Download presentation

Presentation is loading. Please wait.

Published byRenee Trull Modified over 3 years ago

1
Design & Analysis of Algorithms COMP 482 / ELEC 420 John Greiner

2
Math Background: Review & Beyond 1.Asymptotic notation 2.Math used in asymptotics 3.Recurrences 4.Probabilistic analysis 2 To do: [CLRS] A, B, 3.2 #1

3
Comparisons Some useful algebra:a**
{
"@context": "http://schema.org",
"@type": "ImageObject",
"contentUrl": "http://images.slideplayer.com/5/1585052/slides/slide_3.jpg",
"name": "Comparisons Some useful algebra:a
**

4
Floor & Ceilings 4 a>0 integer a integer a>0, b 1

5
Logarithm Notation lg n = log 2 nln n = log e n lg k n = (lg n) k lg lg n = lg (lg n) lg n + k = (lg n) + k lg (0) n = nlg (i+1) n = lg lg (i) n lg* n = min {i 0 | lg (i) n 1} How many times can you take the logarithm before its 1? 5

6
Exponentials & Logarithms 6 a>0 O(log a x) = O(log b x) = O(log x) x=a c=b

7
Summations 7 Arithmetic ? Harmonic ? if |x| < 1 ? Geometric if x 1 ? Telescoping ? Solve as telescoping sum: ?

8
Summations – Combining with Calculus 8 if |x| < 1 Have: Differentiate:if |x| < 1Algebra:if |x| < 1

9
Bounding Summations: Upper Bound 9 ?

10
Bounding Summations: Lower Bound 10 ?

11
Logarithms 11

12
Bounding Summations by Integrals 12 0 1 0123 … 4 Recall: ln 1 = 0

13
Factorials n! = ω(2 n ) n! = o(n n ) log n! = Θ(n log n) 13

14
Permutations & Combinations 14 # of k-combinations of an n-set = # of permutations of an n-set = n!

Similar presentations

OK

تصميم وتحليل الخوارزميات عال311 Chapter 3 Growth of Functions

تصميم وتحليل الخوارزميات عال311 Chapter 3 Growth of Functions

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on acid base indicators Ppt on file system in unix everything is a file Ppt on op amp circuits explained Ppt on travel agency management Ppt on rc coupled amplifier lab Ppt on next generation 2-stroke engine parts Ppt on new product design Ppt on effective communication skills Ppt on bookkeeping and accounting Ppt on automobile related topics