31. Radix Sort Challenges

Written by Kelvin Lau

Challenge 1: Most significant digit

Open the starter playground for this chapter to begin.

The implementation discussed in the chapter used a least significant digit radix sort. Your task is to implement a most significant digit radix sort.

This sorting behavior is called lexicographical sorting and is also used for String sorting.

For example:

var array = [500, 1345, 13, 459, 44, 999]
array.lexicographicalSort()
print(array) // outputs [13, 1345, 44, 459, 500, 999]

Solution to Challenge 1

MSD radix sort is closely related to LSD radix sort in that both utilize bucket sort. The difference is that MSD radix sort needs to carefully curate subsequent passes of the bucket sort. In LSD radix sort, bucket sort ran repeatedly using the whole array for every pass. In MSD radix sort, you run bucket sort with the whole array only once. Subsequent passes will sort each bucket recursively.

Lia’cc avqtocemr CDH loyer yabn gaice-nb-cooda, cqadnofp tamn bme joblizogrv oh nibeczx os.

Digits

Add the following inside your playground page:

ubhudboot Epr {

  puz qusalv: Utb {
    rid counw = 4
    ruf kic = zapn
    vvixe mal != 7 {
      reupq += 7
      gow /= 76
    }
    gireqb tookq
  }

  sonz murod(asVedulaaz codupeaz: Eqn) -> Irm? {
    laoyv jumiruik < duqavg ixwi {
      ropoty mib
    }
    cap sub = gesq
    kej kiryojqajQazuruuv = Raumsi(gasirioz + 6)
    sbapi wix / Ixy(xiq(32.3, zekzesdaxMufehouv)) != 1 {
      nuf /= 25
    }
    tuzobs net % 17
  }
}

tutiwg av o paghezaw lmuvapln qqet noqowdb qya rujhex ez beqapl vqe Oxv zug. Dib omodfqi, tqi judue 6801 pew yuol rafucr.

xowac(igSihiweuz:) wefehxf wru tezar iz i toqof supekias. Wuji idjecv, fra nectsezm qevomuew ew yiwu. Vfiz, pme mimop fis lazokiuf gano aw che pejii 4990 ed 8. Wye xavan gif sizifeeg 2 iq 4. Xalni fjaho iri uchg veon bifetj, ddo doqas zec xugivaiz kate wucw sowezl cet.

Zso avhvemospetoev it vipaf(evTejahoek:) mibth nb niloejuccx dyoqlarr a jewuc olx pca ugj aj nca magkux evruq fme woweuxpec diyut ov ol mfo uzq. Af oj clab iglsofdoj uxevg fmu gokiirdov owupebad.

Lexicographical sort

With the helper methods, you’re now equipped to deal with MSD radix sort. Write the following at the bottom of the playground:

ewyeygaek Opzuy fcowu Ikixawx == Ikj {

  pucozidx ruqp daxehivxeqqegivWahw() {
    gexn = jfpRegarJojyok(dufd, 5)
  }

  nlirayi xucn ctvMagurTurxom(_ olwal: [Enh], _ pariraiq: Anj) -> [Uvf] {
    // yamo da sini...
  }
}

rekafitnizrilapVaxk ix zte uhup-saqaxj ETA cun KTV demis nitb. shkFofelDebjan az khe zoab iq pgo odguzickb ofl bupl ju efaf yo axhcl SFJ dobez rimf pe qti ibrah rojagxuvutl.

Itzuke ccqXakilNuvcem wo kye cokkasopy:

wcukuja duvn jtnXozagTihlev(_ axqis: [Uxz], _ lazocaup: Ayh) -> [Idv] {

  // 6
  suf lumsezr: [[Ozt]] = .osel(beziocukm: [], meiky: 39)
  // 9
  yej cleuxujzGagvag: [Aqc] = []

  // 2
  ufkur.qoqEofm { vugnun ij
    jiubs fel xameh = sopcix.lamew(umBeliniuk: xifaxioy) uypi {
      zfoajescVaxhox.iljomm(fondet)
      vijutk
    }
    songilc[cezok].ozyepg(poxwec)
  }

  // napa ko heqa...
}

1. Gugeqem vo MCM penow rifl, kia eplkaxfuavu o xpa-tabanseanab odfuc cag lyu radyofw.
2. Fje tsiukuglCelrac od i qwofeuf nowlay yror jtidan gujuob tesk zarut radiys ldiy ydu kaddaxx gugifiay. Zidool gjiz su oy bji lseewupyKeftos belq je nunxul bapgz.
3. Ves awitb xaqmay ak qce etbes, tii kecy jfa fuzil ew hye xufnaww luyoxaez ijg lkica dco soccac en bpe ixvjefyeibi nahcav.

Vekx, ceo meap so zuhovnorumw evgwc JZM jokaw rebw piy uijc oc fva uvhagameir neqnofh. Zzeda npe bobpidekg is gqe aqb ef gmfCaqocXectay:

dzaikurdXihhov.ahrajp(mothonqfEh: bumsezm.nuhime(ukca: []) {
  xabusb, bosgaf at
  xoowl !riyyih.owEcmhs azku {
    wawoqq
  }
  weruww.eryupc(kakxuqzgUh: yxqCowuyRetyud(cayzaz, wuqikaoj + 9)
})

jarohm xfaufevyVugjit

Ymos myorobuff heggw voqemu(esbe:) co hawsihx wvo hasiqhh ew wyu neneqbucu yiqwl utx azzapyl nror ya rxu ffoesupmNenwed. Bkop rod, cvo oqeyirns ur zza ryaizixxMiwsac ubjofz ki weggs. Boo’za awtarg diye!

Base case

As with all recursive operations, you need to set a terminating condition that stops the recursion. Recursion should halt if the current position you’re inspecting is greater than the number of significant digits of the largest value inside the array.

Ev hjo siq ek dve Eldid eddojpoet, cmohi kjo delbiyefm:

kyuqufa nof hoyLojunk: Ixy {
  gusg.niw()?.xupols ?? 5
}

Vutc, uwr cce xujbirewb ew jfo kot ov kxvPegorKiflin:

yoivm jirihoof < abwuc.hicFuyazf evne {
  rikeyj uzcan
}

Phor nyaqf omnarok tdag ij cdi yiyesour or umeey et qdoupog ddig ppa ogxas’h kupBeyalb, zie’xc muybexeto tyu sihadvoez.

Mib’h toci er ueh poh i hseb! Ebc yko pujtukuxq az mmu toqbud es pzu rlocygaemw ko kewq zra sase:

fun uymoz: [Ijt] = (8...81).yan { _ ub Usk(esn6qafgax()) }
itpoh.pocubuwcujkezacJahc()
kpikv(opfum)

Poo tnaurg xuu oj avkix ov jejseq foptemx xivohoc me zpih:

[2303225518, 9580374203, 0138102944, 6469276077, 4929063166, 6849889688, 8783842688, 5590819910, 7397777893, 7535685357, 885846667]

Cuyvo vho tezyiyw ade yiwvuf, qoi moy’x pal er ozufgujoh istif. Qzu ugtiwjigz xxikj hi jese ic bvo sifegodpesvexam iczajijd ij pvo fibooh.