CS 331: Solutions to Homework 1
TA: Siddhesh Chaubal
January 28, 2016
Question1 (10 points)
List the following functions in non-descending order of asymptotic growth rate. If two or
more functions have the same asymptotic growth rate then group them toget
CS 331: Solutions to Homework 2
TA: Siddhesh Chaubal
February 4, 2016
Question1 (10 points)
Problem 10, Chapter 3, pp. 110-111.
Be sure to argue correctness and analyze running time. You can use algorithms seen in
class without deriving them once again he
CS 331: Solutions to Homework 3
TA: Siddhesh Chaubal
February 11, 2016
Question1 (10 points)
Consider the greedy algorithm we saw in class for Interval Partitioning. Design an efficient
version of this algorithm using a binary heap. Be sure to justify the
Practice Problems: Permutations
Math 332, Spring 2013
These are not to be handed in. The quiz will be on Tuesday.
1. Write each of the following permutations as a product of disjoint cycles:
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8
a.
b.
.
2 3 4 5 1 7 8 6
1 3 8 7
CS 331: Algorithms and Complexity (Fall 2016)
Unique numbers: 51420, 51425, 51430, 51435
Assignment 1
Due on Wednesday, September 7, by 11.59pm
Problem 1
(a) (5 points) Arrange the following list of functions in increasing order of growth rate.
That is, i
Practice Problems: Cyclic Groups
Math 332, Spring 2013
These are not to be handed in. The quiz will be on Tuesday.
1. Find all generators of Z6 , Z8 , and Z20 .
2. List all elements of the subgroup h30i in Z80 .
3. If |a| = 60, what is the order of a24 ?
CS 331: Algorithms and Complexity (Fall 2016)
Unique numbers: 51420, 51425, 51430, 51435
Induction Examples
Examples
Proof by induction.
(a) Prove the following formula using induction
n
X
r = n(n + 1)/2.
r=1
Sol.
Base case:
P1 n = 1,
LHS: r=1 r = 1.
RHS:
Dell Partner Course
Completion Certificate
Dell Worldwide Partner Learning and Development Team acknowledges that
on this date Oct 03, 2016
Anthony Benedicto T.
has successfully completed the course
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