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[Powered by Google Translate] [Seminar: Technical conloquia]

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[Kenny Yu, Harvard University]

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[Hoc est CS50.] [CS50.TV]

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Hi omnes, Im 'Kenny. EGO sum currently a junior studendo computer quod scientia.

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Im 'prioris CS TF, et volo habui hoc quando fui underclassman,

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et ut 'quare Im isto faciendo seminar.

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Sic spero te frui eam.

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Hoc seminar est circa technical congressi,

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et haec omnia possunt opes amet,

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Haec pagina praesens est, duobus mauris.

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Ita recensuit amet profecto plerique elit.

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Etiam generale resources page ubi possimus invenire tips

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quam parare adito

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Qua in re magna agis colloquium,

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necnon quomodo accedere ad problemata et opibus pro futuro referantur.

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Tota online.

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Et justus, ut praefiges hoc seminar, a Disclaimer,

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sicut hic non moreretur - vos conloquium praeparatio

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non limitatur ad hoc album.

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Non nisi duce destinatum,

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dico vobis et pro certo grano salis decessit,

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sed omnia uti in colloquium uti praeparatione rutrum.

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>> Ego rem intra paucos velocitate labitur

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possumus ita rem ipsam meditari.

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Structuram adito pro software engineering postion,

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typice est XXX ad XLV minutes,

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multiple rounds, fretus company.

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Saepe youll 'exsisto coding in album tabulis.

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Sic alba tabula, sicut hic, sed saepe inter minora lanx.

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Si vestri 'habens phone conloquium, youll probabiliter usura

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aut collabedit vel Google Doc ut videant vixeritis coding

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tu dum capias ens interviewed super phone.

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, Conlocutum se est typice II aut III problems

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tentantes vestri computer scientia scientiam.

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Et erit fere definite involvunt coding.

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Rationes questions ut youll 'animadverto solent notitia structuris et algorithms.

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Facientes has quaestiones

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et interrogavero, ut, tempus et quod multipliciter Deus magnus?

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Saepe quoque interrogo, superiori-level quaestiones,

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sic, cogitans est systema,

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quomodo esset ista reponitis, sicco vestri codice?

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Quid interfaces quaenam genera, quae in moduli rationem habetis,

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et quomodo istae penitus pariter?

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Sic notitia structuris et algorithms necnon cogitans ratio.

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>> Aliqua generali tips antequam nos intendere in nostrae causae studiis.

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Ut semper aliquis cogitet de summis reor magna.

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Occasione sermonis putant esse sententiam ostendendas aliqua.

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Interviewer sermonis est usque ad coniecturam

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quam tu putas, per quam res.

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Taceat licet, maximum totius rei colloqui.

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Quod suus 'iustus non bonum.

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Cum data sit, intelligas volo facio certus vos est.

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Ut tua verba rursus interrogo rursus

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et nitatur operari instructius pauci simplex test casibus

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Certe ut intelligas pertinere.

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Operante per paucos test casibus et dabo tibi intuitionem, in quam ut solve is forsit.

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Vos vires etiam reperire paucis exemplaria ad auxilium vobis problema solvunt.

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Eorum magnus tip est ad non adepto frustrari.

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Non adepto frustrari.

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Quae conloquia amet, pessimus potestis facere

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praeter tacere, frustra visibilis est.

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Non vis dare illam impressionem ad Interviewer.

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Quod aliud - ita multi, ut in conloquium venire,

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prima solutio maxime conantur invenire,

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quando realiter, illic 'usitas a LUCULENTE patet solutio.

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Ne segnis, inutilis esset, sed eas tantum statum,

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unde tantum tibi melius procedit.

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Et tardum est solutio ostendit, secundum

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magnus O tempus complexitate aut spatium complexionem,

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demonstrabimus ad Interviewer, intelligere te

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his rebus cum scribimus code.

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Ne timeas a simplicissimis algorithm primum venire

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et ibi melius.

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Ullus questions tam longe? Okay.

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>> Sic lets 'intendere in nostram primum problema.

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"Datæ intellegeretur compluras n integri, scribere functio, ut shuffles, in aciem

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in locum ita ut omnes permutaciones n integri sunt aequaliter probabile. "

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Et assumere habetis available temere integer generans

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i 0 rhoncus a generante per integrum medium patens.

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Quilibet intelligat hoc question?

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N numeros integros impositam nubem tibi, et quam volo miscere.

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Aliquam meo scripsi paucis id demonstrare elit.

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Ego rem XX impositam nubem miscere principia

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a -10 ad IX,

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et haec nomina output volo.

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Sic hoc est meum sorted input acie, que volo vos shuffle eam.

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Puteus 'operor is iterum.

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Vtrum Intelligant omnes question? Okay.

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Ita est ad vos.

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Quid sunt quidam idearum? Ut facias ^ n II n index n, n?

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Aperi proponendi.

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Okay. Itaque una idea, innutum per Emmy,

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est primum computant temere numero, temere integer, in range ab 0 ad XX.

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Sic assumere nostri array habet longitudinem XX.

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In nostra diagramma XX elementa,

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nostra haec est input ordinata.

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Et nunc, eam suggestione est creare novum apparatu,

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sic haec erit output ordinata.

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Et ex i reversi sunt per Rand -

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Si ita est, quod dicitur XVII,

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effingo 17 elementi in prima positione.

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Nunc debemus ut delete - nos postulo ut amoveo omnia elementa hic

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ut in fine habent nec foramina in medio foramen.

