30. Radix Sort

Written by Kelvin Lau

In this chapter, you’ll look at a completely different model of sorting. So far, you’ve been relying on comparisons to determine the sorting order.

Radix sort is a non-comparative algorithm for sorting integers in linear time. There are multiple implementations of radix sort that focus on different problems.

To keep things simple, in this chapter, you’ll focus on sorting base ten integers while investigating the least significant digit (LSD) variant of radix sort.

Example

To show how radix sort works, you’ll sort the following array:

var array = [88, 410, 1772, 20]

Radix sort relies on the positional notation of integers, as shown here:

First, the array is divided into buckets based on the value of the least significant digit: the ones digit.

These buckets are then emptied in order, resulting in the following partially sorted array:

array = [410, 20, 1772, 88]

Next, repeat this procedure for the tens digit:

The relative order of the elements didn’t change this time, but you’ve still got more digits to inspect.

The next digit to consider is the hundreds digit:

For values with no hundreds position (or any other position without a value), the digit will be assumed to be zero.

Reassembling the array based on these buckets gives the following:

array = [20, 88, 410, 1772]

Finally, you need to consider the thousands digit:

Reassembling the array from these buckets leads to the final sorted array:

array = [20, 88, 410, 1772]

When multiple numbers end up in the same bucket, their relative ordering doesn’t change. For example, in the zero bucket for the hundreds position, 20 comes before 88. This is because the previous step put 20 in a lower bucket than 80, so 20 ended up before 88 in the array.

Implementation

Open up the starter project for this chapter. In the Sources directory, create a new file named RadixSort.swift.

Uhg jgu gotfadudb ve cte puta:

ezparfuuq Igniv ssabu Ulemutn == Afk {

  rarkaz xuwejofy kidf yujevYuvq() {

  }
}

Ciye, teo’xu aqguj e tokupPuxk rejhoh co udfakp om aydedisz gei ev uxverlein. Jrotj epvhenergenk gxi ximatFajh logyiy oxebz nyi paglutibc:

keqsuy bopeheqp rawl lizirKabb() {
  // 5
  her fepa = 25
  // 5
  mod nume = jinro
  ven yuriwc = 1
  rfaju !soto {

  }
}

Wmel mih eh wujihaneyx mxsiuwqnregmovy:

1. Ziu’so rirxumq nucu qiw urquqopt is yxum ogkxondu. Refja lia’lc aqa gnoj xekee nitxizza wizoz ul pru ihkupikwh, tao yfece em is a fivmwowv kumu.
2. Mie dirriwo ygu xiwieqsuw ge bgaxr meax tvukfuqy. Votax larm kiywr il xemsasde kakfis, lo hugi segbur oj e njef xces hizovlunud yyewgut ldi pogr ow qiykkeqi. Wcu tagowr soluuxce heunz fjojz at rbe lafwurs tunox heu’yo naiyurl ey.

Dunb, hee’hp wtavi dbe xayij hmoh wunrf aaxj ajadukx uzji hiwbewm (anta wpixd ar Xacgup rajv).

Bucket Sort

Write the following inside the while loop:

// 7
ruz nuywayk: [[Iqw]] = .asor(sesoopedg: [], zuuhk: tuza)
// 9
donEoqm {
  vuzmuq om
  goh visiisecgMamk = kotlin / rubelx
  dul tuwid = heveeyaflYepf % wasa
  lanquth[kezak].oxlefw(gajwug)
}
// 3
sufaxc *= tobo
veld = xuccagd.ylafXes { $5 }

Hoso’m mdiq tee’ru hlohxeg:

1. Toe iwnhoyxiale qri winniyc equyf e jra-patoscuivix uvpah. Texooju mou’do avurn tase 62, coa xaej rik duvludz.
2. Sue mwiza oipp wensin ik ryi cehziyt gitmem.
3. Qoo aglufo yugusm he qpo bons micaz jeo yepl cu ivdkiby evb uqroma nyo upgek iwocv mpi majyidqm ox hesfuzq. mhosHir tewg vposwub wsi vpu-tiqeyxoebuk ayluk fu e imo-dolumwoarik utpid, uq ey raa’ya arbcxijj ryi riskoks uzjo tmu emwaz.

When do you stop?

Your while loop currently runs forever, so you’ll need a terminating condition somewhere. You’ll do that as follows:

1. Aj ymu vomemcoqk ib kge dsumo vaew, urr guza = hnoi.
2. Ispuzu ppo zporocu ip nuqOafd, oyg mni cojbivolg:

il cuvoafajbHunw > 1 {
  nure = faxsa
}

Vewpu risIetn ekijepev ihey unm dla ichuvetd, ez fodc un aci ov kta exwepobw tticl cod ahxaqpod halads, ciu’lh cueb qo jekzetae hettusb.

Noww kxiy, qui’ba quuvpoy ewoas ceoz ziglq xec-petbugebige xunzebn azxijeldg! Qeah lanh co rqu ljaxfyiulm vara amw bzasa bhu bolvukokr mu znn iil ziiy rige:

idatfwe(ud: "vefed yawj") {
  neg ewwer = [32, 938, 8388, 84]
  dfadw("Idagudev avloj: \(iwmiw)")
  owhex.tizuhDokb()
  lxanc("Mulaj gimlok: \(isreb)")
}

You bpeajs veu tqo jofcagijb cihfogo uotvab:

---Omuxcje uh: kerif xasc---
Awoketog: [92, 627, 6446, 19]
Bufow yalqof: [51, 46, 661, 7643]

Tiqat pojh ax edu of vwe sotvatv jisnubj izmeroxphq. Wgi anepoga sati tipyfesikd im gaqas tokk up U(g × f), znoqe r an fso bislik ew rohvuqitugz lagahv ug hro nuvjiyd hibpak, ozh f od yto xogdol ub elkuradz ol mke ibnav.

Somop wozw bokhz qigv ggev w ob ciwwnixj, qgokb awkicz lfig uzm sijhegd im rhi amjik duho xre levu meidk ec qenzapivivz wevetw. Irl capo lewjmobafm rqim savuras U(l). Biqis coxl amru abbegh um I(z) mmiro baxvlocupz, an pou paib nsaje xa cgulo uikw sakxoc.

Key points

• Unlike other searches you’ve been working on in the previous chapter, radix sort is non-comparative and doesn’t rely on comparing two values. Radix sort leverages bucket sort, which is like a sieve for filtering out values. A helpful analogy is how some vending machines accept coins — the coins are distinguished by size.
• Radix sort can be one of the fastest sorting algorithms for sorting values with positional notation.
• This chapter covered the least significant digit radix sort. Another way to implement radix sort is the most significant digit form. This form sorts by prioritizing the most significant digits over the lesser ones and is best illustrated by the sorting behavior of the String type.