CSCI-GA.1170-001/002 Fundamental Algorithms
October 8, 2014
Problem Set 6
Lecturer: Yevgeniy Dodis
Due: Wednesday, October 15
Problem 6-1 (Find the Josephus Permutation)
10 points
According to Josephus account of the siege of Yodfat, he and his n comrade

CSCI-GA.1170-001/002 Fundamental Algorithms
September 23, 2014
Problem Set 4
Lecturer: Yevgeniy Dodis
Due: Wednesday, October 1
Problem 4-1 (Improving Deterministic Quicksort)
16 points
We give the following procedure StrangeSort to sort an array A of n d

CSCI-GA.1170-001/002 Fundamental Algorithms
September 10, 2014
Problem Set 2
Lecturer: Yevgeniy Dodis
Due: Wednesday, September 17
Problem 2-1 (Mergesort)
10 points
(a) (6 points) Suppose you have some procedure FASTMERGE that given two sorted lists of
le

CSCI-GA.1170-001/002 Fundamental Algorithms
September 17, 2014
Problem Set 3
Lecturer: Yevgeniy Dodis
Due: Wednesday, September 24
Problem 3-1 (Recurrences and Matrix Exponentiation) 22 points
The sequence cfw_Fn | n 0 are dened as follows: F0 = 1, F1 = 1

CSCI-GA.1170-001/002 Fundamental Algorithms
November 26, 2014
Problem Set 11
Lecturer: Yevgeniy Dodis
Due: Wednesday, December 5
Problem 11-1 (Modied Dijkstra - Too Slow?)
15 points
Dijkstras algorithm solves the single-source shortest-path problem on a w

CSCI-GA.1170-001/002 Fundamental Algorithms
November 26, 2014
Problem Set 10
Lecturer: Yevgeniy Dodis
Due: Wednesday, November 26
Problem 10-1 (Greedy Topological Sort)
12 (+4) points
(a) (3 points) Assume directed graph G is acyclic. Show that G has at l

CSCI-GA.1170-001/002 Fundamental Algorithms
November 13, 2014
Problem Set 9
Lecturer: Yevgeniy Dodis
Due: Wednesday, November 19
Problem 9-1 (Party Propaganda)
18 Points
You have an undirected graph G = (V, E) and two special nodes r, d V . At time 0, nod

CSCI-GA.1170-001/002 Fundamental Algorithms
November 5, 2014
Problem Set 8
Lecturer: Yevgeniy Dodis
Due: Wednesday, November 12
Problem 8-1 (Not All Greedy are Equal)
3(+5) points
For each of the following suggested greedy algorithms for the Activity-Sele

CSCI-GA.1170-001/002 Fundamental Algorithms
October 29, 2014
Problem Set 7
Lecturer: Yevgeniy Dodis
Due: Wednesday, November 5
Problem 7-1 (Text Alignment)
6 points
Using dynamic programming, nd the optimum printing of the text Not all those who wander ar

CSCI-GA.1170-001/002 Fundamental Algorithms
October 1, 2014
Problem Set 5
Lecturer: Yevgeniy Dodis
Due: Wednesday, October 8
Problem 5-1 (Sorting in O(n log log n) time)
10 points
(a) (4 points) Suppose we want to sort an array A of n elements from the se

CSCI-GA.1170-001/002 Fundamental Algorithms
September 3, 2014
Problem Set 1
Lecturer: Yevgeniy Dodis
Due: Tuesday, September 10
Problem 1-1 (Polynomial Evaluation)
16 (+4) points
A degree-n polynomial P (x) is a function
n
P (x) = a0 + a1 x + . . . + an1