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Nunc iterum elit.

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Nunc nos pick novum temere integer inter 0 et XIX.

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Hic habemus novum, et imitari in hoc loco aliqua.

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Deinde nos, amoveo items transilit, et iteramus processus donec habemus nostram plenariam novum ordinata.

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Quid est run tempus huius algorithm?

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Bene, lets considerare labefactum of hoc.

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Nos moventes omnis elementum.

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Hunc ego cum nos ea omnia quae in sinistrum verso.

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Quod est o (n) sumptus

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quia remoto primo elementum?

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Sic de singulis remotio, amoveamus -

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singulis remotionem incurrit O (n) operationem,

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et quia sumus ustus in remotiones, hoc perducit ad O (n ^ II) shuffle.

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Okay. Ita bonum exordium. Bonum exordium.

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>> Alius consilium est uti aliquo notus ut Knuth shuffle,

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aut Fisher-Yates shuffle.

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Quod suus 'vere a linearibus tempus shuffle.

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Et similis est ratio.

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Iterum, nos have nostrum input apparatu,

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sed pro usura duo vestit pro nostra input / output,

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utimur prima pars, in aciem ut servo semita nostri lentis portionem,

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et ne vestigia nostri habitus ad reliquas denique partes unshuffled.

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Et dico hic. Nos satus off - nos deligendus, i,

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XX exercitu ab 0.

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Nostri nunc monstratorem indicat ad primum index.

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Eligimus quidam i hic

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nunc nos PERMUTO.

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IV et V si hoc ita esset,

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consecuturo array habebit V hic et IV hic.

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Et nunc nos note titulum hic.

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Omnia ad sinistra lentis,

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et omne ius unshuffled.

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Possumus dicere et aliqua.

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Eligimus temere index inter I et XX nunc.

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Sic nostri opinor novum i est hic.

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Nunc nos PERMUTO hoc i cum nostris current novum situm hic.

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Illuc unde permutando ut sic.

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Fac me certiorem facere iuris adducunt.

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Nos satus cum in arbitrio nostro i -

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nos satus i exaequabo 0, pick temere location j

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in unshuffled portio apparatu, i ad n-I.

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Hic si me potius temere huc index inter cetera acie

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et nos PERMUTO.

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Hoc est tota codice necessarium ut shuffle vestra ordinata.

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Ullus questions?

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>> Bene, unum opus est quaestio, cur hoc recte?

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Cur est omnis alternando aeque?

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Et non per evidentiam,

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sed multa problems in computatrum scientia potest probatur per inductionem.

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Inductione notissimum quot mihi?

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Okay. Frigus.

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Sic vos can probare rectitudinem hoc algorithm per simplicem inductione,

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ubi vestra inductione hypothesis esset, supponas

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mea shuffle redit omnis alternando aeque

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ad primum elementum.

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Nunc, considerate i + I.

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Et in via eligimus noster index j ad PERMUTO,

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hinc - tum singulis elaborare,

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saltem plena probatio, quare hoc algorithm redit

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omnis alternando pariter verisimile probabilitatis.

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>> Omni jure, postero forsit.

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Sic "datum, intellegeretur compluras integri, jus positivum, nulla, negative,

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scribere functio, ut computantem maximum summam

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de ullo continueous subarray de input ordinata. "

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Exemplum est, in qua omnes numeri integri affirmativi,

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tunc currently optimus choice est integrum accipiet ordinata.

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I, II, III, IV, X aequalis.

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Cum habeas aliqua negativis in ibi,

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prima duo in hoc vis

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quia eligens -1 et / vel -3 adducam summae down.

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Nunc media acie inire poterat.

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Nihil volo sumo aliquando, quod non sit aliquid optimum.

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Melius quandoque est peccatum

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Magna res, quia supervacuum est. Sic ullus idearum?

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(Studiosum, potest) >> Yeah.

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Puta me non auferent -1.

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Tunc aut eligo 1,000 et 20000,

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aut ego iustus sumo III billion.

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Atque ut omnibus numeris primis eligit.

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Hoc -1, vocacione negative,

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summa ne ego melior -1.

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Una res est, ut supra dixi, evidenter apparet apice

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et brutis vis solutio primi.

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Quod huius quaestionis solutio vires? Yeah?

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[Jane] Perabunde, puto bruta vis solutio

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omnia accumsan sit addere potest (potest).

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[Yu] okay. Sic Jane scriptor idea est ut tollat ​​omne possibile -

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Im 'paraphrasi - est accipere omne possibile continuum subarray,

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supputant suam totalitatem, et tolle omnium maximum, possibilis continua subarrays.

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Quid unice identifies a subarray in mea input ordinata?

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Qualisque duo mihi opus? Yeah?

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(Studiosum, potest) >> RECTO.

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Inferior ligari ex indicem et superiorem ligatus index

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unice determinat continua subarray.

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[Female studiosum] sumus pensitandisque suus 'intellegeretur compluras unique numeros?

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[Yu] No ergo quaestioni suae est, sumus assumentis nostri array -

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noster est array omnes unique numeros, et responsum non est.

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>> Si utimur bruta vis solutio, tunc satus / finis indices

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unice determinat nostri continui subarray.

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Si igitur RESUMO pro omnibus possibilis satus viscus,

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et pro omnibus finis entries> aut = ut satus, et <n,

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vos supputant summam, et tunc accipiamus maximum summam weve videri quatenus.

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Est hoc patet?

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Quid est magnus O huius solutionis?

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Timewise.

