CS 253: Algorithms. Syllabus. Chapter 1. Appendix A

Transcription

1 CS 5: Algorithms Syllabus Chapter Appedi A

2 Syllabus Istructor : Firet Ercal - Office: CS 4 Phoe: & URL : ercal@mst.edu Meetig Times : :50 pm. M W F Office Hours : Posted o the class website **If there is o prior otice ad the istructor is late for the class, studets are epected to wait ~8 miutes before they leave the classroom. Grader : see the CS-5 homepage for the ame ad the iformatio Tetboo : Itroductio to Algorithms, Third Editio, Corme et al. Prerequisites: CS 8 ad CS 5 Objectives : Desig algorithms, aalyze algorithms for computatioal efficiecy, space, ad correctess. Develop strategies for dyamic programmig ad greedy algorithms, desig ad study fudametal data structures ad algorithms icludig (but ot limited to) heaps, sortig, searchig, graph algorithms, hashig, ad data compressio.

3 Class Policies Class otes (i PPT), syllabus, homewor assigmets, aoucemets, ad other related materials ca be accessed o the class website. Mae sure that you regularly chec these sites for aoucemets ad course related materials. Studets are epected to atted all classes uless they have a reasoable ecuse for beig abset. Whe i class, you are epected to tur o all pagers, phoes, ad beepers. Academic Alert System ( ). Projects ad homewor must be a idividual effort uless stated otherwise. Assigmets which are uusually similar will receive a zero (0) grade. Ay studet iquirig about academic accommodatios because of a disability will be referred to Disability Support Services ( ) so that appropriate ad reasoable accommodative services ca be determied ad recommeded. No late homewor or project will be accepted.

4 The Role of Algorithms i Computig Algorithm a sequece of computatioal steps that trasform the iput (a set of values) ito the output. a tool for solvig a well-defied computatioal problem Eample: Sortig Problem Iput: A sequece of umbers a, a,..., a Output: A permutatio (reorderig) a, a,..., a of the iput sequece such that a a a A algorithm is said to be correct if, for every iput istace, it halts with the correct output

5 What id of Problems are Solved by Algorithms? Huma Geome Project billio ucleotides. 00K gees are idetified usig various algorithms icludig approimate strig matchig, searchig, sortig, aligmet, hashig, clusterig, etc. etc. Eablig Iteret search egies etwor routig algorithms cryptography / etwor security Optimal Use of Resources i Busiess ad Life Eamples: optimal placemet of oil wells to maimize output, flight schedulig, truc routig, bi pacig, ad placemet for political campaigs, chip placemet for miimal routig, etc. etc. Liear Programmig Developig Strategies to Solve Puzzles, Play Mid Games etc. computer chess, othello, chiese checers AI Algorithms

6 Which oe is more importat: advaces i hardware speed or improvemet i algorithmic compleity? Computer A: 0 istructios / sec. Computer B: 0 8 istructios / sec. A is 000 times faster tha B Isertio Sort: # of istructios to be eecuted i order to sort items = Merge Sort: # of istructios to be eecuted i order to sort items = 50 log 0 = millio = 0 items If A uses Isertio sort ad B uses merge sort, which oe rus faster? Time A = [*(0 ) / 0 ] = 0 secods Time B = [50*(0 ) * log 0 (0 ) / 0 8 ] = secods!

7 **here Appedi A Summatios ) ( ) )( ( 4 ) ( 0 lim If 0 0

8 Appedi A (cot.) Harmoic Series H l O() 0 0 for Tae the derivative of You get the followig series ( ) for (show earlier) both sides ad also multiply with summatio :

9 Proof by Iductio Claim: S() is true for all m Proof: Basis: Show formula is true for = m Iductive hypothesis: Assume formula is true for a arbitrary Step: Show that formula is the true for +

10 Iductio Eample : Prove that ( ) for Basis: If =, the =? (+) / Yes, TRUE Iductive hypothesis: Assume formula is true for = (+) / Step (Show that formula is the true for +): ( ) ( )(( )? ( ) ( ) ( ) ( )( ) ( ) )

11 Iductio Eample : Prove that ( )( ) Basis: If =, the =? (+)(*+) / Yes, TRUE Iductive hypothesis: Assume formula is true for Step (Show that formula is the true for +): ( ) ( )( )[*( )? ( )( ) ( )( ) ( ) ( ) ( )( ) ( ) ( )[ ( ) ( )] ( )[ ( ) ( )] ( )( 7 ) ( )( )( ) ( )( ) ]