# This is a computer program that needs to be done in C#. I need this done in 10 days. - 76212

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• From: Computer Science, C Programming
• Due on: Fri 06 Feb, 2015 (04:20pm)
• Asked on: Tue 27 Jan, 2015
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Description

CS472 Assignment 3: Practice with Big-Oh
CS472 - Analysis of Algorithms
January 27, 2015
1 Overview
The assignment contains a set of practice problems covering asymptotic measures
of efficiency and working with recurrence relations.
2 Problems

1. Show directly that \$f(n)=n2+3n3 ∈ Θ(n3
). That is, use the definitions
of O and ? that f(n) is in both O(n
3
) and ?(n
3
).

2. Consider the following algorithm:
Algorithm 1: A Simple Nested Loop
j ← 1
while j <= n/2 do
i ← 1
while i <= j do
Output i and j;
Increment i;
Increment j
What is the output when n = 6, n = 8 and n = 10? What is the time
complexity of this algorithm if we assume that n is divisible by 2?

3. A table game is played on a square grid of cells. Consider an algorithm
that starts with a single cell and on each of its n iterations add new
squares all around the outside of the cell being considered? The results
for n = 0, n = 1, and n = 2 can be found in Fig. 3.
(a) How many 1-by-1 cells are there after n iterations?
1

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