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Non satis n ^ II.

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Nota ut nos RESUMO ab 0 ad n,

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ita ut suus 'unus pro loop.

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Nos RESUMO iterum prope ab initio usque ad finem, aliud ad loop.

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Iamque intra nos habemus omnia denique nomen,

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sic ut 'alium pro loop. Sic habemus tres habitant pro ansas, n ^ III.

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Okay. It is a quo.

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Nostra quidem solutione, non est gravius ​​quam n ^ III.

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Vtrum Intelligant omnes bruta vis solutio?

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>> Okay. A aptiorem solutionem est usura idea vocatur dynamic programming.

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Si accipias CS124, quae est Algorithms et Data structuras,

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Hac arte familiariter fies.

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Et ideam est, tentant, ut ædificarent solutiones ad minora problems primum.

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Hoc tantum dico, cura Duis aute duo principium et finis.

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Quod ut 'molestus. Urna si quid ex iis carere possit?

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Una idea est ad - we're data prima nostra forsit,

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invenire maximum summa quarumcunque subarray in range [O, n-I].

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Ac iam nova subproblem ubi novimus, in Romanorum Nunc ego

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Scimus dicendum est. Nostri subarray ut finem ad current index.

228
00:15:52,520 --> 00:15:57,640
Restat igitur forsit est, ubi nos satus nostrum subarray?

229
00:15:57,640 --> 00:16:05,160
An idcirco sensus? Okay.

230
00:16:05,160 --> 00:16:12,030
Sic Ive 'coded hoc, ascendit, et lets intueri, quid medii.

231
00:16:12,030 --> 00:16:16,230
In codirectory, illic 'a progressio vocavit subarray,

232
00:16:16,230 --> 00:16:19,470
et est numerus paginarum,

233
00:16:19,470 --> 00:16:25,550
ac revertitur maximum subarray summam in mea lentis list.

234
00:16:25,550 --> 00:16:29,920
Ac per hoc nostrum est maxima subarray III.

235
00:16:29,920 --> 00:16:34,850
Et quod suus 'accipitur per iustus usura II et I.

236
00:16:34,850 --> 00:16:38,050
Lets run is iterum. Suus 'quoque III.

237
00:16:38,050 --> 00:16:40,950
Sed nunc adverte quam obtinuit III.

238
00:16:40,950 --> 00:16:46,690
Suscepcionem - nos iustus accipe III ipsa

239
00:16:46,690 --> 00:16:49,980
quoniam suus negativis utrimque cingit,

240
00:16:49,980 --> 00:16:55,080
quae adducam summam <III.

241
00:16:55,080 --> 00:16:57,820
Lets 'run in X items.

242
00:16:57,820 --> 00:17:03,200
Hoc tempus suus 'VII, accipiamus, primoribus III et IV.

243
00:17:03,200 --> 00:17:09,450
VIII tempus illud ac susceptis accepimus I, III et IV.

244
00:17:09,450 --> 00:17:16,310
Sic dare vobis intuitionem, in quam possumus hanc solvere transformamur forsit,

245
00:17:16,310 --> 00:17:18,890
lets 'take a inviso hoc subarray.

246
00:17:18,890 --> 00:17:23,460
Lorem input hac acie VIII dicitur quod scimus.

247
00:17:23,460 --> 00:17:26,359
Accipimus I, IV et III.

248
00:17:26,359 --> 00:17:29,090
Sed lets 'inviso quam nos sumus, esse got responsionem istam.

249
00:17:29,090 --> 00:17:34,160
Intueamur subarray ut maxima quaeque finem Indicis.

250
00:17:34,160 --> 00:17:40,780
Quis 'maximalia subarray quod habet finire primo sedem?

251
00:17:40,780 --> 00:17:46,310
[Discipulus] zero. >> Zero. Iustus non capiant -5.

252
00:17:46,310 --> 00:17:50,210
Hic quoque suus futurus 0. Yeah?

253
00:17:50,210 --> 00:17:56,470
(Studiosum, potest)

254
00:17:56,470 --> 00:17:58,960
[Yu] Oh, rumex, est -3.

255
00:17:58,960 --> 00:18:03,220
II ita est, sit -3.

256
00:18:03,220 --> 00:18:08,690
Okay. Sic -4 comprehenduntur, quis 'maximalia subarray ad finem illa positio

257
00:18:08,690 --> 00:18:12,910
ubi -4 est ad? Zero.

258
00:18:12,910 --> 00:18:22,570
Unum? I, V, VIII.

259
00:18:22,570 --> 00:18:28,060
Sed ut finem ad locum in -2.

260
00:18:28,060 --> 00:18:39,330
Ita VI, V, VII, hoc est IV.

261
00:18:39,330 --> 00:18:43,480
Scientes quod, mea sunt haec entries

262
00:18:43,480 --> 00:18:48,130
pro transformatae forsit ubi uos oportet me finire in singulis Indicis illius,

263
00:18:48,130 --> 00:18:51,410
tunc meus, finalis responsum iustum est, accipe verrunt traiciuntur,

264
00:18:51,410 --> 00:18:53,580
et accipe maximum numerum.

265
00:18:53,580 --> 00:18:55,620
Ac per hoc illud VIII.

266
00:18:55,620 --> 00:19:00,010
Hoc implicat quod maximalia subarray desinit ad hoc indice pro cujusque,

267
00:19:00,010 --> 00:19:04,970
quod coepi alicubi ante eam.

