CSCI-GA.1170-001/002 Fundamental Algorithms
October 9, 2012
Problem Set 6
Lecturer: Yevgeniy Dodis
Due: Wednesday, October 17
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, 2012
Problem Set 3
Lecturer: Yevgeniy Dodis
Due: Tuesday, September 25
Problem 3-1 (Recurrences and Matrix Exponentiation) 18 points
The sequence cfw_Fn | n 0 are dened as follows: F0 = 1, F1 = 1,
CSCI-GA.1170-001/002 Fundamental Algorithms
September 9, 2012
Problem Set 1
Lecturer: Yevgeniy Dodis
Due: Tuesday, September 11
Problem 1-1 (Counting Inversions)
10 points
Let A[1, . . . , n] be an array of n distinct numbers. If i < j and A[i] > A[j ], t
CSCI-GA.1170-001/002 Fundamental Algorithms
November 13, 2012
Problem Set 7
Lecturer: Yevgeniy Dodis
Due: Tuesday, November 20
Problem 7-1 (Bracketings)
8 (+7) Points
Imagine a unary alphabet with a single letter x. A (valid) bracketing B is a string over
CSCI-GA.1170-001/002 Fundamental Algorithms
December 7, 2012
Problem Set 10
Lecturer: Yevgeniy Dodis
Due: Tuesday, December 11
Problem 10-1 (Second Smallest Spanning Tree)
13 (+5) points
(a) (3 points) Using the correctness of the Kruskal/Prim algorithm,
CSCI-GA.1170-001/002 Fundamental Algorithms
September 11, 2012
Problem Set 2
Lecturer: Yevgeniy Dodis
Due: Tuesday, September 18
Problem 2-1 (Mergesort)
10 points
(a) (6 points) Suppose you have some procedure FASTMERGE that given two sorted lists of
leng
CSCI-GA.1170-001/002 Fundamental Algorithms
September 26, 2012
Problem Set 4
Lecturer: Yevgeniy Dodis
Due: Tuesday, October 2
Problem 4-1 (Improving Deterministic Quicksort)
16 points
We give the following procedure StrangeSort to sort an array A of n dis
CSCI-GA.1170-001/002 Fundamental Algorithms
October 2, 2012
Problem Set 5
Lecturer: Yevgeniy Dodis
Due: Tuesday, October 9
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 set
CSCI-GA.1170-001/002 Fundamental Algorithms
November 14, 2012
Problem Set 8
Lecturer: Yevgeniy Dodis
Due: Tuesday, November 27
Problem 8-1 (Uninterrupted Television)
14 Points
Little Johnny is extremely fond of watching television. His parents are o for w
CSCI-GA.1170-001/002 Fundamental Algorithms
November 27, 2012
Problem Set 9
Lecturer: Yevgeniy Dodis
Due: Tuesday, December 04
Problem 9-1 (SOLE Encoding)
9 points
Let B = 64, and the actual block alphabet = cfw_0, . . . 9, a, . . . , z, A, . . . , Z, . (
CSCI-GA.1170-001/002 Fundamental Algorithms
September 23, 2015
Problem Set 3
Lecturer: Yevgeniy Dodis
Due: Tuesday, September 29
Problem 3-1 (Stock Prot)
10 (+5) Points
Sometimes, computing extra information can lead to more ecient divide-and-conquer algo