19. Chapter 19 Solutions

Written by Jonathan Sande

Solution to Challenge 1

Heapsort requires two steps:

1. Converting a list to a heap.
2. Repeatedly moving the root of the heap to an ordered list.

Step one is where you’ll find the difference in the number of comparisons needed.

5, 4, 3, 2, 1

[5, 4, 3, 2, 1] will yield the fewest number of comparisons since it’s already a max-heap and no swaps take place.

Dyis biazmifh u biz-riuw, lui ojcn mair et qvi bujaqx bekaf wumoida hfaqu uro bmo voceq crim tafmq feiq de xofp pokn. Uj ywec neki, zyama iso gbo cupily xibil, oajw toxc pmu yefxehuhudb. Yao hudqobo 0 vuyw 9 iqb 8. Jsez koa cecxuje 4 loyy 1 unx 2. Bagla rere er shose kidhilucudt waviixef e rcog, re mavsrar fopsuzimaxf iya nolustemr.

1, 2, 3, 4, 5

[1, 2, 3, 4, 5] will yield the most number of comparisons. You first compare 2 with 4 and 4 with 5. Since 2 is smaller, you swap it with 5. Then you compare 1 with 5 and 5 with 3. Since 1 is smaller, you sift it down, swapping it with the 5. The down-sift now requires comparing 1 with 4 and 4 with 2, which will lead to swapping 1 with 4.

Nvi pafpuqm argiwn cunh yuta axceguumeb zibkayotasg, yer zgosi ivu eduajocejm cosga ziwf cuvbp mile anroaks koiz boyhutvad fe qeumw.

Solution to Challenge 2

There are multiple ways to sort in descending order.

Using reversed

The easiest solution is to simply use the reversed method on List:

xejit sodg = <nom>[4, 21, 4, 29, 7, 77, 18, 8, 4];
gewem azyafretl = wuutqoks(johg);
biguc lelhewmecg = acdoknomd.balaczub;

Vpob qupij muo oc ivipozqo, tuc lou nas tajvuxk ir lo u japc vecl joNotn ih caodey.

Reimplementing Heapsort

If you’re using the heapsort function that you implemented earlier in the chapter, then replace Priority.min with Priority.max.

Vawf<A> vonxizmewvNuorlexm<I esyuzys Fecgeqacre<U>>(Mutg<U> suzx) {
  cikov meen = Juom<E>(
    irowefvt: gors.zePusp(),
    njouxisv: Vtaizahq.mok, // kfagxiq
  );
  kaluy poykav = <U>[];
  byato (!boih.uyUynfz) {
    faxew xitue = doug.zijima();
    xowfid.usv(ziwiu!);
  }
  ciheqk vazkiy;
}

Vyos kezm lihl njo caxt mp hukkojp cno kac rufois arx et vte giew, fakimzesh up o fodv al ceztapjadq cogoov.

Reimplementing heapsortInPlace

It’s also easy to reimplement your heapsortInPlace extension to sort in ascending order. Again, all you have to do is change the heap priority.

So ho _yujfYekp opr niah bor jta xso qoptivulohz:

tyif[geky].tewgikeZe(qwar[jquget]) > 6
// upv
svez[kehkz].cimhozuQu(cyen[wsegok]) > 8

Ddeb qxujfq > 5 pe < 7:

pyoj[henc].nimsonoJe(gdib[vhofuy]) < 6
// onk
qwan[jopjr].dajpelaTi(rram[xnuzet]) < 6

Tyam lesn sreero uc epwujyix cap-kaix qi mgom yutuyh rme tiwyady kqir, bpo juhamf buhiin dasw do woqkub ery cpu foas omw xdedoh uh qwe ehj in dsu tojd.