268
00:19:04,970 --> 00:19:09,630
Quilibet intelligat hoc transformamur subarray?

269
00:19:09,630 --> 00:19:22,160
>> Okay. Esto enim est figura ex eternum.

270
00:19:22,160 --> 00:19:27,990
Lets considerare iustus primoris pauci introitibus.

271
00:19:27,990 --> 00:19:35,930
Et hic est 0, 0, 0, I, V, VIII.

272
00:19:35,930 --> 00:19:39,790
-2 Et erat ibi usque ad VI duxit.

273
00:19:39,790 --> 00:19:50,800
Ita si ego voco introitu in situ i subproblem (i),

274
00:19:50,800 --> 00:19:54,910
quomodo potest usus sum responsio ad priore subproblem

275
00:19:54,910 --> 00:19:59,360
responderet ad hoc subproblem?

276
00:19:59,360 --> 00:20:04,550
Vide si sit de ista vestibulum.

277
00:20:04,550 --> 00:20:09,190
Quomodo possum supputant responsum VI aspiciendo

278
00:20:09,190 --> 00:20:18,780
a iunctura huius acie atque responsio ad previous subproblems in hoc ordinata? Etiam?

279
00:20:18,780 --> 00:20:22,800
[Female studiosum] es tollis milítia summarum

280
00:20:22,800 --> 00:20:25,430
Ante loco, sic VIII,

281
00:20:25,430 --> 00:20:32,170
et tunc addas current subproblem.

282
00:20:32,170 --> 00:20:36,460
[Yu] Sic eam suggestione est spectare hi duo numeri,

283
00:20:36,460 --> 00:20:40,090
hoc numero et hoc numerus.

284
00:20:40,090 --> 00:20:50,130
Ita intelligitur hoc responso subproblem VIII (i - I).

285
00:20:50,130 --> 00:20:57,300
Quod lets voca me input array A.

286
00:20:57,300 --> 00:21:01,470
Ut habeatur locus desinit esse maxima subarray I

287
00:21:01,470 --> 00:21:03,980
Habeo duas choices: Ego potest aut perseveraverunt subarray

288
00:21:03,980 --> 00:21:09,790
Index priore finita, et incipit novam aciem.

289
00:21:09,790 --> 00:21:14,190
Si ego essem continuare subarray qui coepta est in priore Indecem

290
00:21:14,190 --> 00:21:19,260
erit maxima summa ego consequi potest responsio est ad priore subproblem

291
00:21:19,260 --> 00:21:24,120
plus current array ingressu.

292
00:21:24,120 --> 00:21:27,550
Sed, ego quoque electionem habeat profectionis novum subarray,

293
00:21:27,550 --> 00:21:30,830
0, quo casu summa.

294
00:21:30,830 --> 00:21:42,860
Ita respondendum est, max of 0, subproblem i - I, plus current array ingressu.

295
00:21:42,860 --> 00:21:46,150
An hoc recidivam facere sensus?

296
00:21:46,150 --> 00:21:50,840
Nostri recidivam, ut paulo inventa, est subproblem i

297
00:21:50,840 --> 00:21:54,740
aequalis est maximum of priore subproblem plus mea current array ingressu,

298
00:21:54,740 --> 00:22:01,490
quod interpretatur perseverant priore subarray,

299
00:22:01,490 --> 00:22:07,250
aut 0, satus a novus subarray procul meus current index.

300
00:22:07,250 --> 00:22:10,060
Mensam semel et elit hac aedificavit ergo dicendum ultimum,

301
00:22:10,060 --> 00:22:13,950
iustus facio linearibus verrunt trans subproblem array

302
00:22:13,950 --> 00:22:19,890
et accipe maximum numerum.

303
00:22:19,890 --> 00:22:23,330
Quid sit proprie dictum turpis.

304
00:22:23,330 --> 00:22:27,320
Ita et nos partum a novus subproblem apparatu, subproblems.

305
00:22:27,320 --> 00:22:32,330
Vestibulum vestibulum est vel prima vel 0 primum, maximum illarum.

306
00:22:32,330 --> 00:22:35,670
Et reliqua subproblems

307
00:22:35,670 --> 00:22:39,810
utimur exigere recidivam nos iustus repertis.

308
00:22:39,810 --> 00:22:49,960
Nunc nos supputant maximum of nostri subproblems acie, que ut 'etiam finalis responsum.

309
00:22:49,960 --> 00:22:54,130
>> Sic quam tantumque spatii sumus usura in hoc algorithm?

310
00:22:54,130 --> 00:23:01,470
Lorem CS50 solum si tunc de spatio plurimum posse.

311
00:23:01,470 --> 00:23:07,750
Bene, una res animadvertendum est quod vocavi malloc hic cum mole n.

312
00:23:07,750 --> 00:23:13,590
Quid autem suggeret vobis?

313
00:23:13,590 --> 00:23:17,450
Hoc algorithm utitur linearibus spatio.

314
00:23:17,450 --> 00:23:21,030
Possumus melius?

315
00:23:21,030 --> 00:23:30,780
Oportet animadvertere quod est ultimum dicendum videris?

316
00:23:30,780 --> 00:23:33,290
Suspicor re melius quam ipsum

317
00:23:33,290 --> 00:23:40,680
nonne usque ad finem portent?

318
00:23:40,680 --> 00:23:44,280
Sed si consideremus quarum

319
00:23:44,280 --> 00:23:47,720
utimur tantum curat de priore subproblem,

320
00:23:47,720 --> 00:23:50,910
et nos tantum curat de maximum weve vidit umquam quatenus.

