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by: Haylie Satterfield

ElementsoftheTheoryofComputation CISC401

Haylie Satterfield
GPA 3.84


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This 3 page Class Notes was uploaded by Haylie Satterfield on Saturday September 19, 2015. The Class Notes belongs to CISC401 at University of Delaware taught by Staff in Fall. Since its upload, it has received 22 views. For similar materials see /class/207182/cisc401-university-of-delaware in Computer Information Technology at University of Delaware.

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Date Created: 09/19/15
CISC 320 Introduction to Algorithms F211 2005 Course Overview mean m w i I Administrative a Course syllabus a Course webpage http www ls deledulliaocis320f05 in Of ce hours Tuesdays and Thursdays 1000AM 1130AM ll TA Mani Thomas maniUdelEdu I Tuesdays 330PM530PM 115B Pearson Hall in Your name and email in A random ID will be assigned to you for the purpose of posting grades summzud in A letter from industry Subject lndus1ly pEYSpEEWE ml CS gt D312 12 JulZDD313 48 25 VU7UU gt l n His a eenyeisatien 2 weeks ago Win a eelleague at lniel luupwas leaking tan a ten cs people las1 yeai He saiginai gt almus1 eyeiyeine ne lMENlEWEd was cumplelely useless iney knuw gt neitning abuul algentnms analysis eiany king elmainemaiieal gt ieaseining gt gt gt its like iney gei lei cullegelulA yeais and awe nut kneWing ene gtthlrlg gt gt Has ClS synenegtieim owe Java Thalwuuld be a mistake ilanyeit gtlh2mwanllu weiktei lniel a l ininkine assumpllun neie is ityeiui gt pnmaiy language lsJavath2n yeu ie Weitnless BTW mus1 areui gtweiik is a miket CH and Cwlthth2 eeeasienal Fell scllpt neie and gtineie gt gtllteyin mean m w i What is an algorithm a Stepby step computer executable solution to a prob em a Yes noncomputable problems do exist E g Turlrlg s Haltlrlg Problem Computability is a sublect or study orClsc Am a Computable problems are man The Human Genome Prolect sequence assemoly gene ldel ltlflcatlol l The lntemet information Search 47m In it ErCornrnerce data seounty R SA Puoliokey cryptography El RSA Wurl the Turing Award in ZEIEIZ R is Rivest urlE Elf the authurs Elf uurtextbuuk Alrlll le Scheduling summzud in Logistics by problem types adopted El Part 1 Sorting algorithms and Selection algorithms a Part 2 some advanced Data Structures Hash tables RedBlack Trees and Disjoint Sets in Part 3 Graph algorithms in Part 4 NPcompleteness Approximation algorithms Parallel algorithms mean m w i Workload El Five homework assignments 8 each Four paperandpencilquot and one programming a Two exams 30 each One is on Oct 18 and he other is given during the nal Mainly facts problems eg describing an algorithm learned in the c ass summzud in Bottom line i Contents I Algorithms D Able to recite the rhaih ideas Convince OtherS and yourself it works Complexity Other characteristics e g Othihe v 5 Offrlihe u Able to write pseudo code torit in Methods I Several design techniques I Proof techniques induction decision trees I Ways of abstract thinking mam m mi i I Designing Algorithms I Designing paradigms in Brute Force a Divide and Conquer u Greedy a Dynamic Programming a Randomized a Parallel cummfnzud in Analyzing Algorithms in Correctness I Can be proved recursion and induction I Approximation u Complexity ef ciency I Time and Space I Worstcase Averagecase and Best case I Asymptotical Optimality u Simplicity and Clarity mam m mi i a How to solve it Polya s book I What is the problem I Can we solve it anyway Brute force a Is our solu ion correct a All inputs Special inputs boundaries andoriirnits I Can we solve it more ef ciently u Have we used all info available I Need speci c data structure to store the ihput andor ihte diaries a Can we divide and conquer be greedy do dynamic programming etc a Can we improve averagecase if not worstcase performance Amortizing Do we need to randomize to enforce a favorable averagecase performance cummfnzud in Optimality 1 Ah algorithm is Optirnai it its tirne Complexity the Complexity of roblem Complexity of problems necessary and suf cient work to solve the problem i Lowerbouhd tneieast work orstepsneeded but no guarantee to solve the problem i Upperbourid the sutioientwork or stepsneeded from known aigontnrns that solve the problem a Complexity ofthe problem is giveri bythe iowerand upper her a e 90 E 3 2 an a lta o 43 quotlt0 as Um m o is unknown wnen there is a gap between tne tigntest known iowerand upperoounds E g multiplicatiuri thWEI nrbyrri matrices Tightestluvverbuurid is o n2 and tightest upper buund is 0n2m mam m mi i ii I Example 1 nding the largest entry in an an39a n We do riot know the complexity because the problem is riot Welly ed defiried E g it the array is already sort I Example 2 matrix multiplication 39 ii Z k mri ik ki HALMUJ Brute force na Strassen s algorithm Complexity of matrix multiplication is not yet cummfnzud in Example 3 Sequential searcn or an unordered array E in seqsearch 1n E in n in k i in ans index for 1 o1 lt n1 1mg ml ans break i return ans be of comparisons execution of line 4 Worstcase n Bestcase 1 Averagecase Example 4 Searching an ordered array ll Algl Early stop gt improve the averagecase no impact on the worstcase ll Alg2 Search every entry gt nJ j comparisons ll Alg3 Optimizing onj gt TWEn 2yn comparisons in Alg4 binary search gt TWEn lg n This is an optimal algorithm Why The binary search is not an on line algori hm minim m on i x cumm zuu in i Complexity of searching an ordered array of integers via comparisons is lgn1 where n is the array size o Proof DEElSlEIrl tree a binary tree isto VlSuailZE operation flow or an lgorit Let p max 3 or eompansons r or nodes on tne Lungestpatn or the decision tree LetN maxufnudesln dEElSlDH tree N 5 1 2 4 2quotquot 2quot 1 given tne neignt a balanced pinarytree can nolo more nodes tnan unbalanced p 2 lg N 1 N a n where n is the array size because every enlryin array must appear at least once on the decision tree Ior the algorithm to work correctly o Note tnis does not say every none will actually be Visited during a run or tne algontnm inoexol 23456789 E1213345516D67727E7985 minim m w i u tsunfhzud in it l Spectru m of computational complexity Hllben s Tenth Prublem Undemame Tunng s Halnng Problem Supenapunemal exponential intraetaple NPrcumplEtE proplems traetaple polynomial n1 H Matrix multiplication n log n Sorting by comparisons n subhnear minim m w i ii


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