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:
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
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: 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: 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
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 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
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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