321
00:23:50,910 --> 00:23:53,610
Animadvertere ultimum respondetur, non omne opus ornatus.

322
00:23:53,610 --> 00:23:57,450
Ultimum opus tantum numerum horum numerorum.

323
00:23:57,450 --> 00:24:02,630
Last numerum subproblem apparatu, et novissima numerus pro maximi.

324
00:24:02,630 --> 00:24:07,380
Sic, in facto, possumus DECOCO his ansas simul

325
00:24:07,380 --> 00:24:10,460
et recedam ab linearibus spatio ad constans spatio.

326
00:24:10,460 --> 00:24:15,830
Current summam tam longe, hic, reponit munus subproblem noster subproblem ordinata.

327
00:24:15,830 --> 00:24:20,020
Sic current summa, tam longe, responsio est ad priore subproblem.

328
00:24:20,020 --> 00:24:23,450
Quod denique attinet, maximum locum tenet.

329
00:24:23,450 --> 00:24:28,100
Nos supputant maximum sicut et nos pergam.

330
00:24:28,100 --> 00:24:30,890
Et sic venimus ire a linearibus spatio ad constans spatio,

331
00:24:30,890 --> 00:24:36,650
et etiam nos habere linearibus solutio ad nostrum subarray forsit.

332
00:24:36,650 --> 00:24:40,740
>> Vives in huiusmodi quaestionibus colloqui.

333
00:24:40,740 --> 00:24:44,450
Quid est tempus complexitate: quid est spatium complexitate?

334
00:24:44,450 --> 00:24:50,600
Potes melius? Ibi sunt quæ sunt supervacuis ut custodiant circumspicitis?

335
00:24:50,600 --> 00:24:55,270
Te quoque fecisse digeruntur in lumine tuo

336
00:24:55,270 --> 00:24:57,400
sicut vos erant 'opus per haec problems.

337
00:24:57,400 --> 00:25:01,710
Semper postulare teipsum, 'Num ego possum melius facere? "

338
00:25:01,710 --> 00:25:07,800
Nam melius possumus?

339
00:25:07,800 --> 00:25:10,730
Modi dolum quaestio est. Non potes quia opus

340
00:25:10,730 --> 00:25:13,590
saltem legere input ad forsit.

341
00:25:13,590 --> 00:25:15,570
Unde oportet quod saltem in dubium input legat

342
00:25:15,570 --> 00:25:19,580
quam non poteris quin aliquot diebus

343
00:25:19,580 --> 00:25:22,870
Non semper quam et purus.

344
00:25:22,870 --> 00:25:27,060
Sic enim optima solutio ad hoc.

345
00:25:27,060 --> 00:25:33,040
Quaestiones? Okay.

346
00:25:33,040 --> 00:25:35,190
>> Stock forum problema:

347
00:25:35,190 --> 00:25:38,350
"N numeros integros copia data positiva, nihil aut non,

348
00:25:38,350 --> 00:25:41,680
exhibentes pretium stirpe super n diebus,

349
00:25:41,680 --> 00:25:44,080
scribere functio supputare maximum lucrum vos can planto

350
00:25:44,080 --> 00:25:49,350
dato quod tibi emere et vendere exacte I stirpe intra haec n diebus. "

351
00:25:49,350 --> 00:25:51,690
Essentialiter, nos emere velle humiliabitur, vendere altitudinis.

352
00:25:51,690 --> 00:25:58,580
Ut instar sicco melius proficere volumus possumus.

353
00:25:58,580 --> 00:26:11,500
Regressæ meo tip, quid est statim patet, simplicissima responsum, tamen suus 'tardus?

354
00:26:11,500 --> 00:26:17,690
Etiam? (Studiosum, potest) >> Etiam.

355
00:26:17,690 --> 00:26:21,470
>> Sic et vos esset iustus vado quamvis et inviso stirpe prices

356
00:26:21,470 --> 00:26:30,550
in utroque puncto in tempore, (inintelligibile).

357
00:26:30,550 --> 00:26:33,990
[Yu] okay, ita eam solutio - eam suggerentibus computing

358
00:26:33,990 --> 00:26:37,380
infimo et computo summum non necessario operari

359
00:26:37,380 --> 00:26:42,470
quia supremum infimi contingat ante.

360
00:26:42,470 --> 00:26:47,340
Quid est solutio problematis vires?

361
00:26:47,340 --> 00:26:53,150
Quid sunt duæ quæ ego postulo ut unice determinare lucrum ponam? Rectus.

362
00:26:53,150 --> 00:26:59,410
Vires autem solutio - oh Georgius tantum opus est biduo suggerente

363
00:26:59,410 --> 00:27:02,880
ad unice determinare in utilitatem eorum duobus diebus.

364
00:27:02,880 --> 00:27:06,660
Ita et nos supputant quodlibet par, similis buy / vendere,

365
00:27:06,660 --> 00:27:12,850
fructus spatia, quorum sive positivi sive negativi nulla.

366
00:27:12,850 --> 00:27:18,000
Supputant maximum lucrum, ut demus post iterando super omnia paria diebus.

367
00:27:18,000 --> 00:27:20,330
Ultimum dicendum erit.

368
00:27:20,330 --> 00:27:25,730
Quae solutio erit O (n ^ II), quia non est n eligere paria duo -

369
00:27:25,730 --> 00:27:30,270
dies ut vos can sumo inter finis diebus.

