CSE326:DataStructures Lecture#3 MindyourPriorityQs BartNiswonger - - PDF document

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CSE326:DataStructures Lecture#3 MindyourPriorityQs

BartNiswonger SummerQuarter2001

Today’sOutline

• TheFirstQuiz!
• ThingsBartDidn’tGettoonWednesday

(PriorityQueues&Heaps)

• Extraheapoperations
• d-Heaps

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BacktoQueues

• Someapplications

– orderingCPUjobs – simulatingevents – pickingthenextsearchsite

• Problems?

– shortjobsshouldgofirst – earliest(simulatedtime)eventsshouldgofirst – mostpromisingsitesshouldbesearchedfirst

PriorityQueueADT

• PriorityQueueoperations

– create – destroy – insert – deleteMin – is_empty

• PriorityQueueproperty:fortwoelementsin

thequeue,x andy,ifx hasalowerpriority value thany,x willbedeletedbeforey

F(7) E(5) D(100) A(4) B(6)

insert deleteMin

G(9) C(3)

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ApplicationsofthePriorityQ

• Holdjobsforaprinterinorderoflength
• Storepacketsonnetworkroutersin
• rderofurgency
• Simulateevents
• Selectsymbolsforcompression
• Sortnumbers
• Anythinggreedy

NaïvePriorityQDataStructures

• Unsortedlist:

– insert: – deleteMin:

• Sortedlist:

– insert: – deleteMin:

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BinarySearchTreePriorityQ DataStructure(that’samouthful)

4 12 10 6 2 11 5 8 14 13 7 9 insert: deleteMin:

BinaryHeapPriorityQData Structure

20 14 12 9 11 8 10 6 7 5 4 2

• Heap-orderproperty

– parent’skeyislessthan children’skeys – result:minimumis alwaysatthetop

• Structureproperty

– completetreewithfringe nodespackedtotheleft – result:depthisalways O(logn);nextopen locationalwaysknown

5 20 14 12 9 11 8 10 6 7 5 4 2 2 4 5 7 6 10 8 11 9 12 14 20 12

1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12

NiftyStorageTrick

• Calculations:

– child: – parent: – root: – nextfree:

DeleteMin

20 14 12 9 11 8 10 6 7 5 4 ? 2 20 14 12 9 11 8 10 6 7 5 4 2 pqueue.deleteMin()

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PercolateDown

20 14 12 9 11 8 10 6 7 5 4 ? 20 14 12 9 11 8 10 6 7 5 ? 4 20 14 12 9 11 8 10 ? 7 5 6 4 20 14 20 9 11 8 10 12 7 5 6 4

Finally…

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DeleteMin Code

ObjectdeleteMin(){ assert(!isEmpty()); returnVal =Heap[1]; size--; newPos= percolateDown(1, Heap[size+1]); Heap[newPos]= Heap[size+1]; returnreturnVal; }

intpercolateDown(inthole,Objectval){ while(2*hole<=size){ left=2*hole; right=left+1; if(right<=size&& Heap[right]<Heap[left]) target=right; else target=left; if(Heap[target]<val ){ Heap[hole]=Heap[target]; hole=target; } else break; } returnhole; }

runtime:

Insert

20 14 12 9 11 8 10 6 7 5 4 2 20 14 12 9 11 8 10 6 7 5 4 2 pqueue.insert(3) ?

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PercolateUp

20 14 12 9 11 8 10 6 7 5 4 2 ? 20 14 12 9 11 8 ? 6 7 5 4 2 10 20 14 12 9 11 8 5 6 7 ? 4 2 10 20 14 12 9 11 8 5 6 7 3 4 2 10 3 3 3

InsertCode

voidinsert(Objecto){ assert(!isFull()); size++; newPos= percolateUp(size,o); Heap[newPos]=o; }

intpercolateUp(inthole, Objectval){ while(hole>1&& val<Heap[hole/2]) Heap[hole]=Heap[hole/2]; hole/=2; } returnhole; }

runtime:

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ChangingPriorities

• Inmanyapplicationsthepriorityofanobject

inapriorityqueuemaychangeovertime

– ifajobhasbeensittingintheprinterqueuefora longtimeincreaseitspriority – unix“renice”

• Musthavesome(separate)wayoffindthe

positioninthequeueoftheobjecttochange (e.g. ahashtable)

OtherPriorityQueue Operations

• decreaseKey

– giventhepositionofanobjectinthequeue, reduceitspriorityvalue

• increaseKey

– giventhepositionofananobjectinthequeue, increaseitspriorityvalue

• remove

– giventhepositionofanobjectinthequeue, removeit

• buildHeap

– givenasetofitems,buildaheap

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DecreaseKey,IncreaseKey, andRemove

voiddecreaseKey(int obj){ assert(size>=obj); temp=Heap[obj]; newPos= percolateUp(obj,temp); Heap[newPos]=temp; } voidincreaseKey(intobj){ assert(size>=obj); temp=Heap[obj]; newPos=percolateDown(obj,temp); Heap[newPos]=temp; }

voidremove(intobj){ assert(size>= obj); percolateUp(obj, NEG_INF_VAL); deleteMin(); }

BuildHeap

Floyd’sMethod.Thankyou,Floyd.

5 11 3 10 6 9 4 8 1 7 2 12 pretendit’saheapandfixtheheap-orderproperty! 2 7 1 8 4 9 6 10 3 11 5 12

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Build(this)Heap

6 7 1 8 4 9 2 10 3 11 5 12 6 7 10 8 4 9 2 1 3 11 5 12 11 7 10 8 4 9 6 1 3 2 5 12 11 7 10 8 4 9 6 5 3 2 1 12

Finally…

11 7 10 8 12 9 6 5 4 2 3 1 runtime:

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ThinkingaboutHeaps

• Observations

– findingachild/parentindexisamultiply/divideby two – operationsjumpwidelythroughtheheap – eachoperationlooksatonlytwonewnodes – insertsareatleastascommonasdeleteMins

• Realities

– divisionandmultiplicationbypowersoftwoare fast – lookingatonenewpieceofdatasucksinacache line – withhuge datasets,diskaccessesdominate 4 9 6 5 4 2 3 1 8 10 12 7 11

Solution:d-Heaps

• Eachnodehasd children
• Stillrepresentableby

array

• Goodchoicesford:

– optimizeperformancebasedon #ofinserts/removes – chooseapoweroftwofor efficiency – fitonesetofchildreninacache line – fitonesetofchildrenona memorypage/diskblock

3 7 2 8 5 121110 6 9 1 12

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OneMoreOperation

• Mergetwoheaps.Ideas?

ToDo

• Readchapter6inthebook
• Haveteams
• Doproject1
• Askquestions!

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ComingUp

• Mergeableheaps
• DictionaryADTandSelf-Balancing

Trees

• UnixDevelopmentTutorial(Tuesday)
• Firstprojectdue(nextWednesday)