for every node i other than the root. After the heap is built, the root (leftmost position in the array) has the minimum element. Sorting then repeatedly moves ...
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HeapsortAlgorithmusingmin-heap
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Asked
8years,10monthsago
Modified
4years,2monthsago
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WhenIimplementheapsortusingamin-heapitsortsthearrayfromlargesttosmallest.Isthisthedesiredoutputforaheapsortusingmin-heap?Itseemsredundanttosortagaintooutputsmallesttolargestafterthesortiscompletesincetheheapitselfhasasmallesttolargeststructure.
CODE:
#include
#include
#include"random.h"
#include"print.h"
intparent(inti)
{
return(i-1)/2;
}
intleft(inti)
{
if(i==0)
return1;
else
return2*i;
}
intright(inti)
{if(i==0)
return2;
else
return2*i+1;
}
voidmin_heapify(std::vector&A,inti,intheapsize)
{
intsmallest;
intl=left(i);
//std::cout<&A)
{
intheapsize=A.size()-1;
for(inti=(A.size()-1)/2;i>=0;i--)
min_heapify(A,i,heapsize);
}
voidheapsort(std::vector&A)
{
intheapsize=A.size()-1;
build_min_heap(A);
std::cout<0;i--){
exchange(A,0,i);
heapsize--;
std::cout<B;
fill(B,5);
print(B);
heapsort(B);
print(B);
return0;
}
Outputfromcode:
4165314119
4165314119
4165194131
4119654131
4119314165
1941314165
heapsortafterbuildmaxheap
1931414165
heapsize=3
6531414119
3165414119
heapsize=2
heapsize=1
6541413119
heapsize=0
6541413119
Outputfor20elements:
41653141191572117869372329637545497599
afterbuildmaxheap
45151119232941316937417263756578497599
aftersort
99787575726965634941413731292319151154
c++heapsort
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editedMay27,2018at12:59
JeJo
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askedSep20,2013at17:27
MarsMars
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Canyoushowyourcode?
– ReinstateMonica--notmaynard
Sep20,2013at17:31
1
Lettherebeabinarytreeontheheap.Tosortanarray,youinsertelementsonebyoneintothetree.Obvioussly,theelementsareinacertainorderinthetree,butyouwantthembackinanarray.Soyoutraversethetreetakingthesmallestelementsfirstandyouputthembackintoanarray.
– cpp
Sep20,2013at17:38
Relatedblogpostanddemocode.
– JerryCoffin
Sep20,2013at18:58
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3Answers
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Sortedby:
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6
Order:Usemax-heapifytosortinascedingorder,min-heapifytosortindescendingorder.
Sorting:Buildingtheheapwithmin-heapifydoesnotsortyourarray;itonlyenforcesthe(weaker)min-heapproperty,thatis
A[parent(i)]<=A[i]
foreverynodeiotherthantheroot.Aftertheheapisbuilt,theroot(leftmostpositioninthearray)hastheminimumelement.Sortingthenrepeatedlymoveselementsfromtheroottotherightandcallsmin-heapifyontheroot(bringingtheretheminimumofwhatremains),hencethedescendingorder.
Thecodeyouarepostingappearscorrectataglancebutdoesnotcompileasis,soIcannottest.Ifyourarrayappearssortedrightafterbuildingtheheap,itshouldbeacoincidence.Tryalargertest.
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editedSep20,2013at18:01
answeredSep20,2013at17:38
iavriavr
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Try15-20elementsandyou'llsee!
– iavr
Sep20,2013at17:56
Whenyousaymyarrayappearssorted,youmeanafterIbuildtheheap?
– Mars
Sep20,2013at18:41
Ipostedmyoutputwith20elements.Isthisheapwrong?It'snotinsortedorderbutIdon'tthinkitneedstobe.Allthechildnodesaresmallerinvaluethantheparentnode.
– Mars
Sep20,2013at18:47
1
@ComradeYes.Youroutputshows1931414165rightafterbuildingtheheap.Yousaythisissorted,butitonlysatisfiesthemin-heapproperty,whichhappenstobethesameinthiscase.Min-heappropertyonlysays19<=31,19<=41,31<=41,31<=65.
– iavr
Sep20,2013at18:47
1
Yes.ThatisallIwasreallyasking.Ifthepurposeofusingamin-heapwastosortindescendingorder.IamgladIaskedthoughbecausethefirstoutputcoincidentallyhadtheelementssortedandIhadbelievedthatbuildingtheheapwasalsosortingtheelements,whichitwasn'tofcourse.
– Mars
Sep20,2013at19:10
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Normallyyouuseamax-heaptosortinascendingorder,becauseitseasier.
Usingamax-heap,you'float'themaxtothefront,andbuildthesortedlistfromtheback.
Ifyouwanttouseamin-heaptosortinascendingorder,youhavetobuilditbackwards.(iethelowestisthelastindex).Otherwiseyouwillbechurningyourheap.
start18706131255
min-heap(backwards)->18705513126
then
swap6w18->6,7055131218->sink18->7055131812
swap12w70->612,55131870->sink70->55701813
swap13w55->61213,701855->sink55->705518
swap18w70->6121318,5570->sink70->7055
swap55w70->612131855,70
done
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editedSep20,2013at22:37
answeredSep20,2013at17:37
SanjayaRSanjayaR
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Thatseemstodefeatthepurposeofbuildingaheapinthefirstplace.
– Mars
Sep20,2013at17:53
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Iwasjustwonderingaboutthatveryproblem(isn'tHeapsorthavinganextrastepattheend,theunnecessaryswappingofelements.Justusemin-heapsandletcallmin-heapifyandgetyourworkdone).
Regardingthisway,wecouldhaveachievedO(logn)timewhichsomewhatdisqualifiesthebinarydecisiontreemodel-whichsaysO(nlogn)isacceptabletightestupperboundoncomparisonsortingalgorithms.
Theshortansweris:heapdatastructurearen'tbinarysearchtrees.Aheapmayguaranteeorderingofelementsinsortedtop->bottomway,butabinarysearchtreeguaranteesthey'llbeorderedlefttorightaswell.Wewerejustmixingupbinarytreesandheaps.
Aminheaponlyguarantees,
Amin[Parent]<=A[either_of_the_children]//saysnothingaboutorderingofchildren
Hereisabinarytree(althoughunbalancedandnotsorted):
AndhereisaHeap:
Hopeyougetmypoint.Ifstillnot,thenthinkofitas,aminheaprepresentedanarrayguaranteesthatparentissmallerthanitschild,butsaysnothingaboutareallchildrenarrangedinsortedorderlefttoright?
We'llstillbeperformingmin-heapifyoneachchildofcurrentroottobeswapped.
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editedDec9,2017at4:13
answeredMay13,2015at12:32
AbhinavGauniyalAbhinavGauniyal
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aheapISabinarytree(aparentcanhavemax2children),butitisn'tabinarySEARCHtree(leftchild