370
00:27:30,270 --> 00:27:32,580
Bene, ita vires transire Non sum via est.

371
00:27:32,580 --> 00:27:37,420
Im 'iens ut nuntiarem tibi ut illic' an n log n solutio.

372
00:27:37,420 --> 00:27:45,550
Quid algorithm operor vos currently scient quia est n log n?

373
00:27:45,550 --> 00:27:50,730
Sed dolus non est.

374
00:27:50,730 --> 00:27:54,790
>> Merge huiusmodi. Merge generis est n log n,

375
00:27:54,790 --> 00:27:57,760
et quidem, ut est ratio huius quaestionis solutionem

376
00:27:57,760 --> 00:28:04,400
a merge modi qualem ideam vocatur, in genere, dividite et vincere.

377
00:28:04,400 --> 00:28:07,570
Et ratio talis est.

378
00:28:07,570 --> 00:28:12,400
Vos volo ut supputant optimus buy / vendere par in sinistro dimidium.

379
00:28:12,400 --> 00:28:16,480
Optime possis utilitatis, sicut in primis duobus n.

380
00:28:16,480 --> 00:28:19,780
Tunc vos volo ut oompute optimum buy / vendere par in dextro dimidium,

381
00:28:19,780 --> 00:28:23,930
ita ultimus n super duobus diebus.

382
00:28:23,930 --> 00:28:32,400
Et nunc est quaestio, quomodo nos merge his solutiones revertebantur simul?

383
00:28:32,400 --> 00:28:36,320
Etiam? (Studiosum, potest)

384
00:28:36,320 --> 00:28:49,890
>> Okay. Itaque tabulam trahere.

385
00:28:49,890 --> 00:29:03,870
Etiam? (George, potest)

386
00:29:03,870 --> 00:29:06,450
>> Etiam. George solutio est exigo rectus.

387
00:29:06,450 --> 00:29:10,040
Sic eius suggestio est, primo supputant optimus buy / vendentes coniugatione,

388
00:29:10,040 --> 00:29:16,050
et in sinistra parte fiunt, ita sinistra vocatione reliquerunt.

389
00:29:16,050 --> 00:29:20,790
Optimus buy / vendere par qui contingit in ius dimidium.

390
00:29:20,790 --> 00:29:25,180
Si comparari hi duo numeri tantum, ut si desunt

391
00:29:25,180 --> 00:29:30,460
ubi ememus hic et vendere alicubi in dextro dimidium.

392
00:29:30,460 --> 00:29:33,810
In sinistra parte ememus vendiderit partem rectam.

393
00:29:33,810 --> 00:29:38,490
Et optimus via ut supputant optimus buy / vendentes coniugatione palmis utrumque medietates

394
00:29:38,490 --> 00:29:43,480
est supputant minimum hic et supputant maximum hic

395
00:29:43,480 --> 00:29:45,580
et capessere pro differentia.

396
00:29:45,580 --> 00:29:50,850
Sic duo quibus enim buy / vendentes par occurrit solum hic,

397
00:29:50,850 --> 00:30:01,910
modo hic definitur partes tres vel plures simul.

398
00:30:01,910 --> 00:30:06,450
Ita noster algorithm ut merge nostri solutiones retro simul,

399
00:30:06,450 --> 00:30:08,350
nos volo ut supputant optimus buy / vendentes par

400
00:30:08,350 --> 00:30:13,120
ubi ememus a sinistris dimidiam et vendere in dextro dimidium.

401
00:30:13,120 --> 00:30:16,740
Et hoc est maxime ad primum turpis spatia duarum,

402
00:30:16,740 --> 00:30:20,360
dextra pars maxima pretium, et differentia.

403
00:30:20,360 --> 00:30:25,390
Inde fructus trium tres numero tu maxime e tribus,

404
00:30:25,390 --> 00:30:32,720
et quod suus 'optimus lucrum vos can planto super has primum et finis diebus.

405
00:30:32,720 --> 00:30:36,940
Hic magni momenti sunt lineae in rubrum.

406
00:30:36,940 --> 00:30:41,160
Hoc est recursive vocatio ad supputant responsum in sinistro dimidium.

407
00:30:41,160 --> 00:30:44,760
Hoc est recursive vocatio ad supputant responsum in dextro dimidium.

408
00:30:44,760 --> 00:30:50,720
Duo illa quibus ansas supputant min et max a sinistris et rectum dimidium, respective.

409
00:30:50,720 --> 00:30:54,970
Nunc ego supputant, utilitatem palmis utrumque medietates,

410
00:30:54,970 --> 00:31:00,530
et respondebit finis est maxime haec tria.

411
00:31:00,530 --> 00:31:04,120
Okay.

412
00:31:04,120 --> 00:31:06,420
>> Sic nimirum habemus algorithm sed maior quaestio,

413
00:31:06,420 --> 00:31:08,290
quid sit tempus multiplicitate hoc?

414
00:31:08,290 --> 00:31:16,190
Ideo dixi dividere tale responsum tale merge

415
00:31:16,190 --> 00:31:19,200
in duas et tunc bus nostris solutiones revertebantur simul

416
00:31:19,200 --> 00:31:23,580
est prorsus forma merge huiusmodi.

417
00:31:23,580 --> 00:31:33,360
Itaque tempus transierit.

418
00:31:33,360 --> 00:31:41,340
Si t opus esse (n) numerus graduum

419
00:31:41,340 --> 00:31:50,010
pro n diebus,

420
00:31:50,010 --> 00:31:54,350
nostra, duos recursive vocat

421
00:31:54,350 --> 00:32:00,460
utraque mihi constabit t (n / II)

422
00:32:00,460 --> 00:32:03,540
duo illic 'vocat.

