 1/5
Problem 1, VCp Set Cover, 20 points
Recall the unweighted Set Cover problem. X = cfw_e1 , e2 , . . . , en is a ground set of n elements.
F = cfw_
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CS 3510 A, Springl 2015, Quiz 3, Sample
Page 1/4
Problem 1, MST, Dijkstra, 25 points.
(a) Let G(V, E) be a directed weighted graph, where the weights of all edges are positive: wuv > 0,
for all u v E. Let s V be a sourc
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CS 3510 C, Fall 2014, Homework 1, 8/20/14 Due 8/27/14 in class,
Page 1/6
Problem 1: Sorting Application.
You are given an array of n elements, and you notice that some of the elements are duplicates; that
is, they appea
CS 3510
Georgia Tech, Spring 2015
Homework 1
Instructor: Sarah Miracle
Student: YOUR NAME HERE
This homework is due by the start of class on Tuesday, January 20th. You can either
submit the homework via the course page on T-Square or hand it in at the beg
CS 3510
Georgia Tech, Spring 2015
Homework 2
Instructor: Sarah Miracle
Student: YOUR NAME HERE
This homework is due by the start of class on Tuesday, January 27th. You can either submit
the homework via the course page on T-Square or hand it in at the beg
Solutions to Homework Ten
CSE 101
1. For graph G = (V, E ) with edge weights w(), you already have a minimum spanning tree T = (V, E ).
Then the weight of an edge e increases. How should T be updated?
Case 1: e E . Nothing to do.
Case 2: e E . In this cas
Solutions to Homework Nine
CSE 101
1. (a) One way Alice can choose a set of guests S is to rst let S contain all n people, and then eliminate
any people that absolutely have to be eliminated.
Which people are these? Anybody with less than ve friends.
This
Solutions to Homework Seven
CSE 101
3.4. (ii)
source
C
A,B,E
D,F,G,H,I
sink
The SCCs are found in the order: cfw_D, F, G, H, I , cfw_C , cfw_A, B, E . The additional of a single edge (such
as D A) will make the graph strongly connected.
3.15. (a) Construc
Solutions to Homework Four
CSE 101
2.4. Algorithm A has running time
TA (n) = 5TA (n/2) + O(n),
to which we can apply the general recurrence formula, giving TA (n) = O(nlog2 5 ).
Algorithm B has running time
TB (n) = 2TB (n 1) + O(1).
To solve this one, l
Solutions to Homework Six
CSE 101
3.1. In the gure below, pre and post numbers are shown for each vertex. Tree edges are solid, back edges
are dashed.
1,12
2,11
A
B
C
E
F 4,9
3,10
13,18
D
5,6
G
H
I
14,17
15,16
7,8
3.2(a). Solid edges are tree edges. (D, B
Mystery(n)
if n > 1 then begin
for i := 1 to 71* print(x);
Mystery(%);
and
If we call Mystery(n), where n is a. power of 4 and n > 1, how many xs (as a function of 71)
does call Mystery(n) print? Justify your answer/show your work (ie give recurrence and
Georgia Institute of Technology
College of Computing
February 26, 2015 Miracle
CS 3510
Name:
Test 2
Id:
Ask questions if you are not sure what a problem is asking.
GOOD LUCK!
Problem
Points
1
20
2
20
3
30
4
30
Bonus Points
5
Total
100
Score
1. Recall the
CS 3510
Georgia Tech, Spring 2015
Homework 8
Instructor: Sarah Miracle
Student: YOUR NAME HERE
This homework is due by the start of class on Tuesday, April 21st. You can either submit the
homework via the course page on T-Square or hand it in at the begin
CS 3510 C, Fall 2014
Design and Analysis of Algorithms
Syllabus
Description and list of Topics and Methods:
Recursive Algorithms, Divide and Conquer, Sorting
(bubblesort, mergesort, quicksort, heapsort), Searching
(median finding and order statistics), S
CS 3311
Name of Course: Project Design
Time and Location: Open
Semester Fall, Spring, Summer
Instructor: Robert Waters
Phone: 385-6712
Office hours: Tuesday 0800-1300
Website: t-square
Course Description:
CS 3311 fulfills the initial portion of the design
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CS 3510 A, Spring 2015, Homework 5, 2/3/15 Due 2/18/15 in class
Page 1/4
Problem 1: Scheduling All Intervals/Interval Partition, Greedy, 25 points.
Consider requests R = cfw_1, 2, . . . , n. The i-th request corresponds
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CS 3510 A, Spring 2015, Homework 3, 1/23/15 Due 1/27/15 in class
Page 1/2
Problem 1: Weighted Median (50 points).
For n distinct elements x1 , x2 , . . . , xn with positive weights w1 , w2 , . . . , wn such that
the wei
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CS 3510 A, Spring 2015, Homework 2, 1/16/15 Due 1/23/15 in class
Page 1/5
Problem 1: Analysis of Recursive Algorithm (20 points).
Consider the function Mystery dened below.
Mystery(n)
for i = 1 to n print(xx);
if n > 16
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CS 3510 A, Spring 2015, Homework 1, 1/7/15 Due 1/14/15 in class
Page 1/8
Problem 1: Analysis of Recursive Algorithm (10 points).
Consider the function Mystery dened below.
Mystery(n)
if n > 1 then begin
print(x);
Myster
CS 3510
Georgia Tech, Spring 2015
Homework 6
Instructor: Sarah Miracle
Student: YOUR NAME HERE
This homework is due by the start of class on Tuesday, March 24th. You can either submit the
homework via the course page on T-Square or hand it in at the begin
CS 3510
Georgia Tech, Spring 2015
Homework 7
Instructor: Sarah Miracle
Student: YOUR NAME HERE
This homework is due by the start of class on Tuesday, March 31st. You can either submit
the homework via the course page on T-Square or hand it in at the begin
CS 3510
Georgia Tech, Spring 2015
Homework 2
Instructor: Sarah Miracle
Student: YOUR NAME HERE
This homework is due by the start of class on Tuesday, January 27th. You can either submit
the homework via the course page on T-Square or hand it in at the beg