today Syllabus questions you Some little about me for all overview ...

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1 Bo lgs Into

2 A Some tody Syllbus overview little bout me questions you ll for

3 Whotisnlgorithnp Frst, question Wht CS bckground do you ll hve? Lnguges Clsses " Intro dte structures discrete mth

4 ' Algorthm ( Ch 1 of text ) Something In between n English prose description nd Why? Gol n implementtion Cvet

5 Atgornthmfdefn ) A to sequence of instructions order perform in to solve well specified problem Given Wellstone ) specified & inputs n outputs, unmbiguous from inputs to ccept ble outputs mpping All bit consider hzy, some so let's exmples

6 Pseudo code write Formlly CS, people pseudo code to specify lgorithms Vrible ssignment 12 Arilhnetc t,,*, 1 Conditionl If A B elsec # MAX (,b ) if < b return else return b ftso procedures Arry ccess ( or Afi ] )

7 troops b '0 qcoipffep et Sun INTEGERS ( ) n 0 sum for i 1 to n sum sum + i return sum 2 [ Whitesel #we3 et ADD UNTIL (b) i 1 totl i while ( totl E b) I i+1 totl totl + i return i

8 Corrednesstrte Our 2 core Concerns in this clss 1 Correctness How do you lgorithm il inputs? know works the on 2 Effency When is one lgorithm better thn nother?

9 An exmple ( Sec in book ) How do mke you chnge? ( s few coins s using possible) Algorithm

10 Is this correct? Consider the US system 450 yers go Coins 25 e 20 / O 5 1 Will our lgorithm work?

11 A more the interesting exmple stble mrrige problem Q How do doctors mtched to get internships?

12 " if Dff doctor We sy mtching doctor hospitl is unstble doctor is ssigned to A hospitl b is ssigned to hospitl B nd prefers B B prefers In other words both, doctor hospitl B would be with ech hppier other thn will current ssignments Resident mtching problem Given residents ( w/ preferences) / preferences ), compute tht mtching is stble

13 Solution or Gle " Boston pool " lgorithm Shpley lgorithm Repet in rounds rbitrry hospitl position 1 An unssigned H offers to the best doctord( who hs not sid no ) yet 2 Ech doctor the best offer ccepts ultimtely d they get So if she doesn't hve better offer in hnd, dtnttuey ccepts H If d hs n offer but prefers H, rejects prior offer Otherwise, rejects It

14 ( Exmple BE Qzuo BE ' ng Shephrd Tm Hospitls Arkhm Asylum Between Royl Hospitl County Generl Hospitl Dhrm Inithve Result As ) Stble?, ( B,t ), ( Gg ), ( Rr )

15 Correctness? Well the lgorithm continues s is leomngpfg ny hospitl So when it termintes, every position is filled Suppose is ssigned to A, but prefers B we know got no better offer so

16 Efficiency ( 27 28in book ) Exct speed cn depend on mny lgorithm vribles besides the Issues t ply Alterntive Count re pproch Prime opertors, which smllest opertions In ddition generlly only worst running Why? time exmine

17 Also ctully compre? How to Nee Remember lgorithm be due to smll difference my processor lnguge,, or number of ny things tht on in't dependent the need eg for inputs serching to wy chnging list ccount

18 BgOnoth= We sy th > no, fcn ) An ) is Ocgcn ) ) if F C > O such tht Ecogcn )

19 Commonruntmes 1 OCD 2 oclogn ) 3 Och ) 4 OC nlogn ) O(n2 SO ) Cpiblynomil ) And 0( 2 " ) Oln! )

20 Next time Connecting run times lgorithms Also Sty tuned for HW 1!