423
00:32:03,540 --> 00:32:10,020
Nunc eget sinistram partem minime computato,

424
00:32:10,020 --> 00:32:17,050
quam possum facere in n / II tempus, plus maximum of ius dimidium.

425
00:32:17,050 --> 00:32:20,820
Sic hoc, iustus est n.

426
00:32:20,820 --> 00:32:25,050
Et tunc plus constante quadam opus.

427
00:32:25,050 --> 00:32:27,770
Et hoc recidivam aequatio

428
00:32:27,770 --> 00:32:35,560
est prorsus recidivam aequatio pro merge huiusmodi.

429
00:32:35,560 --> 00:32:39,170
Et nos omnes scimus ut merge generis est n log n tempus.

430
00:32:39,170 --> 00:32:46,880
Ideo nobis algorithm etiam ustus in log n tempus.

431
00:32:46,880 --> 00:32:52,220
An hoc iteratione facere sensus?

432
00:32:52,220 --> 00:32:55,780
Iustus a brevis recap huius:

433
00:32:55,780 --> 00:32:59,170
T (n) est numerus gradus ad supputant maximum lucrum

434
00:32:59,170 --> 00:33:02,750
n decursu dies.

435
00:33:02,750 --> 00:33:06,010
Via diducitur nostri recursive vocat

436
00:33:06,010 --> 00:33:11,980
est vocando solutionem nostram in primo n / II diebus,

437
00:33:11,980 --> 00:33:14,490
ita ut suus 'unus invocabis,

438
00:33:14,490 --> 00:33:16,940
et etiam secunda parte dicemus.

439
00:33:16,940 --> 00:33:20,440
Sic ut 'duo vocat.

440
00:33:20,440 --> 00:33:25,310
Et deinde sinistra parte minima, in quibus aliquot diebus

441
00:33:25,310 --> 00:33:29,010
invenire maximum of ius dimidiam, quae facere possumus in linearibus tempus.

442
00:33:29,010 --> 00:33:31,570
Sic n / II + n / II iustum est n.

443
00:33:31,570 --> 00:33:36,020
Constanti erit opus, hoc est arithmetica.

444
00:33:36,020 --> 00:33:39,860
Hoc recidivam aequatio est exigo recidivam aequatio pro merge huiusmodi.

445
00:33:39,860 --> 00:33:55,490
Unde, nostri shuffle algorithm est etiam n stipes n.

446
00:33:55,490 --> 00:33:58,520
Sic quam tantumque spatii sumus usura?

447
00:33:58,520 --> 00:34:04,910
Eamus ad Codicis.

448
00:34:04,910 --> 00:34:09,420
>> Melior est quaestio, quot ACERVUS tabulas operor nos unquam habere quolibet nunc?

449
00:34:09,420 --> 00:34:11,449
Cum nos erant 'usura recursion,

450
00:34:11,449 --> 00:34:23,530
numerum ACERVUS tabulas determinat nostris spatium instructio.

451
00:34:23,530 --> 00:34:29,440
Lets considerare n = VIII.

452
00:34:29,440 --> 00:34:36,889
Vocamus shuffle in VIII,

453
00:34:36,889 --> 00:34:41,580
quod mos vocare shuffle in primo quattuor viscus,

454
00:34:41,580 --> 00:34:46,250
quod mos vocant shuffle in primo duo introitibus.

455
00:34:46,250 --> 00:34:51,550
Ita noster ACERVUS est - huius noster est ACERVUS.

456
00:34:51,550 --> 00:34:54,980
Et tunc vocamus shuffle rursum super I,

457
00:34:54,980 --> 00:34:58,070
et quod est scriptor quid nostri basi casus est, ita et nos redire statim.

458
00:34:58,070 --> 00:35:04,700
Facere nos semper habere plus quam hoc multi ACERVUS tabulae erunt?

459
00:35:04,700 --> 00:35:08,880
No Quia utrumque tempus nos facere invocatione,

460
00:35:08,880 --> 00:35:10,770
a recursive invocatione ad shuffle,

461
00:35:10,770 --> 00:35:13,950
nos nostras dividat quantitatis in dimidium.

462
00:35:13,950 --> 00:35:17,020
Sic numerus maxime ACERVUS tabulas nos semper habere simul quodlibet momentum

463
00:35:17,020 --> 00:35:28,460
est ex ordine log n ACERVUS tabulae erunt.

464
00:35:28,460 --> 00:35:42,460
Singulis ACERVUS frame firmiter spatio,

465
00:35:42,460 --> 00:35:44,410
ideoque summa loci

466
00:35:44,410 --> 00:35:49,240
maximum amount of tractus umquam nobis uti est O (log n) spatium

467
00:35:49,240 --> 00:36:03,040
ubi n est numerum dierum.

468
00:36:03,040 --> 00:36:07,230
>> Sed cur ipse 'melius possumus? "

469
00:36:07,230 --> 00:36:12,390
Et in specie ad hanc reduci potest solvi quaestio superius diximus?

470
00:36:12,390 --> 00:36:20,040
Indicant: duae quaestiones de hoc tantum, quod suus 'non iens ut miscere.

471
00:36:20,040 --> 00:36:26,200
Nos possit convertere stirpis forum forsit in maximalia subarray forsit.

472
00:36:26,200 --> 00:36:40,100
Quomodo possumus hoc facere?

473
00:36:40,100 --> 00:36:42,570
Unus ex vobis? Emmy?

474
00:36:42,570 --> 00:36:47,680
(Emmy intellegens)

475
00:36:47,680 --> 00:36:53,860
[Yu] Etiam.

476
00:36:53,860 --> 00:36:59,940
Ita maximalia subarray forsit,

477
00:36:59,940 --> 00:37:10,610
nos 'vultus pro summam super continua subarray.

478
00:37:10,610 --> 00:37:16,230
Et Emmy suggerente pro nervum forsit,

479
00:37:16,230 --> 00:37:30,720
considerate mutationes, aut deltas.

480
00:37:30,720 --> 00:37:37,440
Imago haec et - id pretium velit,

481
00:37:37,440 --> 00:37:42,610
Si autem acceperunt singulos continuos dies inter -

482
00:37:42,610 --> 00:37:45,200
Sicut patet quod maximum pretium commodo eget poteramus

483
00:37:45,200 --> 00:37:50,070
est si ememus hic et vendere hic.

484
00:37:50,070 --> 00:37:54,240
Sed lets 'inviso continua - lets' inviso subarray forsit.

485
00:37:54,240 --> 00:38:02,510
Ita hic possumus - hinc euntem hic

486
00:38:02,510 --> 00:38:08,410
mutatio positiva sunt et hinc euntem hinc negativa fiunt.

487
00:38:08,410 --> 00:38:14,220
At ingens hinc ire hinc positivum mutatio.

488
00:38:14,220 --> 00:38:20,930
Denique et hae mutationes velimus arcessere summam profutura.

489
00:38:20,930 --> 00:38:25,160
Tunc nos sumus negativum maiorem mutationes hic.

490
00:38:25,160 --> 00:38:29,990
Clavem ad redigo nostra stirpe forsit in nostram maximalia subarray forsit

491
00:38:29,990 --> 00:38:36,630
consideret deltas inter diebus.

492
00:38:36,630 --> 00:38:40,630
Ita et nos partum a novus array vocavit deltas,

493
00:38:40,630 --> 00:38:43,000
initialize primum ingressum ad sit 0

494
00:38:43,000 --> 00:38:46,380
Quisque et Delta (i) sit differentia

495
00:38:46,380 --> 00:38:52,830
mei input array (i), et array (i - I).

496
00:38:52,830 --> 00:38:55,530
Deinde nos, nostrum appellare translaticiarum procedendi ratio maxima subarray

497
00:38:55,530 --> 00:39:01,500
transeunter Delta est scriptor ordinata.

498
00:39:01,500 --> 00:39:06,440
Et quia maximalia subarray est linearibus tempore,

499
00:39:06,440 --> 00:39:09,370
et hoc reductionem, hoc processus of partum hoc Delta apparatu,

500
00:39:09,370 --> 00:39:11,780
est etiam linearibus tempore,

501
00:39:11,780 --> 00:39:19,060
tunc finalis solutio pro nervo est O (n) opus plus O (n) opere, est adhuc O (n) opus.

502
00:39:19,060 --> 00:39:23,900
Est ergo nobis linearibus tempus solutio ad nostrum problema.

503
00:39:23,900 --> 00:39:29,610
Vtrum Intelligant omnes hac transformatione?

504
00:39:29,610 --> 00:39:32,140
>> Fere semper ut utilem

505
00:39:32,140 --> 00:39:34,290
est minuere novum forsit ut vestri 'videns.

506
00:39:34,290 --> 00:39:37,700
Si is vultus familiar ad vetus, forsit,

507
00:39:37,700 --> 00:39:39,590
experiri reducendo eam ad vetus forsit.

508
00:39:39,590 --> 00:39:41,950
Et si dici possit ex vetere re feceris omnia instrumenta

509
00:39:41,950 --> 00:39:46,450
solvere novum forsit.

510
00:39:46,450 --> 00:39:49,010
Ut ita involventque et technicae conloquia prouocas.

511
00:39:49,010 --> 00:39:52,280
Ex quo forte ista difficilia problemata

512
00:39:52,280 --> 00:39:54,700
ut videre adito

513
00:39:54,700 --> 00:39:57,690
Si igitur intelligere non modo quaestiones, quas operuit suus bonus.

514
00:39:57,690 --> 00:40:01,080
Haec ex pluribus quaestionibus amet.

515
00:40:01,080 --> 00:40:03,050
Exercitatione, usus, usus.

516
00:40:03,050 --> 00:40:08,170
Dedi multus of problems in handout, ita definite reprimendos foras.

517
00:40:08,170 --> 00:40:11,690
Et bonam fortunam in vestri conloquia. Haec mea pagina copia cornu,

518
00:40:11,690 --> 00:40:15,220
et unus ex senioris meo amicos obtulérunt ad facere illudere technical congressi,

519
00:40:15,220 --> 00:40:22,050
sic si vos es quorum interest email Arbitrio Yao illo email oratio.

520
00:40:22,050 --> 00:40:26,070
Percunctari si possis quaeris.

521
00:40:26,070 --> 00:40:28,780
Operor vos guys habeat specificam quaestionibus relatis ad technicae conloquia

522
00:40:28,780 --> 00:40:38,440
aut ullus problems weve videri tam longe?

523
00:40:38,440 --> 00:40:49,910
Okay. Bene, fortuna in vestri conloquia.

524
00:40:49,910 --> 00:40:52,910
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